POLITICAL ECONOMY
FOR PUBLIC POLICY
POLITICAL ECONOMY
FOR PUBLIC POLICY
Ethan Bueno de Mesquita
PRINCETON UNIVERSITY PRESS
Princeton and Oxford
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Names: Bueno de Mesquita, Ethan, author.
Title: Political economy for public policy / Ethan Bueno de Mesquita.
Description: Princeton, N.J. : Princeton University Press, 2016. |
Includes bibliographical references and index.
Identifiers: LCCN 2015047630 | ISBN 9780691168739 (hardcover : alk. paper) |
ISBN 9780691168746 (pbk.)
Subjects: LCSH: Economics. | Political planning. | Policy sciences.
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For my parents, Arlene and Bruce Bueno de Mesquita
Summary of Contents
Policy Applications xvii
Preface xix
Introduction 1
I NORMATIVE FOUNDATIONS 11
1 Normative Frameworks 13
2 Collective Goals 51
3 Pareto Concepts 74
Summing Up Normative Foundations 95
II SOCIAL DILEMMAS 97
4 Externalities 99
5 Coordination Problems 150
6 Commitment Problems 173
Summing Up Social Dilemmas 191
III CONSTRAINTS ON GOOD GOVERNANCE 193
7 Strategic Adjustment 197
8 Dynamic Inconsistency 218
9 The Need for Information 244
10 Influence over Elected Officials 282
viii Summary of Contents
11 Institutions, Incentives, and Power 305
Summing Up Constraints on Good Governance 328
Concluding Reflections on Politics and Policy 331
IV APPENDICES ON GAME THEORY 335
A Utility, Strategic-Form Games, and Nash Equilibrium 337
B Extensive-Form Games 362
Bibliography 385
Index of Referenced Authors 393
General Index 396
Contents
Policy Applications xvii
Preface xix
ForWhom Is This BookWritten? xx
AWord on Tone and Technicality xx
Acknowledgments xxi
Introduction 1
Three Goals 4
The Role of Models 5
Why Rationality? 7
I NORMATIVE FOUNDATIONS 11
1 Normative Frameworks 13
1.1 What Is a Normative Framework? 15
1.1.1 Private vs. Public Morality 16
1.2 Utilitarianism 17
1.2.1 Why Be a Utilitarian? 18
1.2.2 Some Problems for Utilitarianism 21
1.3 Egalitarianism 27
1.3.1 Equality of Outcomes 28
1.3.2 Equality of Opportunity 32
1.4 Kantian Deontology 37
1.4.1 Deontology and the Challenges to Utilitarianism 39
1.4.2 Challenges for Deontological Thinking 39
1.5 Libertarianism 41
1.5.1 Why Be a Libertarian? 43
1.5.2 Some Problems for Libertarianism 44
1.6 Takeaways 45
1.7 Further Reading 46
1.8 Exercises 47
2 Collective Goals 51
2.1 Rational Individuals 52
2.2 Aggregation Procedures 53
x Contents
2.3 Evaluative Criteria for Aggregation Procedures 55
2.3.1 Transitivity of Social Preferences 56
2.3.2 Unanimity 57
2.3.3 Independence of Irrelevant Alternatives 58
2.4 Arrow’s Theorem 60
2.5 Social Decisions Instead of Social Preferences 61
2.6 The Public Interest? 63
2.6.1 Only Two Alternatives: May’s Theorem 63
2.6.2 Ruling Out Some Collections of Preferences: TheMedian
Voter Theorem 64
2.6.3 Intensity of Preferences 69
2.6.4 Agreement 70
2.7 Takeaways 70
2.8 Further Reading 71
2.9 Exercises 71
3 Pareto Concepts 74
3.1 Pareto Concepts 75
3.2 From Pareto Efficiency to Pareto Improvements 76
3.3 AModel of Policies and Preferences 77
3.3.1 Actions and Transfers 77
3.3.2 Quasi Linearity: A Bridge from Pareto Efficiency to
Pareto Improvement 78
3.4 A Bridge Too Far? 84
3.4.1 Limited Transfers and Distributional Concerns 84
3.4.2 Non Quasi Linear Preferences 85
3.5 Relationship to Cost-Benefit Analysis 87
3.6 Are Pareto Improvements Unambiguously in the
Public Interest? 89
3.7 Takeaways 90
3.8 Further Reading 91
3.9 Exercises 91
3.10 Appendix: Proof of Theorem 3.3.1 93
Summing Up Normative Foundations 95
II SOCIAL DILEMMAS 97
4 Externalities 99
4.1 Collective Action 101
4.1.1 The Social Dilemma 104
4.1.2 Interpretations 104
Contents xi
4.2 Public Goods 105
4.2.1 Comparison to the First Best or Utilitarian Optimum 107
4.2.2 Interpretation 108
4.2.3 Concentrated vs. Diffuse Interests 109
4.3 The Tragedy of the Commons 114
4.3.1 A Pareto Improvement 118
4.3.2 The First Best 118
4.3.3 Interpretation 119
4.4 Policy Interventions 120
4.4.1 The Failure of Persuasion 120
4.4.2 Pigovian Subsidies and Taxes 122
4.4.3 Regulation 124
4.5 The Theory of the Second Best 124
4.5.1 The Second Best Pigovian Subsidy 126
4.6 Alternative Responses 129
4.6.1 Altruism 130
4.6.2 AMarket in Externalities 131
4.6.3 Ongoing Relationships and Self Organization 135
4.7 Takeaways 144
4.8 Further Reading 144
4.9 Exercises 145
5 Coordination Problems 150
5.1 Coordination Failure 153
5.1.1 Interpretation 158
5.2 Coordination Traps 159
5.2.1 A Basic Model of Coordination Traps: Investment in
Developing Countries 160
5.2.2 AModel of Bank Runs 162
5.2.3 AModel of Revolutions 163
5.2.4 Interpretation 165
5.3 Policy Responses 165
5.3.1 Communication 165
5.3.2 Short Run Intervention 167
5.3.3 Insurance and the Second Best 167
5.4 Takeaways 168
5.5 Further Reading 169
5.6 Exercises 169
6 Commitment Problems 173
6.1 AModel of Conflict 174
6.1.1 Inefficient Conflict 178
6.1.2 Interpretation 178
xii Contents
6.2 The Hold-Up Problem 180
6.2.1 Interpretation 183
6.3 Policy Responses 183
6.4 Takeaways 185
6.5 Further Reading 185
6.6 Exercises 185
Summing Up Social Dilemmas 191
III CONSTRAINTS ON GOOD GOVERNANCE 193
7 Strategic Adjustment 197
7.1 Strategic Adversaries 199
7.1.1 Do Terrorists Really Strategically Adjust? 201
7.1.2 TheWar on Drugs 203
7.2 IncentivizingMultiple Tasks 205
7.2.1 High Stakes Testing 211
7.3 Takeaways 213
7.4 Further Reading 214
7.5 Exercises 215
8 Dynamic Inconsistency 218
8.1 Time Inconsistency 219
8.1.1 The First Best 221
8.1.2 WhatWill the Government Do? 221
8.1.3 HowMuchWill a Consumer Consume? 222
8.1.4 Is the Government Time Consistent? 223
8.1.5 Time Inconsistency and Externalities 224
8.1.6 Rules vs. Discretion 224
8.1.7 Applications 225
8.2 Fiscal Manipulation 227
8.2.1 The First Best 229
8.2.2 Electoral Risk 230
8.2.3 Discounting the Future 231
8.3 When Policy Affects Future Power 232
8.3.1 The (Political) Second Best 239
8.4 Takeaways 241
8.5 Further Readings 241
8.6 Exercises 242
Contents xiii
9 The Need for Information 244
9.1 Auctions 246
9.1.1 Second Price Auction 247
9.2 Providing a Public Good 248
9.2.1 Split the Costs 250
9.2.2 Veto and Split 251
9.2.3 General Mechanisms 251
9.2.4 The Second Best 257
9.3 Regulating aMonopolist 259
9.3.1 Monopolistic Equilibrium 261
9.3.2 Regulation with Full Information 263
9.3.3 Regulation with Uncertainty 264
9.3.4 An Informed Regulator 271
9.4 Takeaways 276
9.5 Further Reading 276
9.6 Exercises 277
10 Influence over Elected Officials 282
10.1 Particularistic Interests 283
10.2 Special Interests and Campaign Donations 286
10.3 Electoral Accountability 290
10.3.1 Rewards of Office 293
10.3.2 Term Limits 293
10.3.3 Incentives and Screening 294
10.3.4 Voter Information 295
10.3.5 The Risk of Electoral Pandering 300
10.4 Takeaways 301
10.5 Further Reading 302
10.6 Exercises 302
11 Institutions, Incentives, and Power 305
11.1 A Selectorate Model 307
11.1.1 Equilibrium 308
11.1.2 Outcomes and Institutions 312
11.2 Institutions and Development 314
11.2.1 Settler Mortality, Institutions, and the Economy 315
11.3 Foreign Aid 318
11.3.1 Poverty Traps and Foreign Aid 319
11.3.2 Does Foreign AidWork through Poverty Traps? 319
11.3.3 Effective Aid? 321
11.3.4 A Political Economy of Foreign Aid 322
xiv Contents
11.4 Takeaways 325
11.5 Further Reading 326
11.6 Exercises 326
Summing Up Constraints on Good Governance 328
Concluding Reflections on Politics and Policy 331
IV APPENDICES ON GAME THEORY 335
A Utility, Strategic-Form Games, and Nash Equilibrium 337
A.1 Utility 338
A.1.1 Expected Utility 338
A.2 Games in Strategic Form 342
A.2.1 Where to Eat? 342
A.2.2 Matching Pennies 343
A.2.3 Cleaning an Apartment 344
A.2.4 Choosing a Number 345
A.3 Nash Equilibrium 345
A.4 Why Nash Equilibrium? 347
A.4.1 No Regrets and Social Learning 347
A.4.2 Self Enforcing Agreements 348
A.4.3 Analyst’s Humility 349
A.5 Solving for Nash Equilibrium 349
A.6 Nash Equilibrium Examples 350
A.6.1 Where to Eat? 351
A.6.2 Matching Pennies 352
A.6.3 Cleaning an Apartment 352
A.6.4 Choosing a Number with Two Players 356
A.7 Takeaways 358
A.8 Exercises 358
B Extensive-Form Games 362
B.1 Games in Extensive Form 362
B.1.1 AModel of International Crisis 363
B.2 Game Trees 364
B.2.1 International Crisis Game 365
B.2.2 A Budget Game 365
B.2.3 The Centipede Game 366
B.3 Strategies as Complete Contingent Plans 366
B.3.1 International Crisis Game 366
Contents xv
B.3.2 Budget Game 366
B.3.3 The Centipede Game 367
B.4 Representing an Extensive-FormGame as a
Strategic-FormGame 368
B.4.1 The International Crisis Game 368
B.4.2 The Budget Game 368
B.4.3 The Centipede Game 369
B.5 Nash Equilibria of Extensive-FormGames 369
B.5.1 International Crisis Game 370
B.5.2 The Budget Game 371
B.5.3 The Centipede Game 372
B.6 Subgame Perfect Nash Equilibrium 373
B.6.1 Subgame Perfection 374
B.6.2 Backward Induction 375
B.6.3 Indifference andMultiple Equilibria 378
B.6.4 Continuous Choices 379
B.7 Discounted Payoffs 380
B.8 Takeaways 381
B.9 Exercises 381
Bibliography 385
Index of Referenced Authors 393
General Index 396
Policy Applications
Application Page
Cap-and-Trade vs. Carbon Tax 2
Charter Schools 13
Time Discounting, Cost-Benefit Analysis, and Intergenerational Equity 25
NAFTA 74
Trade Adjustment Assistance 80
Stem Cell Research 90
Antibiotic Resistance 99
Interstate Highways and Urban Revitalization 110
Space Debris 114
Grand Banks Fishery 119
Great Pacific Garbage Patch 119
Overlapping Jurisdictions 120
Norms, Self-Regulation, andWater Use 136
Tennessee Valley Authority and Agglomeration Economies 150
Accounting Standards and Financial Harmonization 154
Automobile Safety Regulation in the United States and Europe 158
Foot Binding 159
Bank Runs and Deposit Insurance 168
Argentine Nationalization of YPF 173
IRAWeapons Decommissioning and the Good Friday Agreement 175
Yugoslav Civil War 179
xviii Policy Applications
Protection of Local Dealerships 180
CAFE Standards 197
Welfare toWork 197
Pell Grants and College Affordability 198
Airport Security 201
Operation Swordfish and theMexican DrugWar 203
No Child Left Behind 211
HealthCare.gov 218
Global Financial Crisis and the EU Bailout of Greece 225
Negotiating with Terrorists 226
Public Sector Pensions 227
Workfare 244
Off-Cycle Elections 286
Campaign Finance and the Tullock Paradox 288
Term Limits 294
School Boards, Testing, and Electoral Accountability 299
Leopold II in Belgium and the Congo Free State 305
Foreign Aid 318
http://HealthCare.gov
Preface
This is a book about political economy for people interested in public policy.
Traditionally, policy analysis and policy education have tended to focus
on technocratic concerns—cost-benefit analysis, program evaluation, public
administration—and on identifying optimal policies, whether or not those
policies could possibly be implemented. A political economy approach takes a
different perspective.
Themaking and implementation of public policy is fundamentally political.
The leaders and bureaucrats who write, pass, and enforce our policies operate
within political environments that shape and constrain their behavior. A policy
that would perfectly address some serious problem, but which could never be
passed or enforced because of the politics of the policymaking process, is not
optimal. Such a policy, doomed as it is to never be deployed, cannot solve any
problems. An optimal policy response to a problem must be optimal given all
the constraints, including the political constraints.
The study of political economy for public policy, then, is the study of optimal
public policy, taking seriously the constraints imposed by the political process.
Understanding these politics is essential for any serious student of public policy
and certainly for anyone, in or out of government, interested in leading policy
debate or policy change. This is why political economy is, or ought to be, a core
element of a public policy education.
For a political scientist, such as myself, the most natural way to think about
introducing students to the politics of the policymaking process is to focus on
how specific political institutions constrain and shape policy choices. But this
is not the approach I take. Before explaining what I do, I want to say a word or
two about why I don’t go the institutionalist route. I think this will help make
clear what I’m up to and why.
Teaching the politics of policymaking through institutions poses some
formidable challenges. Let me highlight two.
A first challenge is breadth. The policymaking process involves many po-
litical actors—interest groups, elected and appointed officials, grassroots orga-
nizations, voters, lobbyists, foreign leaders, the media—working within many
institutions—courts, legislatures, bureaucracies, campaigns, international and
non-governmental organizations. If you try to teach the details of each actor
and institution in a single course you risk covering none well.
A second challenge is the diversity of student backgrounds in many policy
schools. Political science majors might find an introductory course in political
institutions boring, while students who are new to this material might feel lost
xx Preface
if an accelerated pace is adopted. Moreover, with a student body from many
different countries, no matter which institutions we focus on, some students
will find them familiar while others will be starting from scratch.
In light of these tricky issues, I have eschewed any attempt at exhaustive
coverage of political institutions. In my view, such topics are often most suc-
cessfully covered inmore specialized courses. So what do I do instead?
The approach I take is to teach political economy. Rather than focusing on
details of the policymaking process in any particular country or institutional
setting, I develop general principles. These principles are lenses through which
we can view the politics of policymaking in any environment. This has the twin
virtues of providing a general approach to understanding politics and policy
that can be covered in a single course and of offering newmaterial to nearly any
student.
There is also amethodological component tomy approach that is important
to highlight. Almost all policy educations offer a rigorous introduction to policy
analysis through micro-economics and statistics. But the approach to teaching
politics is more varied. In many places, the view seems to be that experience,
rather than analysis or scholarship, is the best guide to politics. I couldn’t
disagree more. In my view, the rigor that serves us so well in analyzing policy
should also be brought to bear in analyzing politics. Thus, I employ the same
mathematical and analytical tools to teach about politics that students are
accustomed to seeingwhen they learn economics and statistics. In this way, the
political economy approach also helps to unify the standard policy curriculum
by offering methodological coherence and drawing clearer connections across
fields.
For Whom Is This Book Written?
I wrote this book for my MPP students at the University of Chicago. It is my
hope that it will be useful to other policy students. That said, the book has
also proven useful to colleagues teaching in other settings. It certainly works
as an introduction to modern political economy for advanced undergraduates,
as long as they know just a little bit of calculus. Colleagues have also found
the book useful for PhD students in political science. The most common such
use is for first-year doctoral students, often as a parallel reading in a game
theory course, where it provides some context for the formal tools students are
learning. In this setting, the book can help students avoid losing the forest for
the trees.
A Word on Tone and Technicality
In Parts II and III, I assume that the reader knows some basic game theory (pure
strategy Nash equilibrium and subgame perfection) and can use simple calculus
Preface xxi
to maximize a function. Game theory is a set of mathematical tools that are
used to study situations of strategic interdependence. An interaction between two
ormore people features strategic interdependence if the outcome for oneperson
depends not only on her own actions, but also on the actions of others. Since
most of life is strategically interdependent, having a theoretical frameworkwith
which to study strategic interdependence is useful. Readers who have already
had an introductory game theory class should have no problemwith the simple
models I develop. For readers who have not previously been introduced to game
theory, Appendices A and B cover everything that is needed.
This book is full of mathematical models. But it is not super technical. No
mathematics beyond the very basics of calculus (maximizing a function of one
variable) is required. Nonetheless, the reader should be prepared to sit at a desk,
pen and paper in hand, to work through themodels.
While my taste in models runs to the formal, my taste in writing does not.
You will find that my tone is conversational. For readers accustomed to formal
academic writing, this may be a bit jarring at first, so I want to prepare you.
My hope is that a conversational tone will perhaps blunt the sharp edge of the
mathematics. As one reviewer put it, “At first, I felt that the author’s first-person
writing style seemed a little casual or chatty for such a text. However, I grew
quickly to like that approach. To an extent, the author is the guide, helping
students through sometimes difficult material with his good-natured insights
and humor.” That is preciselywhat I’m going for. I hope the tone doesn’t bother
you too much. In any event, I’m not a good enough writer to switch tones at
will, so we’re both going to have to live with it.
Acknowledgments
I am particularly indebted to Scott Ashworth, with whom I have discussed this
material many times over the years. He has provided an enormous amount of
feedback and insight. To the extent that this book organizes ideas in a useful
way, the credit is as much due to him as it is to me.
I first encounteredmuch of thematerial in this book when, as an undergrad-
uate at Chicago, I took the course for which the book is named from Duncan
Snidal. When I joined the faculty, Duncan graciously allowedme to teach it.
During that time as anundergraduate, I had the great good fortune, privilege,
and delight of studying with Amy Kass, a teacher of extraordinary depth and
commitment. Mrs. Kass changed my life—inspiring me to take ideas seriously
and demanding more than mere cleverness. I believe she would have been
pleased that I’ve written a book whose purpose is to teach.
I am also in the debt of several other colleagues. At Chicago, Chris Berry,
Will Howell, Pablo Montagnes, and Anthony Fowler made helpful suggestions
on much of the content. More importantly, they make the Harris School, to
mymind, the most interesting place in the world to work in political economy.
xxii Preface
It is also, I think, important to note thatmy hot chocolate doesn’t hold a candle
to Chris’s carbonatedManhattan or smoked Brooklyn.
Bruce Bueno de Mesquita read and commented on the first draft and then
harangued me until I agreed to stop editing. Andy Eggers and Dimitri Landa
provided particularly thoughtful comments on Chapters 1 and 3. Jeff Ely
generously allowed me to shamelessly rip off his remarkably clear approach
to teaching basic mechanism design in Chapter 9.1–9.2. Several anonymous
referees made suggestions that pushed me to rethink structure and style in
exceptionally productive ways.
Scarlett Swerdlow and Zhaosong Ruan provided outstanding research assis-
tance.
This manuscript grew out of lecture notes that I developed while teaching an
MPP course at Chicago. I am appreciative of the many students who bore with
meover the yearswhile I figured outwhat I think such a course should cover.My
apologies to those students who came along early in the process. All I can say is
that the contents of this book are what I meant to tell you. Special recognition
is due the many students in the 2011–2013 Harris School Political Economy
for Public Policy classes who used the earliest drafts of this manuscript. They
identified a truly staggering number of typos, mistakes, and places where I
could have been clearer, to say the least. Notable among these students for the
excellence and sheer number of their suggestions are Boris Angelov, Anthony
Austin, Baur Bektemirov, Constance Boozer, Leah Calvo, Matt Chaney, Jennifer
Cowhy, Bradley Crawford, Mark Demming, Craig Denuyl, Mary Desmond,
Sarah Dickson, Elc Estrera, Kaci Farrell, Jenny Gai, Jonathan Grabinsky, Evan
Johnson, Binbin Lin, Laura Martin, Antonio Moreno-Torres Galvez, Sara Beth
Hoffman, Gillian Kindel, Emily Modlin, Diane Nimchuk, Song Yoon Park,
Corinne Stephenson-Johnson, Elizabeth Stovall, Jacob Rosch, Alice Song, David
Spearman, RobertoGerhard Tuma, Abra LyonsWarren, and ErinWatts. I’m sure
at least one of themwill find amisplaced comma in this paragraph,
Finally, a word of thanks to my family. I’m privileged to share my life with
three outstanding martial artists. I am as deeply appreciative for the love and
support of my wife, Rebecca, as I am proud of the extraordinary work she does.
My kids, Abe and Hannah, are the best. The best. And who knows, given the
family business, maybe one of themwill even read this some day.
This book is dedicated to my parents, Arlene and Bruce Bueno de Mesquita.
My mother is unrelenting in her dedication to her children. I am where I am
today because of her support. My father is the person I know most committed
to the idea that the scientific study of politics is genuinely important. His career
is an inspiration, even if his productivity is, frankly, offensive. It is a particular
pleasure to get to teach some of hismost important ideas inChapter 11. Thanks,
Mom and Dad. Sorry about high school.
POLITICAL ECONOMY
FOR PUBLIC POLICY
Introduction
In June of 2013, the Obama administration released its Climate Action Plan. The
plan starts bymaking a case for action:1
Climate change is no longer a distant threat—we are already feeling its
impacts across the country and the world. Last year was the warmest year
ever in the contiguous United States and about one-third of all Americans
experienced 10 days or more of 100-degree heat. The 12 hottest years on
record have all come in the last 15 years. Asthma rates have doubled in
the past 30 years and our children will suffer more asthma attacks as air
pollution gets worse. And increasing floods, heat waves, and droughts
have put farmers out of business, which is already raising food prices
dramatically.
These changes comewith far-reaching consequences and real economic
costs. Last year alone, there were 11 different weather and climate disaster
events with estimated losses exceeding $1 billion each across the United
States. Taken together, these 11 events resulted in over $110 billion in
estimated damages, which would make it the second-costliest year on
record.
The plan proceeds with a list of many proposals for regulations and incentives
to reduce carbon emissions andmitigate climate change. These include (among
many others) upgrading the electric grid, strengthening regulatory standards
for automobile fuel economy and power plant carbon pollution, increasing
funding for clean energy, advanced transportation technologies, energy
efficient construction, and accelerating clean energy permitting.
There is a fairly simple diagnosis of the source of climate change that is
agreed to quite broadly by social scientists. Carbon emissions—from factories,
passenger vehicles, or what have you—cause climate change. Each of us who
consumes fossil fuels bears only a tiny fraction of the costs associated with our
personal emissions. I don’t suffer much from the increased probability that you
get asthma caused by my car. As a consequence, each of us emits too much
carbon relative to what would be socially desirable. Put differently, if we could
1Executive Office of the President. June 2013. The President’s Climate Action Plan.
https://www.whitehouse.gov/sites/default/files/image/president27sclimateactionplan.pdf
https://www.whitehouse.gov/sites/default/files/image/president27sclimateactionplan.pdf
2 Introduction
all agree to emit less, we’d all be better off. But each of us, as individuals, has an
incentive to keep emitting.
There is also a pretty simple, andwidely agreed upon,way to address this kind
of problem. Increase the price of carbon so that people’s individual costs reflect
something closer to the true social costs of emissions. This price-based approach
has at least two virtues. First, an increase in prices works directly on individuals’
incentives. If the price of carbon is higher, people will use less of it all on their
own. They don’t need to be monitored or further regulated. Second, a price
increase incentivizes people and businesses to reduce carbon consumption in
as cost-effective a way as possible. Even among existing technologies, there
is uncertainty about whether the most cost-effective way to reduce emissions
is through increased fuel economy, greater investment in alternative energy
sources, cleaner power plants, or what have you. Moreover, who knows what
new approaches to reducing emissions will emerge if people have stronger in-
centives to innovate? Programs of the sort proposed in the President’s Climate
Action Plan incentivize particular approaches. A price increase on carbon in-
centivizes reduced emissions, but is agnostic as to how this should be achieved.
This gives people and firms the flexibility to choose the most cost-effective
strategies and encourages them to innovate.
As we will discuss throughout this book, there are a variety of political rea-
sons that, despite itsmerits, a price-based approachmight lose out. Policies that
work through targeted subsidies and regulations do a worse job at mitigating
carbon emissions. But, by creating specific winners from the policy process,
they allow political leaders to build a coalition of support. This coalition build-
ing is often the critical step in achieving policy change. So perhaps we should
not lament this outcome toomuch.
Suppose, however, that we wanted to think seriously about a price-based
approach. Broadly speaking, there are two largely equivalent ways of directly
increasing the price of carbon through policy. First, the government could
impose a carbon tax. Mankiw (2009) describes studies suggesting the optimal
such tax is somewhere between $30 per ton (roughly 8 cents per gallon of
gasoline) to $300 per ton (80 cents per gallon). Second, the government could
directly cap the level of carbon emissions—issuing permits for emissions and
allowing companies to trade those permits. Such a system is typically called cap-
and-trade.
Textbook policy analysis prefers the carbon tax to cap-and-trade (see
Mankiw, 2009, for a clear articulation of this position). Here are two reasons.
First, the carbon tax is more flexible. If there is significant fluctuation in
the demand for carbon emissions over time, cap-and-trade might impose an
inefficiently low level of emissions in a high-demand year. By contrast, a carbon
tax allows firms the flexibility to use more carbon, if it is worth it to them, in
such years. Second, a carbon tax generates government revenue. Such revenue
Introduction 3
could be used to offset other, less efficient sources of government revenue. A
cap-and-trade system does not generate such revenue unless the permits are
auctioned off at the outset. Thus, standard policy analysis suggests that a carbon
tax is preferable to cap-and-trade and that if we must do cap-and-trade, we
should auction the permits, using the revenues to reduce other distortionary
taxes.
These arguments have a lot of merit. But, in my view, they are incomplete. If
we are interested in actually reducing carbon emissions and mitigating climate
change, we have to take the political incentives just as seriously as the economic
incentives.
I would argue that the politics flip the standard policy advice on its head.
If you want to achieve an increase in carbon prices and reduction in carbon
emissions, you should prefer cap-and-trade without a permit auction (i.e.,
permits distributed to current emitters) over cap-and-trade with an auction,
which you should prefer to a carbon tax. Why do I say that?
First, let’s think about adoption. Thewinners from a carbon tax are the broad
public who benefit from mitigating the risks of climate change. But the broad
public is a diffuse and unorganized interest. It can exert very little political
power. The losers from a carbon tax include oil and gas companies, automobile
manufacturers, and emitting industries. These are highly concentrated and
organized interests. They can exert significant political power to block a carbon
tax. What about cap-and-trade? If cap-and-trade is coupled with an auction for
emission permits, the same analysis holds. Powerful, concentrated, and well-
organized interests are being asked to pay for emissions that they previously
made for free. They have every incentive to block such a policy. But what about
if permits are given for free? Now the policy has costs and benefits for emitters.
On the one hand, they are being forced to reduce emissions, a cost. On the
other hand, they are being given control over a tradable asset of considerable
value. Current emitters who believe they can reduce emissions relatively cost-
effectively will be able to sell those permits for a profit. This might create the
sort of organized and powerful interest needed to move the policy through the
political process.
Second, let’s think about sustainability. Even if a carbon tax were somehow
implemented, the analysis above holds. The supporters of a carbon tax are
diffuse, unorganized, and relatively weak. The opponents of such a tax are
concentrated, organized, and strong. It would require remarkable vigilance to
keep a carbon tax on the books. Cap-and-trade, with or without an auction,
is just the opposite. Once permits are issued, they become a valuable financial
asset. In addition to the owners of the permits themselves, once a market for
such permits emerges, there are brokers, investment bankers, and a variety
of financial services providers with a stake in the market. An organized and
4 Introduction
powerful set of interests will fight to sustain the policy. Again, then, the politics
favor cap-and-trade.2
I hope you find these arguments provocative. My goal, at this point, is not to
convince you about the right way to think about environmental policy. Rather,
I want you to see that, while traditional policy analysis is an essential input to
thinking carefully about policy, it is not the end of the story. Policy is made
in political environments. If you want to understand policy or effect policy
change, youmust take the politics of the policymaking process seriously. So let’s
get going.
Three Goals
In service of the broad aim of understanding the politics of public policy, this
book pursues three interrelated goals.
The first goal—tackled in Part I—is to spend some time thinking about
the normative foundations of policymaking. That is, to ask questions like,
“What are the proper goals of public policy?” In so doing, we will discover
how difficult it is to come up with a coherent, unified, normative framework
to motivate policy decisions. We will arrive at one limited version of such a
framework, but we will also see that the ambitious program of formulating a
broad conceptualization of the public interest that everyone can endorsemight
be a fool’s errand. Nonetheless, along the way we will discover some useful
and provocative ideas that will make our thinking about these issues more
structured and nuanced.
The second goal is to think through some fundamental aspects of social life
that create opportunities for public policy to make the world a better place. I
call these aspects of social life—which are developed in Part II—social dilemmas.
These social dilemmas are ubiquitous features of human interaction that give
rise to predictably regrettable outcomes. We will discuss ways in which policy
might improve those outcomes. The objective, in this part of the book, is
to develop some habits of mind that let you see the world through a few
analytical lenses. I believe you will find that once you get used to viewing the
world through the lens of these social dilemmas, you will start to see them
everywhere. This may be a bit depressing, but it is also useful in identifying
opportunities for policy to do good.
The third goal is to think seriously and conceptually about the politics. As
I said in the preface, I’m not going to do this by analyzing the politics of
policymaking institution by institution. Instead, in Part III, we look at two
classes of explanations for why governments might not always achieve good
policy outcomes. The first focuses on technological constraints—facts about the
2This argument is based on the discussion of the success of cap and trade in curbing sulphur
dioxide emissions in Patashnik (2008, Chapter 8).
Introduction 5
policymaking process that limit the government’s ability to achieve goodpolicy
outcomes even when policymakers are genuinely motivated to do so. The
second focuses on incentive constraints. Policymakers are people with their own
interests and concerns. We analyze how some fundamental facts of politics—
most especially leaders’ desire to remain in power—interact with political in-
stitutions to determine when policymakers have better or worse incentives to
pursue good policy. We end this part of the book by looking at a bit of evidence
on how the organization of government affects policy outcomes—including an
extended discussion of foreign aid policy.
The Role of Models
The main analytic tool we will use in this book is theoretical models—mostly
mathematical models. As such, it is important to think a little bit about how to
relate to or evaluate a model. What is a model, and what is one good for?
The world—be it physical, biological, or social—is too complicated for us to
think through coherently all at once. To make sense of the world, we need to
break it up into bite-size pieces that we can think about carefully. The hope is
that, in so doing, we will figure out some general principles that help guide our
thinking. Models are an attempt at doing this.
Given this, the goal of a model is emphatically not to describe the world in
all its richness. A model is an abstraction and a simplification. Its purpose is
to isolate some aspect of a problem or phenomenon, so that you can think it
through carefully and without distraction. If a model captured all the richness
of the world, you would be just as perplexed thinking about your model as you
are thinking about the world. That would be a lousy model.
Let me be a little more concrete. A classic example of a model is a map.
A map of a city, for instance, is a model of a particular part of the earth. It
abstracts away from almost everything that is interesting about that part of the
earth—the people who inhabit it, the quality of the restaurants, the crime rate,
school districts, in some cases the topography, and so on. To be a successful
model, a map must ignore this richness. A map of place and street names
isolates precisely those bits of theworld that you need to navigate the city.More
information would distract from the task at hand—trying to get around. Less
information would leave the map insufficiently rich to be useful. It’s a delicate
balance.
The analogy to a map points to an important fact about models. What a
model should and should not include depends critically on what you intend
to do with it. Consider two maps—one a street map and the other a topo-
graphical map. One cannot say, in the abstract, which of these is the better
model of a bit of the earth. If one’s goal is to drive, then the street map is the
6 Introduction
right model. If one’s goal is to hike without trails, then your map needs topo-
graphical information.
The same holds true with models of social interaction. It is tempting, when
presented with a model of human beings, to start listing things that you
consider important but that are not included in the model. To react that
way, however, is to miss the point of a model—just like criticizing a street
map for failing to include restaurant information is to miss the point of a
street map. If you evaluate a model by asking whether it captures everything
that is interesting about some question or situation, you will be perpetually
dissatisfied. Theworld is an infinitely interesting andwondrous place. Our poor
powers to abstract and to generalize are not up to the task of capturing all its
richness. So, yes, all our models will leave you wanting, if you expect them to
be full representations of the world, or even of some little slice of the world.
But this doesn’t mean our models are bad. It just means that expecting models
to capture everything that is interesting about some aspect of the world is the
wrong goal. What, then, is the right goal?
First, for a model to be useful, it cannot be a purely abstract object. We must
be able to relate it to some aspect of the world in which we are interested. As the
philosopher of science Ronald Giere puts it, models are “artful specifications
. . .designed so that elements of the model can be identified with (or coordi-
nated with) features of the real world” (Giere, 2006, p. 63). Notice the key point
here. Some element of the model must correspond with some feature of the
world. The model need not capture everything that is interesting or important
about the bit of reality you are interested in. But it must capture something that
is interesting or important about it.
Second, the purpose of a model is to help you think through some aspect of
the world that is too complicated to think through in its totality. As such, the
model should teach you something that you didn’t see before you broke the
situation up into bite-sized pieces. Otherwise, the model wasn’t terribly useful.
Inmy view, the right way to evaluate amodel involves asking something like
the following two questions:
1. Is something in themodel like something I am interested in out there
in the world?
2. Did the analysis of the model teachme something about that aspect of
the world that I didn’t know before?
If the answer to both questions is yes, then the model has done its job. It has
laid out an abstraction that you are able to relate to the world in some way. And
the abstraction did in fact help you learn about that aspect of the world. These
are the goals of a model.
If this is what a good model does, how should someone interested in public
policy think about applying the insights of amodel? I like to think of amodel as
Introduction 7
a really smart adviser who understands only one narrow aspect of a policy issue.
You, the policymaker, should listen to your model and the ideas it suggests. But
you should not do so slavishly. After all, you know a lot more about the world
you are dealing with than your model does. A third question, then, that you
might want to ask before applying the insights or policy suggestions that come
out of your model is something like this:
3. Is there something about the world that is missing frommymodel that
I believe wouldmaterially change the conclusions of the model were it
included?
If the answer is no, then it seems the insights of yourmodel are applicable. If the
answer is yes, however, then you should proceed to apply the model’s insights
only in a cautious and somewhat skeptical way.
With all of this inmind, I should perhaps say aword or two about how I chose
and constructed the models that appear in this book. My goal is not to bring
you to the technical frontier. Rather, it is to introduce what I take to be some of
political economy’s most important insights in a rigorous, but accessible, way.
As such, two principles guide mymodeling choices.
First, I always present the absolutely simplest, least technical version of
a model that makes all of the points I want to make. The goal is to make
substantive insights clear and rigorous. This requires some technicality. But I
emphatically do not want you to get lost in the math.
Second, I only present models whose messages I believe are general. I am not
interested in presenting simple models whose main point is fragile. To do so
would privilege clever formalization over substance. That’s not what I’m about.
So, for every simple model I present, I’m asking you to take my word that there
is a body of scholarship (too technical for our purposes) that has developed
the arguments in sufficient depth to convince me that the main idea is both
important and robust. At the end of each chapter, I point the interested reader
to some of these further resources.
Why Rationality?
Almost all of our models build on the assumption that people are rational.
Rationality, here, means several things. In its most stripped down form,
rationality simply means that people have coherent preferences over outcomes
and they act to pursue those preferences. I discuss this a bit more formally in
Appendix A.1.1.
But we will generally assume something stronger than just coherence of
individual preferences. In particular, we will assume that people have coherent
preferences over outcomes, that they pursue those preferences, and that those
preferences are mostly centered on their own personal welfare. That is, we will
8 Introduction
assume that people are not primarily motivated by altruism or concern for
others, but rather bymaking themselves better off.
Notice, the assumption of rationality of this kind is already a model. It is a
model of human agency.Why should we adopt this particular model? After all,
we regularly hear stories of great acts of charity and heroism. Surely a coherent
analysis of social life would take into account the fact that human beings are
not entirely selfish and avaricious.
I don’t disagree. People are, at times, altruistic. (Though the fact that such
stories are newsworthy suggests that they may be the exception, rather than
the rule.) But, remember, we are building amodel.We are trying to simplify the
world in away that is useful for the problemswithwhichwe are concerned. And
the problems with which we are concerned here are problems of public policy.
Public policy is, at least in one conceptualization, what society does when
people, left to their own devices, do not act in one another’s interests. Given
this, if we are going to think about a model of people to motivate the making
of public policy, surely we do not want to assume that people are primarily
motivated to look out for one another. If we base our thinking on such an
optimistic model of human motivations and proceed to design policies on the
basis of that assumption, we may find ourselves disappointed by the actual
behavior of our fellow humans. If, instead, we start with the assumption that
people are basically selfish, we put ourselves in a position to think about policy
interventions that will work even under the worst of circumstances. To be sure,
such an assumption may be overly pessimistic, leading us to take precautions
against bad behavior in excess of what is necessary. But, in the context of
policymaking, this seems like the safer kind of mistake to make, at least as a
starting point.
There is another (perhaps more pragmatic) reason for restricting our atten-
tion to rational individuals. Doing somassively simplifiesmany of our analyses.
And, remember, the goal of model building is to come up with something that
corresponds in some way to the world, but that is simple enough that you can
think it through and learn something you didn’t see before. For this purpose,
the assumption of rationality (in the sense of having coherent preferences, not
the assumption of selfishness) is indispensable.
Further Reading
The appendices contain all the game theory you need to understand this book.
But if you are looking for an alternative introduction to game theory, there is
none better than Martin Osborne’s An Introduction to Game Theory. If you need
a basic calculus refresher, I recommend Daniel Kleppner and Norman Ramsey’s
Quick Calculus.
Introduction 9
Many philosophers of science have deep things to say about the role of
models. My favorite is IanHacking’s Representing and Intervening. In the chapter,
I mentioned Ronald N. Giere’s Scientific Perspectivism. Perhaps most relevant for
the kindofmodels exploredhere isMary S.Morgan’s fantastic bookTheWorld in
theModel. Themap analogy as ameans of explaining the pragmatics ofmodels is
certainly not mine. For instance, in her Essays in the Theory of Economic Growth,
Joan Robinson wrote, “A model which took account of all the variegation of
reality would be no more use than a map at the scale of one to one.” Paul
Krugman’s essay “The Fall and Rise of Development Economics,” which is the
first chapter of his Development, Geography, and Economic Theory, has a fantastic
discussion of the history of map making, its role in thinking about economic
development, and the conceptual importance of simplified models in social
science.
PART I
Normative Foundations
In Chapter 1 we look at some models proposed by political philosophers to
answer questions like “what are the proper goals of public policy?” but, sadly,
fail to arrive at a principled answer. One of the central lessons we draw is that
life is full of trade-offs. Pursuing one normatively admirable goal often entails
sacrificing another. Reasonable people can disagree about these trade-offs and,
consequently, can disagree about the proper goals of public policy.
Undeterred, we push forward with our quest to find a normative foundation
onwhichournotions of goodpolicy or the public interest can rest. InChapter 2,
we consider another path. We want to allow reasonable people to disagree. So
we abandon the hope of finding a normative framework that simply identifies
good policy. Instead we consider the possibility that, while we disagree on
basic normative questions, we might nonetheless agree on a procedure for
aggregating our disparate views into a collective view. The idea is that if we
can find an aggregation procedure that is itself normatively defensible, then
we might all agree to endorse the output of that procedure, even when the
output turns out contrary to our own personal views or convictions. Unfor-
tunately, even this more limited approach to determining the goals of public
policy yields little in terms of progress toward a coherent notion of the public
interest. Though in a limited set of circumstances, majority rule has some
appeal.
Finally, we curb our ambitions even further in Chapter 3. We define a notion
of the public interest that is arguably uncontroversial—policies thatmake some
people better off and no one worse off. Assuming we can all agree that any
such policy is a good policy, we set this as our normative standard, although we
12 Part I
will see that there might indeed be principled objections even to this limited
notion of the public good. We show that if we are willing to make a few
extra assumptions about the kind of preferences people have, then the class of
situations where such improvements are possible might not be as limited as it
first seems. This discussionmotivates our study of social dilemmas in Part II.
1
Normative Frameworks
An important current debate in education policy surrounds the issue of charter
schools. Oversimplifying, the basic terms of the debate are the following. In
many cities, public schools are struggling to provide good educational out-
comes, especially for students from disadvantaged backgrounds. In an attempt
to reform the education system, policymakers have embraced “school choice”
in the formof charter schools. Charter schools are run by private organizations,
but at public expense. Students can opt out of the public schools to attend a
charter school. (Although often demand for charter schools outstrips supply, so
the charter schools hold admissions lotteries, which turns out to be very helpful
for assessing the school’s efficacy by creating a natural control group of students
who wanted to get in but didn’t.)
Evidence on the efficacy of charter schools is mixed. However, there is grow-
ing evidence that certain charter schools—so-called “no excuses” schools—
are quite effective at improving educational outcomes. The hallmarks of such
schools include a longer than typical school day and year, performance-based
compensation of teachers, high academic and behavioral expectations coupled
with strict behavior norms and discipline, and a focus on traditional college
preparatory reading andmath skills. The best evidence of which I am aware sug-
gests that no excuses schools improve academic achievement across the board
and are particularly successful at improving the performance of themost disad-
vantaged students (Angrist et al., 2012; Angrist, Pathak, andWalters, 2013).
Given these facts, one might think that almost anyone without a personal
interest in preventing the spread of charter schools would favor funding no
excuses schools. After all, they seem to improve outcomes for all students
and to especially aid those students most in need. So whether one’s con-
cern is improving overall social well-being, improving opportunity, reducing
inequality of opportunity, or what have you, no excuses schools seem to fit
the bill.
Let me muddy the waters just a bit with one more piece of evidence.
Although no excuses schools benefit the most disadvantaged students, those
students are by far the least likely to seek enrollment in such a school (Walters,
2014). Hence, no excuses schools present the following policy paradox. On
the one hand, by helping all students, and particularly the disadvantaged, no
14 Chapter 1
excuses schools improve both educational outcomes and educational equality
among enrolled students. On the other hand, since disadvantaged students
are much less likely to enroll in no excuses schools than are advantaged stu-
dents, overall, the existence of no excuses charter schools increases educational
inequality.
Now ask yourself whether promoting no excuses charter schools is good or
bad education policy. The answer depends on your framework for normative
evaluation. If you think that any policy that improves educational outcomes for
some set of students, without hurting anyone else, is good policy, then you are
probably a big fan of no excuses charter schools. If you are a person who thinks
the top policy challenge for education is to improve equality of educational
opportunity, again you might advocate for no excuses charter schools, which
provide the opportunity for better educational outcomes across the board. By
contrast, if you are primarily concernedwith equality of educational outcomes,
you might think that no excuses charter schools are bad policy because, while
in theory they could decrease inequality, in practice they end up disproportion-
ately benefiting advantaged students. To knowwhat you think about no excuses
charter schools, you have to know what you believe the proper goals of public
policy are and why. Thinking about normative frameworks is intended to help
you wrestle with such questions.
The purpose of this chapter is not to identify the normative framework that
we can all agree on—such a thing does not exist. Nor is it to convince you that
one set of standards is better than another. I havemypersonal viewswith regard
to thesematters, but I’mnot so confident in themas to think you should believe
them too. Rather, before we dive into theorizing about social dilemmas and
their solutions, it seemsworth spending a bit of time looking at somenormative
frameworks that various thinkers have found both compelling and useful in
evaluating public policy and social outcomes. Each has its problems, some of
which we will discuss. Each also offers useful and thought-provoking insights
into thorny questions about the goals of public policy. Reasonable people can
disagree about the relative merits of these ideas, but all are, I believe, worth
having spent some time with.
Thinking about normative frameworks is not, primarily, the work of social
scientists. It is the work of philosophers and, in particular, normative political
theorists. I am not an expert in normative political theory, so this discussion
will not pretend to be a comprehensive or deeply nuanced take. Indeed, I will
purposefully leave out much of the richness and subtlety that exists in the
discourse on each of our normative frameworks. My hope is to give you a rough
overview of some important ideas and the dialogue amongst those ideas. I do so
with three goals in mind.
First, if you are going to use a particular normative standard to set goals
for public policy, you should have a clear-minded understanding of the
Normative Frameworks 15
implications of your normative commitments. Similarly, if you are going to
advocate for certain positions, it may prove helpful to have a more robust
understanding of the kinds of normative arguments that might lead people to
disagree with you. Entering into dialogue with your opponents in a way that
addresses their actual concerns and values is a more productive means toward
reaching understanding (if not agreement) than is simply repeating your own
position in an ever louder voice.
Second, in my view, the public discourse on the normative justifications
for various public policies is often hopelessly confused. People on different
sides of various debates use the same words to mean different things, often
without noticing that they are doing so. I hope that a discussion of some core
ideas from political philosophy can improve the clarity of your thinking about
your own views and values, if nothing else, by disambiguating some important
concepts.
The third goal is closely related to the second. One reason that people like to
use one word to mean many things is so that they do not have to face the fact
that life is full of trade-offs. For instance, there may be real trade-offs between
liberty (understood as freedom from coercion) and equality of opportunity. Yet,
if we define liberty to mean everyone has the same capacity to pursue his or
her goals, rather than everyone is similarly free from coercion, then achieving
liberty requires equality of opportunity. This conflation makes the concept of
liberty redundant—whynot just call it equality of opportunity? This kind of no-
trade-offs thinking is insidious. Public officials, for instance, often like to talk as
though all good things go together—we can have a cleaner environment and
stronger economic growth, lower taxes and more government revenues, and
so on. What we will see in the discussion to come is that many of our most
cherished values are, at least some of the time, in tension with each other. If
we want to hold informed and mature policy positions, we should face up to
these trade-offs and take them seriously.
1.1 What Is a Normative Framework?
Defining a normative framework is itself tricky work. So let’s try to answer
this question, not from first principles, but by thinking about what it is that
normative theorists do.
It seems to me that normative theorists focus on three interrelated tasks.
First, they identify and clarify various normatively valuable goals. For instance,
they might talk about the idea that freedom is normatively valuable and
distinguish various notions of freedom from one another. Second, normative
theorists often attempt to describe some of the trade-offs that exist between var-
ious goals. So a normative theorist might point out that the goal ofmaximizing
freedom from coercion and the goal of equality of wealth are in tension with
16 Chapter 1
one another. Third, they offer foundational arguments about which normative
goals are actually valuable and how to balance the trade-offs between various
normative values. For instance, one theorist might argue that the fundamental
standard for all normative decisions is equality and, as a consequence, might
advocate for accepting some diminution in freedom from coercion in order
to redistribute wealth. Another normative theorist might argue that the fun-
damental standard for all normative decisions is respect for individual self-
ownership and, thus, might advocate for accepting high levels of inequality so
as to avoid any compromise on freedom from coercion.
To my mind, it is this third step that is at the heart of normative analysis. A
normative framework proposes a system that allows one to think systematically
about the trade-offs among competing values. As I’ve said, it is not my view
that any one normative framework is right. Nor do I think that you must
commit yourself to one normative framework in order to balance trade-offs in
a principled way. Normative policy questions are just not the sort of topic with
deeply satisfying foundations like that. (I’m not sure any topic is, but that is
another discussion.) What I do believe is that it is a useful exercise to adopt
the mind-set of a particular normative framework in order to see what that
way of thinking has to teach you about a particular question. Of course, for
any given policy question, you may want to repeat that process with several
normative frameworks and then think about what you believe the right way to
balance all the trade-offs is, informed by your understanding of what different
normative frameworks have to say about the issue. Put differently, I want us to
treat normative frameworks as differentmodels, each of whichmay be useful in
some circumstances.
1.1.1 Private vs. Public Morality
Normative frameworks provide guidance on two different sorts of questions
which are usefully distinguished. The first type of question is about private
morality—how ought I to behave? The second type is about public morality—
how ought the government to behave? While each of the normative frame-
works we will discuss have things to say about both sorts of questions, the
questions are not the same. To see why, it is useful to talk about a couple
examples.
Imagine a wealthy person who favors a policy of significant redistribution
from the rich to the poor, but gives little to charity. Is such a position nor-
matively tenable? If public and private morality are the same, then it seems
the answer is no—your normative commitments call for both a policy of
redistribution and a personal duty to give your wealth to those less fortunate.
But one can imagine an argument for pulling apart the two moralities.
Virtually any individual giving away her personal wealth has essentially no
Normative Frameworks 17
impact on the total level of inequality. Hence, a person might reasonably hold
the following position:
I am happy to give away much of my wealth as part of a societal effort to
achieve greater equality. But if the rest of the members of my society are
not going to participate, I don’t want to make a large personal sacrifice
with no appreciable consequences for overall inequality.
This positionmakes a distinction between private and public morality. Govern-
ment policy can achieve large-scale redistribution. And so, it says, the govern-
ment should do so because social equality is important. But individual charity
cannot achieve large-scale redistribution. So, it says, an individual is not
duty-bound to unilaterally give away her wealth.
One can imagine similar arguments in many settings. Only the government
can achieve large-scale reductions in carbon emissions. Hence, one might
simultaneously argue that good policy requires reducing emissions and that,
absent such a policy, it is okay to drive an SUV. Of course, one might also argue
that, in some domains, public and private morality coincide. (Broome (2012)
considers both sides of the argument for the case of climate change.)
In other settings, it is straightforward that public and private ethics come
apart. Consider a parent’s duty to a child. Most (though not all) normative
frameworks suggest that parents have a special duty to their children. Indeed,
on many views, I have a duty to protect my children, even if that means failing
to protect others’ children. (To see this, ask yourself whether I would have done
the right thing if, in some emergency, I chose to save my own two children,
instead of four children of strangers.) But it seems crazy to think that this
personal duty implies an analogous public duty. No one (other than me, of
course) thinks the government should care more about my children than other
people’s children.
It is useful, as you think through the various normative frameworks, to keep
this public versus private distinction in the back of yourmind. Now let’s turn to
our normative frameworks.
1.2 Utilitarianism
Utilitarianism is the classic example of a consequentialist normative
framework—that is, a normative framework that assesses the rightness
or wrongness of an act based on its consequences. Within the class of
consequentialist normative frameworks, it is welfarist—the consequence with
which it is concerned is human well-being or utility. The basic motivating
thought of utilitarianism is that good acts, policies, or social arrangements
are those that tend to maximize the aggregate utility in society. Each person
has his or her own individual preferences over many things. As such, each
18 Chapter 1
possible act, policy, or social arrangement has implications for many people’s
utility—making some better off and others worse off. In a choice between two
acts, policies, or social arrangements, the one that results in the larger aggregate
utility is taken to be right.
To seehow tricky even seemingly simplenormative frameworks canbe, here’s
a little thought experiment. One way to define aggregate utility is as the sum of
individual utilities. Another perfectly reasonable definition is the average of the
individual utilities.
Under both of these definitions, utility is aggregated by adding, treating
all individual utilities equally. So, at first blush, these two definitions might
seem equivalent. They are not. To take an example, they have very different
implications for the desirability of policies that encourage people to have
children. On the first definition, it is pretty clearly a good, utilitarian policy to
encourage people to have children, at least up until the point of overcrowding.
(More people, more total utility in society.) On the second definition, adding
a person increases aggregate utility only if that person has higher than average
utility. Thus, under this second definition, you’d want a policy that encourages
people to have children if their children are expected to have higher utility
(be happier) than the average citizen and that discourages people from having
children if their children are expected to have lower utility than the average
citizen. How you define your utilitarian objective matters.
1.2.1 Why Be a Utilitarian?
There is much to like about utilitarianism. First, it has the important virtue
of treating all people equally.
Second, and perhaps most importantly, utilitarianism is a powerful tool for
balancing trade-offs. Often, when we think through complicated policy ques-
tions, we findmultiple competing values. Perhaps in order to save lives, we need
to deceive people. Or, in order to improve health or environmental outcomes,
we have to reduce economic growth. Undermany normative frameworks, it can
be hard to see how tomake choices among competing, fundamental values. Not
for a utilitarian. A utilitarian evaluates such trade-offs simply by figuring out
the utility value of each outcome to each individual, adding, and comparing.
Utilitarianism transforms philosophical conundrums (how do I compare two
fundamental values?) into empirical questions (howmuch do individuals value
these two outcomes?) and, thus, always provides an answer. For this reason,
utilitarianismhas become the guiding normative framework underlying almost
all of modern policy analysis.
A third argument in favor of utilitarianism is less pragmatic and more philo-
sophical. A long-standing tradition in political theory suggests that we think
about the legitimacy of a set of societal institutions as deriving from a social
contract, agreed to in mythical negotiations amongst our ancestors some time
Normative Frameworks 19
in the distant past. This type of contractarian argument is most typically used
(for instance, in the Hobbesian tradition) as a way to establish the legitimacy
of state authority by allowing the argument that the state rules by the consent
of the governed. If we push the contractual analogy a bit, we might also offer a
contractarian defense of amore specific social arrangement or set of social goals.
A concern with such a contractarian approach to normative justification
is that, during contract negotiations, people will tend to push for a social
arrangement that serves their individual interests, not the interests of society.
As such, any actual social contract will reflect particularistic interests and power
relationships, not the social good.
The economist John Harsanyi proposed a thought experiment (later made
famous by the philosopher John Rawls) to develop a theory of normative
justification that simultaneously retains some of the appealing features of
contractarianism—in particular, the idea that wemight all agree to some social
arrangement—while also suggesting a way around (at least for the philosopher)
the problem of particularistic interests sullying the social contract. Imagine
yourself behind a veil of ignorance, so that you don’t know any of the particular-
ities of yourself—whether you will be smart or dumb, attractive or unattractive,
born to rich or poor parents, and so on. Now ask the following: Suppose we
were all behind the veil of ignorance and we could sign a contract which would
specify the rules for our society. What kind of contract would we sign? Rawls
refers to this fictional state of ignorance as “the original position.”
Before we get to Harsanyi’s answer, let’s see what’s going on here. The veil
of ignorance has two important features. First, we are all identical behind the
veil of ignorance. That is, you and I are both equally likely to end up with
any particular set of skills, talents, and so on. This makes it easy to agree to a
contract, since we all have the same interests. Second, in the absence of any
particularistic knowledge about ourselves, we are in the common position of
humanity. Hence, from behind the veil of ignorance, whatever decision you
come up with about what kind of society you want to live in is not based on
particularistic interests. This last fact is the real force of the thought experiment.
It lets us get at a notion of the sort of society in which we’d like to live that does
not depend on anything about ourselves as individuals, but rather, depends
only on our shared humanity.
Harsanyi argues that, behind the veil of ignorance, we are all utilitarians.
(Rawls disagrees. We’ll talk a bit about this later.) It is worth noting that
Harsanyi’s position is controversial. Nonetheless, it is an interesting argument
worthy of our consideration. Here are its bare bones.
Suppose our society is made up of N individuals. We are choosing a social
arrangement from a set, A, of potential social arrangements. A social arrange-
ment is a description of how we will organize our society, what policies we will
implement, and so on.
20 Chapter 1
Consider some particular social arrangement, a ∈ A.1 Under this social
arrangement, there will be some person who has the highest utility, some
person who has the second highest utility, and so on, all the way down to the
person with the Nth highest (i.e., lowest) utility. Call the utility of the best-off
person under social arrangement a, u1(a). This utility is a numerical measure
of that person’s happiness or well-being. Call the utility of the second-best-off
person under social arrangement a, u2(a), and so on all the way down to uN(a).
We can do likewise for any other social arrangement.
Now, recall, we are behind the veil of ignorance.When evaluating themerits
of various social arrangements, you don’t know whether you will be the person
with the highest utility, the secondhighest utility, or the personwith the lowest
utility. You find each equally likely. In particular, since there are N individuals,
the probability you are in any given social position is simply 1/N.
To evaluate themerits of a particular social arrangement frombehind the veil
of ignorance, we need to know how people deal with uncertainty. It is clear, if
offered two certain outcomes, a person prefers the outcome with higher utility.
Thus, within a given social arrangement, everyone prefers to be the personwith
the highest utility to the person with the second highest utility, and so on. But
things are less clear if people are offered uncertain outcomes.
To see the issue, imagine a society with two people and two possible social
arrangements, a1 and a2. Under social arrangement a1, each person gets a utility
of 10. Under social arrangement a2, the best-off person gets a utility of 100 and
the worst-off person gets a utility of 0. From behind the veil of ignorance—that
is, not knowing whether you will be the high or low utility person under social
arrangement a2—it is not obvious which social arrangement you should prefer.
Social arrangement a1 offers an okay outcome for sure. Social arrangement a2
offers a coin toss between a really good and a really bad outcome.
I am a bit more formal about this in Appendix A, but essentially the as-
sumption we will make is that people evaluate such uncertain “lotteries” over
various outcomes by calculating the expected utility. One calculates an expected
utility by multiplying the probability of each outcome times the utility from
that outcome and then adding. So, in our example, the expected utility of
social arrangement a1 is just 10, since a person gets a utility of 10 for certain.
The expected utility of social arrangement a2 is
1
2 × 0 + 12 × 100 = 50. This
calculation comes from the fact that, under social arrangement a2, a person gets
a utility of 0 with probability one-half and gets a utility of 100 with probability
one-half. Hence, given these payoffs and probabilities, a personwhomaximizes
expected utility would prefer social arrangement a2 to social arrangement a1.
1If you don’t know what the symbol ∈ means, feel free to ask. There is no sense getting lost in
notation. It means “element of.” Capital A is a set (or collection) of possible social arrangements.
Little a is an element of the set A, which means a is one particular social arrangement from the
collection of possible social arrangements, A.
Normative Frameworks 21
Of course, if the payoffs had been different, preferences over social arrange-
ments might have been different. For instance, suppose there was some third
social arrangement, a3, where one person gets utility 0 and one person gets
utility 18. Like under social arrangement a2, under social arrangement a3 one
outcome is worse than the assured payoff under social arrangement a1 and one
outcome is better. But the expected utility of social arrangement a3 is
1
2 × 0 +
1
2 × 18 = 9. Thus, from behind the veil of ignorance, a person who maximizes
expected utility prefers social arrangement a1 to social arrangement a3.
Now, consider your evaluation of some arbitrary social arrangement, a, from
behind the veil of ignorance. You think that with probability 1/N you will get
utility u1(a), with probability 1/N you will get utility u2(a), and so on. So, your
expected utility from social arrangement a is
EU(a) = 1
N
× u1(a) +
1
N
× u2(a) + . . . +
1
N
× uN(a).
This can be rewritten:2
EU(a) =
∑N
i=1 ui(a)
N
.
Given this, from behind the veil of ignorance, you strictly prefer social arrange-
ment a to some other social arrangement a′ if and only if
∑N
i=1 ui(a)
N
>
∑N
i=1 ui(a
′)
N
.
That is, from behind the veil of ignorance, you prefer one social arrange-
ment to another if and only if the average utility is higher under that social
arrangement. Thus, Harsanyi concludes that we are all average-social-utility
maximizing utilitarians behind the veil of ignorance.3
1.2.2 Some Problems for Utilitarianism
Utilitarianism is a powerful normative framework. It provides a clear set of
standards, has systematic arguments in its favor, and offers guidance on a wide
array of questions. That said, utilitarianism is not without its problems. A utili-
tarian assessment involvesmeasuring, aggregating, and comparing individuals’
utilities. From a conceptual point of view, this is a demanding informational
requirement—we must conceive of each individual’s well-being as something
that can be put on a common scale, so that they can be compared. From a
2Again, don’t let notation get in the way of understanding. The symbol
∑
means “sum.” So
∑N
i=1 ui(a) means the sum of u1(a) + u2(a) + . . . + uN (a).
3Harsanyi’s argument, clever as it is, is controversial. A reader interested in a deep, but techni
cally difficult, critique of Harsanyi’s argument should consult Roemer (1998, Chapter 4.4).
22 Chapter 1
practical standpoint, this is a demanding measurement requirement—if we
want to use utilitarianism to evaluate policies, we need to measure the effects
of these policies on a lot of individuals’ well-being.
In addition to these conceptual and practical worries about the informa-
tional demands of utilitarianism, there are also a variety of concerns about some
of the implications of utilitarianism. Before I discuss a few classic examples, let
me offer a caveat.
While the coming examples (and the examples I will point to for the other
normative frameworks) raise some serious questions about utilitarianism, you
should interpret themwith some care. Remember, any normative framework is
a model, meant to help us think about complicated decisions in a simplified
way that clarifies some key issues. No such model could be perfect—for any
normative framework, no matter how compelling, we are going to be able to
come up with some situations where it seems to lead us astray. It is important
to know in what situations it will do so. But it is also important to bear in mind
the many situations in which the normative framework provides us with good
and useful guidance. As John Rawls puts it in A Theory of Justice (p. 52):
Objections by way of counter-examples are to be made with care, since
these may tell us only what we know already, namely that our theory is
wrong somewhere. The important thing is to find out how often and how
far it is wrong. All theories are presumably mistaken in places. The real
question at any given time is which of the views already proposed is the
best approximation overall.
PHILISTINES
In Jeremy Bentham’s classic formulation of utilitarianism, people’s prefer-
ences are their own. We have no moral standing to judge that from which
another person derives utility. If you derive happiness from great literature and
I derive happiness from blowing stuff up in my backyard, we have no way of
saying that one activity is more meritorious than the other. (Up to, of course,
the point where your enjoyment of some activity causes me to suffer or vice
versa.) If being a Philistine makes me as happy as being refined and highbrow
makes you, then both are equally moral acts.
An even more extreme version of this same problem is Nozick’s idea of a
pleasure machine. Suppose we could hook people up to the Matrix (is that
reference already dated?) and make them believe they are fantastically happy.
Would that be morally preferable to letting people live their actual lives?
Philosophers, at least since John Stuart Mill, have been unhappy with this
aspect of utilitarian theories. They’ve proposed a variety of fixes. But, as a
general matter, I think a person committed to a classical utilitarian kind of
view has to accept that these problems exist for the theory. I don’t find them
Normative Frameworks 23
terribly upsetting. If you derive lots of utility from watching reality TV and
drinking bad beer, good for you. I kind of wish I did. It would be cheaper than
my taste for avant-garde cuisine and single-malt scotch.
MONSTERS
The problem of monsters is closely related to the problem of Philistines, but
perhapsmore troubling. Consider a personwho derives pleasure from inflicting
pain on others. If the utility he derives from inflicting that pain is greater than
the utility loss suffered by his victims as a result of the pain, then his actions
could be construed as right and proper from a utilitarian perspective.
Youmay think this is not a serious problem, since no one actually cares about
the welfare of such monsters. You are incorrect. I once sat in an academic sem-
inar in which a scholar showed evidence that removing children from abusive
homes improved their futures (e.g., less criminal behavior, greater educational
attainment) and that the benefits to the kids exceeded themonetary costs of the
program.Having presented this evidence, the scholar tried tomake a normative
claim about themerits of the particular policy interventionhewas studying. An
audience member quickly jumped in to ask how the presenter could possibly
reach such normative conclusions, not having calculated the impact of the
policy on all the affected parties’ utilities. The presenter seemed confused by
the question, since it struck him as obvious that a policy that removed kids from
abusive homes and improved future outcomes for those kids in a cost-effective
way was normatively desirable. After a bit of back and forth, it became clear
that the interlocutor’s concern was that the presenter had failed to estimate
how much the abusive parents valued keeping (and presumably continuing
to abuse) their kids. A fair point from a strictly utilitarian standpoint. But, in
my own view, such a thoroughgoing commitment to utilitarianism is fairly
alarming.
TRANSPLANTS AND TROLLEYS
Another potential problem for utilitarianism comes from the following
two scenarios. (These and many related scenarios have been extensively
discussed. Here, I paraphrase thought experiments due to Foot (1967) and
Thomson (1985), but also remind you of Rawls’s admonition regarding counter-
examples.)
1. There are ten people on a trolley that somehow got on an unfinished
track. If the trolley continues to the end of the track, it will plunge into
an abyss, killing all ten people. A person is standing at the last switch on
the track. If the person pulls the switch, the trolleywill be diverted onto
a siding, saving the people on board. But a worker on the siding will be
killed. The people on the trolley will never know how they were saved.
24 Chapter 1
2. There are ten people, each of whom needs a different organ transplant
through no fault of his or her own.Without the organ transplants
all ten will die. The head of medicine at the hospital where all ten
are being treated can call a local thug, who will randomly kill a person
on the street and bring the body to the hospital for harvesting. All ten
people will be saved and will never knowwhere the organs came from.
Most people share a common set of moral intuitions about these two cases.
They think the person should pull the switch, but are horrified at the idea of the
doctor allowing the thug to kill a person to harvest organs.
It is difficult tomake sense of these intuitions within a utilitarian framework.
In both scenarios one life can be sacrificed to save ten. In both cases the
utilitarian answer is clear—sacrifice the one for the ten. Yet most people find
it hard to wrap their head around the idea that randomly killing people to
harvest their organs is good policy. Perhaps this is a strength of utilitarianism—
the model has taught us something about the situation that we couldn’t see
without the model. Or perhaps it is a weakness—killing people to harvest their
organs is insane. (Please don’t go around telling people that I taught you that
murder-for-organ-harvesting is good policy.)
In Chapter 1.4 we will revisit these problems and see how another normative
frameworkmay provide a more satisfying approach in such cases.
EQUITY ACROSS GENERATIONS
One of the virtues of utilitarianism is that it treats all individuals equally. But
this also raises some hard questions.Many policy changes affect individual wel-
fares now and in the future. For instance, the costs of an intervention limiting
carbon emissions to slow global warming might well exceed the benefits over
the course of a single generation. After all, it is unlikely that the climate will
change drastically enough over the next twenty years to have a huge impact
on the quality of your or my lives. But suppose that same policy, over the long
run, prevents catastrophic climate change. It might ultimately save the lives of
billions of people. The benefits for future generations could be huge.
And herein lies a deep challenge. The future is essentially endless. And the
population is expanding. This means that if we treat the utilities of members
of each generation equally, a policy that offers even a small benefit to future
generations has a huge positive effect on aggregate welfare, since those future
benefits affect so many people.
This creates two problems. First, if we believe that the members of each
generation should be treated equally in our utilitarian calculations, we ought to
be spending most of our current resources on policies that benefit the future—
even large costs to a few billion people today are a drop in the bucket when
compared to the benefits to hundreds of billions of people over the course of
Normative Frameworks 25
future generations. I hope you don’t like air conditioning, or travel, or meat.
Second, since all policies that benefit the future have basically infinite benefits
(what with all the people in the future), it is really hard to compare one
future-benefiting policy to another. Everything looks either infinitely good or
infinitely bad.4
Practical utilitarians respond to this problem with an idea called “discount-
ing the future,” which derives from themethodology used to analyze how indi-
viduals make inter-temporal trade-offs. (The basics of discounting are discussed
in Appendix B.7.) Let’s see how this works.
For a variety of reasons—impatience, returns on investment, the risk that you
won’t survive—a dollar today is worth more to you than is the promise of a
dollar a year from now. So, suppose that you’d be indifferent between receiving
90 cents today or a dollar a year from now. We say that you discount the value
of money a year from now by a factor of 0.9. Now suppose I asked you the same
question a year from now. Assuming your time preferences hadn’t changed,
you’d give the same answer—that is, a dollar in two years is worth 90 cents in
one year. Since a dollar in two years is worth 90 cents in a year and 90 cents
in a year is worth 81 cents today, a dollar in two years is worth 81 cents today.
And, of course, this diminution in the value of a dollar continues as the delivery
datemoves further and further into the future. A dollar in twenty years is worth
about 12 cents today. A dollar in fifty years is worth half a cent today.
When we do a utilitarian cost-benefit analysis for policy, we directly extend
this methodology of discounting the future to thinking about the benefits of
a policy for future generations. The government justifies this practice along
exactly the lines described above. For instance, the United States’ Office of
Management and Budget says, “Discounting reflects the time value of money.
Benefits and costs are worth more if they are experienced sooner.”5 So the
further into the future some future generation is, the more we discount its
benefits or costs. As you can see, this solves the problem of infinite future
benefits.We essentially write off the distant future through discounting and get
on with the business of quantifying benefits and costs.
But there is something fishy about this kind of discounting. Discounting for
an individual and discounting across generations are different. It makes sense
to value a benefit to me today more than an equal benefit to me in thirty
years. If you asked me whether I would like the benefit today or in thirty years,
I would choose today. After all, I might be dead in thirty years. It is something
entirely different, however, to value a benefit to me more than a benefit to my
grandchildren, simply because my grandchildren won’t be around for another
4There are theorems along these lines. The basic upshot is that intergenerational equity is
incompatible with our standard utilitarian approach. See, for example, Zame (2007).
5Office ofManagement and Budget, “Guidelines andDiscount Rates for Benefit cost Analysis of
Federal Programs,” Circular A 94, December 1992.
26 Chapter 1
thirty years. If you asked them, “Would you prefer a benefit to granddad BdM
when he was 40 or a benefit to yourself when you are 4?” I suspect the ingrates
would choose themselves. More fundamentally, if we value everyone’s well-
being equally, there is just no reason to care less about people in the future than
in the present (other than the small chance that the world will cease to exist, so
they won’t be around to enjoy the benefits). Their happiness or suffering will be
no less real for happening a couple generations from now.
It is this kind of logic that led Frank Ramsey (1928)—who in the 1920s laid
the intellectual foundations for how we think rigorously about intertemporal
considerations in policymaking—to argue that discounting the welfare of fu-
ture generations “is ethically indefensible and arises merely from the weakness
of the imagination.” Or, more poetically, as put by the midcentury economist
R. F. Harrod (1948), it is “a polite expression for rapacity and the conquest
of reason by passion.” The great theorist of economic growth, Robert Solow
(1974), was perhaps clearest, saying,“We ought to act as if the social rate of time
preference were zero.”6
We discount future generations in policy analysis because, if we don’t, we
can’t quantify costs and benefits in a way that makes for a coherent utilitarian
analysis. But once we’ve accepted discounting, we’ve given ourselves license to
ignore costs or benefits that occur more than a generation or two in the future.
If you are discounting at a rate of 0.9 per year and someone asks you for ten
million dollars for a policy that is guaranteed to save a billion people in two
hundred years, a standard utilitarian cost-benefit analysis would tell you not to
do it.7
This may sound theoretical, but it has practical implications. For instance,
environmental regulators frequently complain that it is difficult to persuade
the government to take actions on issues—like global warming—with limited
short-run impact, but potentially catastrophic long-run consequences. The
reason they cite is that utilitarian-based cost-benefit analysis with discounting
just doesn’t caremuch about those long-run consequences because they will be
suffered by someone else.
RELATIONSHIPS
Another objection to utilitarianism, and other forms of consequentialism,
has to do with the nature of human relationships. In particular, utilitarianism
seems to have little room for people to have special duties to certain other
people.
6Arrow (1999) is also interesting on this subject.
7If the discount factor is 0.9 and the value of a statistical life is $7 million, the discounted value
of a billion lives in 200 years is just under $5million.
Normative Frameworks 27
Figure 1.1. Ethan’s very cute kids.
To take an extreme example, suppose I could choose to save my own two
children from a terrible accident or save four children whom I don’t know.
I would certainly save my own kids. (See Figure 1.1.) Assuming the parents of
the kids I would fail to save love their kids as much as I love mine, my act is not
justifiable on utilitarian grounds. But this seems like a failing of utilitarianism
to capture an essential aspect of what it means to live a good and moral life—
which involves taking seriously the relationships among human beings and
their meaning. Indeed, recent research by Bartels and Pizarro (2011) shows
that people who choose the utilitarian solution to various moral dilemmas in
an experimental setting also have higher scores on measures of “psychopathy,
[M]achiavellianism, and life meaninglessness.”
Here it is useful to recall the distinction we made earlier between public and
private morality. The failure to take relationships seriously is, perhaps, a weak-
ness for utilitarianism as a source of private morality. But it may be a strength
for utilitarianism as a source of public morality. Utilitarianism disciplines the
policymaker to dispassionately weigh everyone’s welfare equally, abstracting
away from personal ties.
1.3 Egalitarianism
Utilitarianism is certainly not the only plausible consequentialist framework.
Under egalitarianism we judge the rightness or wrongness of an act, policy,
28 Chapter 1
or social arrangement by whether it increases or decreases equality, rather than
overall well-being.
Defining egalitarianism is itself somewhat tricky. For egalitarians, equality
is the key principle of justice. But, as Amartya Sen (1980) puts it, the critical
question is “equality of what?” Should society seek to achieve equality of well-
being, equality of wealth, equality of opportunity, or what? I’ll review several
arguments for various kinds of egalitarianism, pointing to some issues along
the way.
1.3.1 Equality of Outcomes
There are at least two reasonable definitions of equality of outcomes. To try to
get a handle on the issues, think about a society with just two individuals. You
might say that the society is more equal under policy a1 than under policy a2
if the two individuals have more equal wealth under a1 than under a2. Or, you
might say that the society is more equal under policy a1 than under policy a2
if the two individuals have more equal utility under a1 than under a2. The two
definitions are not equivalent.
To see this, consider an example. Suppose the two people in our society are
named Eeyore and Tigger. Both are happier the more resources they have, but
other than that, they are as different as different can be. Eeyore is strongly
inclined toward unhappiness, while Tigger is strongly inclined toward happi-
ness. Society has a finite amount of resources to distribute between the two. If
we are egalitarians with respect to wealth, then we would split those resources
equally. However, if we are egalitarians with respect to well-being, we would
give almost all (maybe all) of the resources to Eeyore, since Eeyore, with his
negative disposition, has much lower well-being than does Tigger, with his
positive outlook.
A similar problem arises when you think about matters of taste. Suppose we
have two people with very different tastes. One is made happiest by drinking
beer and watching football on broadcast television. The other is made happiest
by drinking fancy wine and traveling in the south of France. If we are egali-
tarians with respect to wealth, these differences in taste don’t affect our policy
decisions. However, if we are egalitarians with respect to utility, then we believe
our friend with expensive taste deserves more resources because he requires
those resources to reach the same level of utility as our friend with more down-
to-earth preferences.
Given the rather perverse recommendations that come from being
an egalitarian with respect to well-being, let’s focus on equality of wealth.
Although more coherent than equality of well-being, a strict argument for
equality of wealth also faces a variety of conceptual challenges. Consider a few.
A first issue is the problem of prioritization. Imagine two people, one
quite intellectually gifted, the other not the brightest bulb in the chandelier.
Normative Frameworks 29
Society only has sufficient resources to educate one of them. Left without an
education, the smart personwill do pretty well on raw talent alone, but the dull
person will struggle to make a living. If educated, the smart person will go on
to do truly great things—cure cancer, invent a cool iPhone app, or what have
you. If educated, the dull personwill do nothing special, but will be able to hold
down a job and support himself. What is society to do?
From a wealth egalitarian perspective, the dull person should be educated.
Society faces a choice between two states of the world. If it educates the bright
person, that person is very well off while the dull person fares terribly. If,
instead, it educates the dull person, both people do okay.Wealth egalitarianism
prefers the latter outcome.
This conclusion stands in stark contrast to that suggested by utilitarianism.
From a utilitarian perspective, society should invest its educational resources
in the person who will derive the greatest benefit from them and from whom
society will benefit themost. If educating the bright personmeans that we get a
cure to cancer, the benefits to society of this contribution far outweigh the costs
of the dull person’s suffering.
Perhaps the hardest challenge for wealth egalitarianism is the problem of
incentives. The most direct way to achieve equality of wealth is to collect re-
sources generated by eachmember of society and redistribute them. Indeed one
solution to the prioritization problem discussed above might be to educate the
bright person and then give some of her money to the dullard.
A problem with such a system is that it reduces people’s incentives to work
hard, since they know they will enjoy only a portion of the fruits of their
individual labors. Hence, the argument goes, a completely egalitarian society
will be a poor one.
A closely related issue is the so-called leveling downproblem. Imagine a society
made up of two people. Under one social arrangement, person 1 has one
million dollars and person 2 has half-a-million dollars. Under another social
arrangement, each person has half-a-million dollars. Strict wealth egalitarian-
ism prefers the second social arrangement, which seems strange, since all we’ve
done to move from the first arrangement to the second arrangement is make
person 1 worse off by destroying some of her resources. That is, we’ve leveled
the wealth in society by dragging one person down, without pulling another
person up.
Reasonable people might well prefer the second social arrangement on egal-
itarian grounds. But what about the following? Under one social arrangement,
person 1 has one million dollars and person 2 has half-a-million dollars.
Under a second social arrangement, neither person has any resources. Again,
from a strictly wealth egalitarian point of view, the second social arrangement
is to be preferred. But could any reasonable person actually prefer to level down
by destroying everyone’s resources rather than allowing some inequality?
30 Chapter 1
These problems notwithstanding, there are more nuanced arguments for
various versions ofwealth egalitarianism that aremore satisfying. Let’s consider
a few.
UTILITARIAN EGALITARIANISM
Perhaps themost straightforward argument in favor of equality of wealth is a
utilitarian argument.We typically believe that people have diminishingmarginal
utility in money. That is, the more wealth you have, the less your well-being
increases with each additional dollar. If people have diminishing marginal
utility in money, then a dollar is worth more to a poor person than to a rich
person. Hence, aggregate well-being increases if wealth is redistributed from the
rich to the poor.
The utilitarian argument straightforwardly deals with the problems of in-
centives, leveling down, and prioritization. In particular, under utilitarianism,
wealth equality is not a goal unto itself. It is a goal only insofar as decreasing
wealth inequality increases aggregate well-being. Hence, leveling down holds
no appeal under a utilitarian analysis. And the problems of prioritization and
incentives just become other factors to take into consideration in the utilitarian
calculus. For a utilitarian, one simply balances the benefits of redistribution
(which come from the diminishing marginal utility of money) with the costs
in terms of incentives and efficient targeting of resources (e.g., educating bright
people) to identify the optimal amount of wealth equality.
COMMUNITARIANISM
A wholly different kind of argument for egalitarianism comes from thinking
not aboutwell-being, but about community. Such an argument goes something
like this. In a non-egalitarian society, resources are not shared, but rather
competed over. Competing for resources is debasing and dehumanizing. The
right way to interact with your fellow humans is in a spirit of cooperation,
not competition. But doing so is not possible in the midst of the competition
for resources. And so, if we want to live properly human lives, we must share
resources equally.
The philosopher G. A. Cohen (2009) provides an analogy to a camping trip,
whichhe views as ametaphor for the ideal society.On a camping trip, he argues,
it is unimaginable that someonewould say something like, “I cooked the dinner
and therefore you can’t eat it unless you payme formy superior culinary skills.”
Rather, one person cooks dinner, another pitches the tent, another purifies the
water, and so on, each in accordancewith his or her abilities. All these goods are
shared and a spirit of community and dignity uplifts all participants. A camping
trip where each person attempted to extract the maximal concessions from
the other campers in exchange for the use of his or her talents would quickly
Normative Frameworks 31
end in disaster and unhappiness. Moreover, the experience would be ruined
if people were to behave in such a way. So, too, the argument goes, we would
all be uplifted and our humanity enhanced by living in a more egalitarian and
cooperative society.8
It is tempting to reject Cohen’s argument for failing to deal with the problem
of incentives. But such a dismissal depends on already embracing the view of
human nature Cohen is seeking to reject—one in which people are motivated
towork by thematerial returns they get from thatwork.Cohen, likeMarx before
him, believes this to be, at best, a partial understanding of human nature.
Neither Cohen nor Marx deny that people, as we observe them today, are
in fact motivated to work, at least in part, by the incentives that come from
increased personal wealth. However, both deny that this state of affairs is
inevitable. In Cohen’s view, the social system of competition and incentives in
which we are embedded from the earliest age indoctrinates us into behaving
in such a way. Were society to be radically transformed along egalitarian lines,
Cohen believes, people would behave differently. People embedded in a social
framework of sharing and cooperation would find it as natural to produce
and share for the collective interest as we, embedded in our competitive and
individualistic social framework, find it to produce in service of our individual
interests. Hence, the argument goes, it will not do to reject egalitarianism on
the grounds that people indoctrinated into behaving competitively would not
do well in an egalitarian system. Part of the point of the egalitarian system is
to free people from the dehumanizing indoctrination inherent in competition
and inequality.
RAWLSIAN EGALITARIANISM
Rawls (1971) makes an argument for a kind of wealth egalitarianism by in-
voking the veil of ignorance.9 Rawls believes that, behind the veil of ignorance,
rational individuals prefer, say, social arrangement a1 to social arrangement
a2 if and only if the worst off person under a1 is better off than the worst
off person under a2. That is, if and only if uN(a1) > uN(a2). Rawls’s analysis is
flawed, and I won’t discuss it in depth. (You can see the problem by recalling
that Harsanyi’s argument for utilitarianism proceeds from the same premise
8Cohen, who admits he isn’t actually much of an outdoorsman, seems to camp with a some
what better class of person than I do. I can certainly remember being in the High Rockies and
thinking, “My pack weighs 80 pounds and the pack of the person who divided the gear this
morning looks like itweighsmore like 65 pounds.”Maybe I’m just petty and caught in a competitive
mind set.
9While Rawls comes to a somewhat consequentialist, egalitarian conclusion, it is worth noting
that his veil of ignorance argument is not consequentialist. Rather, he is making an argument that,
in spirit, is a modern version of something like Kant’s deontological argument which we discuss in
the next section.
32 Chapter 1
and reaches a different conclusion.) Nonetheless, Rawls’s argument leads to an
interesting and helpful idea, which Rawls called the difference principle:
Rawls’s Difference Principle: A society should have inequality only to the
extent that such inequality tends to increase the welfare of the worst off
member of that society.
The difference principle is clearly egalitarian in spirit—giving lexicographic
priority to society’s worst off. Under the difference principle, one can only
change from one policy to another if that policy change makes the worst off
person better off. Only once that requirement has been met can one even
ask questions about what the policy change does for other people. First and
foremost, we worry about the bottom of society.
But the difference principle also differs from what I have called strict wealth
egalitarianism in a couple of important ways. First, it avoids the leveling down
problem. The difference principle favors the society where one person has a
million dollars and the other person has half-a-million dollars over the society
where both people have nothing. Second, the difference principle acknowl-
edges incentives. Rawls argues that a just social arrangement must make the
worst off person as well off as possible. You might, intuitively, think that this
means Rawlsian justice calls for complete equality. But it does not, as the formu-
lation of the difference principle (which suggests some persistent inequality)
makes clear. Why not?
As we have already seen, one way to design a society that achieves complete
equality is to collect all resources generated by each member of society and
redistribute them evenly. But such a system provides only very weak incentives
for hard work. Allowing some inequality creates stronger incentives. If people
know that some people get to be rich, while others will be poor, and that
working hard or taking risks is a necessary condition for becoming rich, then
people have some incentive towork hard or take risks. In so doing, people create
wealth, knowledge, art, apps, and all sorts of other good stuff. This stuff may
well make everyone, even the poor, better off than they would be in a system
of complete equality but weak incentives. Thus, Rawls is prepared to tolerate a
fair bit of inequality, as long as that inequality has the effect ofmaking even the
worst off people better off.
1.3.2 Equality of Opportunity
Equality of opportunity is a considerably less controversial goal than is
equality of outcomes. The basic argument goes something like this. People
should have the chance to make something of themselves. And so, as a society,
we ought to eliminate those disadvantages that are due to discrimination or to
the idiosyncrasies of where and to whom an individual was born. Let’s start our
Normative Frameworks 33
discussion of equality of opportunity by clarifying exactly what it means and
what arguments it has on its behalf.
Cohen (2009) suggests three versions of equality of opportunity. I’ll label
them as Cohen does, though I don’t find the names particularly helpful:
1. Bourgeois Equality of Opportunity: Eliminating “status restrictions, both
formal and informal, on life chances.” The idea is that equality of
opportunity requires that a person’s access to various opportunities
should not be affected by irrelevant facts about that person (e.g., race,
gender, parentage, wealth, sexual orientation, and so on). Rather, it
should be determined only by that person’s fitness for the opportunity.
2. Left-Liberal Equality of Opportunity: Eliminating “circumstances of birth
and upbringing that constrain not by assigning an inferior status to
their victims, but by nevertheless causing them to labour and live
under substantial disadvantage.” The idea is that irrelevant
characteristics of a person should not affect a person’s chance of
acquiring the relevant fitness for a given opportunity.
3. Socialist Equality of Opportunity: Eliminating “inequality that arises out
of native differences.” The idea is that a person’s access to various
opportunities also should not be affected by characteristics that are
relevant to that person’s fitness for a given opportunity (e.g.,
intelligence, work ethic, physical ability).
The first notion of equality of opportunity—that people ought not be
discriminated against based on irrelevant characteristics—is, I suspect, pretty
uncontroversial. So too, I would guess, is the second. People should not be
denied access to the chance to acquire relevant skills as a result of race, parent-
age, wealth, or what have you. Indeed, I think this second notion is what most
people mean by equality of opportunity. People born to difficult circumstances
or to historically mistreated groups should be ensured access to education,
networking opportunities, and the like, so that they have the chance to acquire
the requisite skills necessary to seize life’s opportunities.
The third notion of equality of opportunity strikes many people as going a
bit too far for two reasons. First, to be sure, being smart or physically able is, to a
large degree, luck. Yet it is hard to think about organizing a society around the
idea that those characteristics ought not affect a person’s access to opportunity.
(Though perhaps Cohen’s radically egalitarian society could make this work.)
Society might want to compensate or insure people against the risk of various
kinds of natural disadvantage. But most people don’t think that some highly
athletic person and I should have had equal access to the opportunities offered
by a college football career. (Though that would have been awesome.)
Second, there is a sense in which the third version of equality of opportunity
equivocates too much on who I am. It is relatively easy for me to imagine
34 Chapter 1
a person who is me, only with a different level of access to education or
networking. Thus, I understand what it means to remove the kind of barriers
suggested by the second version of equality of opportunity. It is much more
difficult for me to imagine a person who is me, only with a different level of
intelligence or physical ability. After all, my capacity to think or to run is not
separate fromme, it is part of me. This leavesme somewhat confused as to what
itmeans that I amdisadvantaged bynot being terribly bright. A personwhowas
brighter wouldn’t be me. He’d be a hedge fundmanager.
To try to get a handle on these issues, let’s consider two different arguments
for equality of opportunity.
LUCK ELIMINATION
Dworkin (1981b) posits a classic argument for a certain kind of equality
of opportunity. On Dworkin’s view, justice requires that a person’s fate be
determined by things that are within that person’s control, not by brute luck.
Insofar as differences in well-being are determined by circumstances lying
outside of an individual’s control, they are unjust. On this argument, inequality
of well-being that is driven by differences in individual choices or tastes are
acceptable. But we should seek to eliminate inequality of well-being that is
driven by factors that are not an individual’s responsibility and which prevent
an individual from achieving that which he or she values.We do so by ensuring
equality of opportunity or equality of access to fundamental resources.
As we saw with Cohen’s typology, a challenge is figuring out what factors
that affect well-being are within the realm of individual responsibility and
what factors are brute luck. We can probably all agree that an individual’s
racial, ethnic, socio-economic, and genetic background are outside of his or
her control. So, on this view, any inequality of well-being due to such factors
is unjust and ought to be corrected.
But notice, even this relatively uncontroversial position creates some dif-
ficulties. Think about genetic background. Genes affect intellectual capacity,
physical ability, creativity, health, appearance, work ethic, and so on. Each
of these, in turn, may affect well-being. Do we want to commit ourselves to
the position that differences in well-being that are due to, say, differences
in intellectual capacity, physical ability, or creativity are unjust and require
correction?Wemight, but it is certainly not obvious.
Consider an even harder case. Are people responsible for their own pref-
erences or values? Preferences—for labor vs. leisure, socially acceptable vs.
unacceptable behavior, and so on—affect the choices people make and the
actions they take. Those choices and actions affect well-being. Are differences
in well-being that are due to differences in preferences a matter of individual
Normative Frameworks 35
responsibility or brute luck? Preferences appear, at least in part, to be deter-
mined by a variety of matters of luck—for example, the gene pool, family, and
culture into which you happen to have been born. Given this, do we wish to
conclude that a person’s preferences are beyond his or her control and, thus,
that justice mandates that we correct difference in well-being resulting from
differences of preference?
Dworkin makes a possibly useful distinction, here, between preferences with
which a person does and does not identify. A person identifies with some
preference she holds if she is glad she holds it. A person does not identify with
some preference she holds if she wishes she didn’t hold it. This distinction is
useful if you think, for instance, about the case of addiction. An addict might
demonstrably hold a strong preference for using drugs that reduce her well-
being. But if that addict wishes she didn’t hold that preference, even if she
has been unable to overcome her addiction, she does not identify with the
preference. We might be more comfortable saying that a person is responsible
for the consequences of those preferences that she both holds and is glad she
holds, but not responsible for the consequences of preferences that drive her
behavior, but which she wishes she could overcome.
It is, perhaps, clear at this point that using personal responsibility to draw
the line where we stop equalizing opportunity gets us into some thorny issues.
The resolution of such issues ultimately turns on the stance we want to take on
questions like free will. Once you see that it is reasonable to question whether
people are responsible for their own preferences, it is only a hop, skip, and a
jump to the question of whether people are responsible for their own actions.
At that point we must ask whether we draw the line anywhere or whether
everything is just a matter of brute luck? And, if everything is a matter of luck,
does that mean that a luck-elimination argument for equality of opportunity
ultimately requires complete equality of well-being?
My own view is there is a line to be drawn, but for pragmatic, rather than
fundamental, reasons. Deep down, everything (ability, preferences, actions)
may well be determined by luck or, put differently, by physics. But that isn’t
a terribly helpful thought, as it provides little guidance about trade-offs. By
contrast, in all sorts of settings, it is useful to think of people using their
cognitive capacities to make decisions for which they are responsible, despite
perhaps having limited control over their preferences. For instance, such a
thought provides a foundation for punishment in criminal justice settings.
It also provides a way to acknowledge that education and parenting shape
character, while still permitting the possibility that a person is responsible for
the consequences of his or her actions. Whether the line is properly drawn at
the level of actions, preferences with which a person identifies, or somewhere
else, I don’t know. But it seems a line must be drawn.
36 Chapter 1
UTILITARIANISM AND EQUALITY OF OPPORTUNITY
All this conceptual confusion suggests thatmaybewehave thewrongdefense
of equality of opportunity. Perhaps we shouldn’t be defending it on purely
egalitarian or luck-elimination grounds. Another defense might be more prag-
matic. The world is full of talented, smart, hardworking people born to bad
circumstances. It would be a tragedy, not just for them, but for society, to
waste those talents. Maybe one such kid could grow up to cure cancer, prevent
asteroids from hitting the earth, solve a really cool game theory model, or help
the Bears’ passing game. Thus, for the good of society, we want to make sure all
individuals have access to the opportunity to gain the skills necessary to realize
their potential.
This defense of equality of opportunity, while perfectly sensible, is a very
different kind of argument than the ones we typically make. In particular, it is a
thoroughly utilitarian argument. On this argument, equality of opportunity is
no longer an end unto itself. Rather it is a means to an end.
This embrace of utilitarianism as a defense of equality of opportunity is
itself interesting. It is another instance of a phenomenon we saw in our earlier
discussion of welfare egalitarianism—often values that we cherish can be (at
least partially) justified on utilitarian grounds. One advantage of such an in-
strumental, utilitarian defense is that it also provides a framework for thinking
about trade-offs. Just because equality of opportunity tends, all else equal, to
increase social utility, doesn’t mean that we must slavishly pursue that goal to
the exclusion of everything else. Instead, we balance competing goals against
one another in proportion to their importance for overall social utility.
But even if we embrace a utilitarian argument for Cohen’s left-liberal equality
of opportunity, there is a second problem. Suppose we start our society with
complete equality of opportunity of this sort. Over the course of a generation,
we will not end up with equality of outcomes. People differ in terms of their
natural talents, their interests, their willingness to trade off labor and leisure,
and so on. As such, even with complete equality of opportunity, some people
will end up rich and other people will end up poor.
Wedidn’t set out to achieve equality of outcomes, so this state of affairsmight
not worry you. And I’d agree, if it weren’t for the children. Here is the problem.
Most parentswant tohelp their children live happy, productive, successful lives.
As it turns out, parents can turn money into opportunities for their children.
As such, the first generation’s outcomes will be a major input into the second
generation’s opportunities. A second generation personwith successful parents
has better opportunities than a second generation person with unsuccessful
parents.
This is not good. We created a society with equality of opportunity. But
the nature of human relationships intervened and, in just one generation,
eradicated equality of opportunity. The only way to get it back, of course,
Normative Frameworks 37
is to impose equality of outcomes on the first (and all subsequent) generations.
But as we’ve already seen, there are lots of problems with equality of outcomes.
So it seems that we may be stuck. Although we may very much like equality
of opportunity, it might not actually be achievable without sacrificing a lot of
other things that we also care about.
1.4 Kantian Deontology
Both utilitarianism and certain kinds of egalitarianism are consequentialist
frameworks. A different class of normative frameworks, called deontological
frameworks, addresses many of the problems of consequentialist normative
arguments. Of course, they do so at the expense of introducing new problems.
Nonetheless, they are worth spending some time thinking about.
Deontological normative frameworks are those that judge a policy or social
arrangement by its conformity to some moral norm or duty, rather than by
its consequences. A deontological framework that is familiar in our political
discourse concerns rights. Loosely speaking, a person has a right to something
if another person can be said to have a duty to allow her to have it. We typically
talk about such rights in deontological terms. We think of ourselves as having
rights to life, liberty, and the pursuit of happiness, not because the existence of
such rights increases the social welfare, but because those are our birthrights as
human beings. (We are endowed by our creator with certain inalienable rights
and so on.)
It is important that, when we talk about rights, we are asserting something
deontological. To see why, notice that there is a tendency in political debate to
proliferate claims to rights. Arguments for increasing the scope of government
(with respect to health care, education, the economy) are often framed in terms
of rights. Arguments for decreasing the scope of government (with respect to
gun control, taxation, social programs) are also often framed in terms of rights.
But claiming toomany rights seems to cheapen the idea.
While it may be a useful rhetorical trick, labeling every policy you like as a
right and every policy you dislike as a violation of rights renders the concept of
a rightmore or less useless. It simply comes tomean “good.” It is, then, perhaps
useful to keep in mind the notion that a right for you entails a duty for others.
Asking yourself whether you believe others have a duty to provide you some
thing will help to clarify whether you have a right to that thing. For instance,
I really can’t claim that I have a right to chocolate cake because,much as Imight
like a piece of chocolate cake, you are under no obligation to provide it to me.
(Unless you’d like extra credit.) But I might assert a right to freedom of religion
if I believe you have a duty not to prevent me from exercising my religion of
choice, and I have the same duty to you.
38 Chapter 1
This idea that the existence of a deontological right or duty is closely tied
up in our willingness to extend that right or duty universally comes from Kant,
the most important of the deontological philosophers. But for Kant, the source
of deontological duties is neither divine revelation nor natural law. Rather,
deontological principles are derived from human nature itself.
Humans, on Kant’s view, are rational creatures whose fundamental purpose
is autonomy, which he understands as full actualization of our rational selves.
For Kant, a rational person is autonomous if she is bound only by those moral
laws that she would rationally will herself to be bound by. For this to be the
case, Kant argues, those laws must be internally generated by the person’s own
rationality. A person bound bymoral laws or duties that derive fromoutside the
individual is said to be heteronomous, the opposite of autonomous.
When Kant insists that moral laws be rationally willed, he means that a
rational person would be willing to universalize the law—binding herself, and
others, to it everywhere and always. Thus, for Kant, to act autonomously is to
behave in away that is guided by thosemoral laws and duties that onewould be
willing to universalize. (It is worth noting that “veil of ignorance” arguments,
which we used as a foundational argument for various types of consequential-
ism, can be viewed as Kantian-style deontological arguments which then yield
a certain kind of consequentialism as an implication. Something like this was,
in fact, Rawls’s view.)
From this basic principle of autonomy, Kant derives his fundamental, deon-
tological, moral precept: the Categorical Imperative. The Categorical Impera-
tive has many formulations, but two are particularly useful, in my view. Here I
paraphrase:
1. For an action to bemoral, it must be that I would be willing to make
themaxim (principle) that motivates the action a universal law (i.e., a
principle to be followed everywhere and always by rational agents).
2. We should never treat another person’s humanity as merely a means,
but rather always as an end unto itself. (Note, this doesn’t mean you
can never use another person as a means, i.e., as in when you use a
professor as a means to learn. But rather, you cannot treat your
professor as though he or she were simply a means, rather than having
an independent humanity that is an end unto itself.)
Kant’s formulations are useful in several ways. First, they provide an example
of a deontological framework that is philosophically respectable. Kant does not
simply assert some deontological principle of morality. Rather, the Categorical
Imperative is derived from axioms (withwhich you should feel free to disagree).
Moreover, the Categorical Imperative is not a specific instruction of some duty
you have. Instead, it is a tool by which you can derive a variety of duties. For
any action, you can first identify themaxim that underlies it and then question
Normative Frameworks 39
whether youwould bewilling to universalize thatmaxim. If yes, then, onKant’s
view, you are on firmmoral ground. If no, then you are taking an action which
is inconsistent withmorality and rational autonomy.
Second, a Kantian view raises some interesting questions for thinking about
policy, especially if we focus on the latter formulation of the Categorical
Imperative above. For instance, consider the relationship of the state to
criminals. Kant’s analysis admits certain justifications for polices such as in-
carceration. A rational agent can universalize the maxim that criminals should
be punished and security maintained. However, other views of the purpose
of incarceration—such as crime deterrence—are inconsistent with a Kantian
framework. In particular, to incarcerate a person in order to deter other poten-
tial criminals is to use that person as merely a means.
1.4.1 Deontology and the Challenges to Utilitarianism
Deontological frameworks have the advantage of addressing some of the
primary objections leveled against utilitarianism. For instance, standard deon-
tological argumentsmake sense of our sharedmoral intuitions about the trolley
and transplant problems. According to the Categorical Imperative, it is clearly
immoral to kill a person to harvest her organs—doing so uses her as merely a
means, rather than as an end unto herself. But, according to the Categorical
Imperative, it is permissible to pull the switch in the trolley example. The
maxim of that action is that you should preserve human life—an easily uni-
versalized principle. The key distinction between the transplant and trolley
problems is that in the trolley problem, the worker who will be killed is not
being used as a means to save the lives of the trolley passengers. Pulling the
switch would save those lives whether the worker were on the siding or not.
Unlike in the case of transplants, his death is not themeans to the end of saving
the lives of the trolley passengers. Rather, the worker is just an unfortunate
bystander.
Deontological arguments also leave considerably more room than do con-
sequentialist frameworks for taking seriously special human relationships. For
instance, in many deontological frameworks, parents have special obligations
to their children. One would not want to universalize the maxim that every
person should devote enormous time and resources to the care and nurturing
of every child. But one can easily universalize the maxim that parents should
do so for their children.
1.4.2 Challenges for Deontological Thinking
Although deontological frameworks have some appeal, both philosophically
and intuitively, like any normative framework, they also have their challenges.
Here I highlight some common critiques of deontological approaches.
40 Chapter 1
A first problem arises when multiple duties come into conflict with one
another. (An eventuality that Kant seems to have thought impossible.) Let’s
look at a classic example.
Standard deontological frameworks give rise to a duty not to lie. To see this
in a Kantian framework, think about the maxim underlying a lie—to render
communication deceptive. If one were to universalize this maxim, one would
will that all communication be deceptive, something a rational agent could not
do. Thus, the Categorical Imperative suggests a duty not to lie.
Standard deontological arguments also typically give rise to a duty to respect
the lives of fellow human beings. This follows more or less directly from
our second formulation of the Categorical Imperative. And so arises a classic
question for Kant (and other deontological frameworks). Suppose a murderer
asks you the location of his intended victim. Do you have a moral obligation
not to lie to the murderer? A similar moral dilemma arises in thinking about
problems like themorality of torture in the face of a “ticking time bomb.”
While extreme cases, these examples highlight a broader point about deon-
tological theories. There is no reason to believe that duties will not frequently
come into conflict with one another. If we cannot adjudicate among duties on
the basis of consequences, how are we to know how to act in the presence of
competing duties?
A second problem, sometimes called the paradox of deontology, is closely
related. You are not permitted to violate a deontological duty, even to prevent
others from violating a deontological duty. Thus, on the Kantian argument,
it would be wrong for me to deceive you into taking some action, even if
that action would prevent ten murderers from killing ten people. Why is this?
Because deceiving you into taking an action is using you as ameans, rather than
an end.And this is forbidden, even if doing sowould stopnot just a badoutcome
(let’s not be consequentialists!), but actually prevent many other people from
violating deontological duties (e.g., the duty not to murder).
Both of these problems, in some sense, come down to the question of how
weweigh different wrongs andmake trade-offs in a deontological framework. It
is a violation of deontological duty to lie. It is a violation of deontological duty
to kill. But those things can’t be compared or added. That is, it is not obviously
worse to kill than to lie. Nor is it obviously worse to lie twice than to lie once. To
say that it is morally permissible to lie in order to prevent two lies is to slip into
consequentialism.
A final note on the usefulness of deontology is also merited here. The use-
fulness of, say, the Categorical Imperative depends on your ability to correctly
identify the maxim of your action. For instance, consider whether my slapping
my own forehead (perhaps to signal surprise) is moral. If the maxim of that
action is “slapping my forehead is moral,” then I don’t want it universalized, as
I do not want to live in a world where anyone feels free to come up and slap me
Normative Frameworks 41
in the head. But if the maxim of that action is “slapping one’s own forehead is
moral,” then fine by me.10 While silly, this example highlights a real challenge
for the applicability of deontological frameworks. Unlike utilitarianism, where
the final judgment is an empirical one, for the Categorical Imperative, the final
judgment of an act’s morality is a conceptual one that depends on whatmaxim
you take to underlie it.
1.5 Libertarianism
Libertarianism can be thought of as a particular type of deontological norma-
tive framework. It again provides a stark contrast from either utilitarianism
or egalitarianism. Libertarians do not evaluate the merits of policies or social
arrangements based on utility (be it the sumor the difference). Instead, they are
interested inmaximizing human freedom.
Human freedom is an appealing norm for many people. Politicians often
frame debates over policy in terms of ensuring our freedom or preventing our
freedom from being abridged. Yet, as one can see from those debates, there is
considerable disagreement as to what freedom actually is.
Consider, for instance, the debate over same-sex marriage. Both sides of that
debate frequently frame the discussion in terms of freedom. Those in favor
of legalized same-sex marriage argue that the government should not deny
people the freedom to marry the partner of their choice. Those opposed to
legalized same-sexmarriage argue that the government should not deny people
the freedom to live and raise families in communities whose laws reflect their
values.
How can it be that both sides of a debate have freedom on their side? The
answer, I believe, derives from the fact that freedommeans at least two different
things in our political discourse. These two meanings are worth pulling apart
and thinking about separately, lest we get horribly confused.
What does it mean to be free? One view is that true freedom is about self-
actualization. For Kant, to be free means to live in accordance with the dictates
of rationality—that is, to achieve autonomy. On Kant’s view, if all we do is
pursue utility or happiness or wealth, we aren’t really free. Rather, we are slaves
whose actions are dictated not by our rational wills, but by things external to
ourselves.
A second definition of freedom is perhaps more straightforward—freedom is
the absence of coercion. That is, a person is free when she is able to do what she
wants, subject to the restriction that she not diminish the freedom of others.
10I thank Scott Ashworth for this example.
42 Chapter 1
These views are, at times, in tensionwith one another, though they need not
always be. Let’s first think about why they might be in tension and then come
back to how they can, for some thinkers, be reconciled.
If freedom is defined in terms of autonomy, then there can be room for a
fairly active government, in service of freedom. A state that seeks to facilitate
citizen autonomy can justify all sorts of interventions on the grounds that they
advance self-actualization. Some policies that might be justified in this way
could strike you as fairly benevolent. For instance, onemight argue for universal
access to education on the grounds that autonomous individuals must develop
critical capabilities. One might also argue for universal access to subsistence on
the grounds that the pursuit of autonomy requires physical nourishment.
Autonomy-based freedom arguments can also be used to justify less
benevolent-seeming policies. A state that believes people are taking actions
that are not in their true interests—say, worshipping a false god, engaging
in immoral behavior, pursuing heretical scientific inquiry, or betraying their
ethnic group or economic class—might argue that, in order tomake people free,
it must massively restrict their actions. For some thinkers, true autonomy can
only be achieved within a collective—be it one’s class (for Marx), one’s nation
(for Fichte), or what have you. Such notions of autonomy can (though need
not) lead to a defense of totalitarian government on the grounds of preserving
freedom.
An alternative view is that freedom is maximized when coercion is mini-
mized. Interestingly, as political philosophers at least since Hobbes have noted,
the goal of living an uncoerced life requires that one accept no small measure
of government coercion. In particular, in order to free oneself from coercion
by others, one must accept the rule of law. That is, one must allow the state
to use the threat of violence to coerce you and others not to engage in acts of
violence against one another. While the rule of law is clearly a constraint on
one’s actions, it can be defended on the grounds that it increases, rather than
decreases, freedom by reducing the risk of other forms of coercion.
This coercion-minimizing view of freedom raises some interesting questions
about the proper role of the state. In defense of this sort of freedom, we want
the state to use its coercive power to prevent violent coercion by other people.
But what of other forms of coercion? A person can be coerced into taking
actions she wouldn’t otherwise take in a variety of ways. Does it increase or
decrease freedom for the state to use the threat of violence to prevent coercion
through social sanction? What about coercion through indoctrination? What
if the people being indoctrinated are children? These are tricky questionswhich
involve trade-offs of one kind of freedom against another.
Finally, it is worth noting that the two views of freedom need not be in
fundamental tension. Kant, for one, believed that true freedomwas to be found
in autonomy. His vision of autonomywas an individualistic one. As such, in his
Normative Frameworks 43
view, the job of the state is to facilitate autonomy by allowing people to live as
uncoerced a life as possible. (Notice, this is another useful distinction between
private and public morality.)
For now, we need to make a choice about what we mean by freedom. So, for
the remainder of this discussion, I will focus on a view of freedom that is about
the absence of coercion, not about self-actualization.
1.5.1 Why Be a Libertarian?
Like utilitarianism and egalitarianism, there are many reasons why one
might be a libertarian. Indeed, one might even be a libertarian on utilitarian
grounds. (That is, one might think that absence of coercion maximizes incen-
tives, which maximizes societal wealth, which maximizes aggregate utility.)
But here I will focus on a freestanding, deontological defense of libertarianism
associated with the philosopher Robert Nozick (1974).
Nozick argues that the essential evaluative criterion for a social arrangement
is the degree of respect for self-ownership. On Nozick’s view, individuals have
absolute ownership of their own bodies. This means that if you use your body
to create things of value, then you own those things. To take them from you is
to deny your self-ownership.
For Nozick, because things of value are created by mixing human labor (and
thought) with the natural world, it makes no sense to ask howmuch stuff each
person deserves, as an egalitarian might. Given that people own their own
bodies, they are due whatever they create with that body. The things of value
in theworld are owned by individuals because theywere created by individuals.
For the social arrangement to take things from one person and give them to
another is to deny individuals’ ownership of themselves.
To see the force of Nozick’s idea, imagine two people born owning equal
pieces of the natural world. Suppose one is very professionally ambitious, while
the other prefers to spendmore time with family. The professionally ambitious
person produces a lot from the natural resources he owns and thus becomes
wealthy. The family-oriented person produces less material wealth. This is not
an unjust or bad outcome for a libertarian. Each person has been respected as a
self-owning individual. The fact that they made different life choices, and thus
ended up with unequal levels of wealth, is neither here nor there with respect
to justice, and certainly cannot be used as a justification for redistributing the
professionally ambitious person’s (self-owned) wealth to the family-oriented
person. (This example also highlights the importance, for consequentialists, of
not conflatingwealth and utility. It is not clearwhich of these people has higher
utility.)
Nozick’s famous parable involves the basketball playerWilt Chamberlain. He
imagines a world in which each person starts with equal amounts of wealth.
But people are willing to pay to see Wilt Chamberlain play. Each person is
44 Chapter 1
made better off by these transactions, since if she is willing to spend some
amount of money to see Wilt Chamberlain play, it must be that she enjoys
the experience more than the money. Yet, in the end, we end up with lots
of inequality. Wilt Chamberlain is very rich. There is nothing unjust, for
Nozick, about this outcome. Chamberlain came by his money as a simple
extension of his ownership of his own body. And the people who paid to
see him play were justified in spending money to enjoy the experience as a
simple extension to their self-ownership. The ultimate inequality of wealth is
normatively irrelevant.
On Nozick’s analysis, both consequentialist and redistributivist views of
justice are in contradiction with what is, to him, the fundamental moral fact of
human life: self-ownership. Thus,Nozick argues, the right social order is the one
thatmaximizes respect for self-ownership byminimizing coercion, regardless of
the consequences.
1.5.2 Some Problems for Libertarianism
Like any normative framework, libertarianism has some places where it runs
into problems. Below I discuss a couple important ones.
OWNERSHIP OF PROPERTY
In my description of Nozick’s theory of self-ownership, I slipped in what is
perhaps the greatest challenge for Nozick’s thinking on these issues. Things of
value are never created by a human using her body alone. Rather, she mixes
her labor and thought with the natural world to create something of value. On
Nozick’s argument, if I own a part of the natural world and I ownmy body, then
it follows that I own whatever it is that I use my body to make out of the part of
the natural world that I own. But, even if you grant this argument, you can still
question how I came to own part of the natural world.
Nozick is not unaware of this issue. On his account, at the beginning of
time, the natural world is unowned. It comes to be owned by acts of legitimate
acquisition, which involve people claiming and improving unowned land.
Here he draws on John Locke’s thinking about property rights, most clearly
articulated in Chapter V of the Second Treatise of Government. (It is worth noting
that Locke’s ideas on the matter were developed, at least in part, to justify
colonial expropriation of native lands.)
As amatter of historical record, of course, this is not how things went. Lots of
land was owned by one person, in the Nozickian sense, only to have it taken by
force by another. Nozick is also aware of this fact. In response, he endorses some
kinds of temporary redistribution in order to reset the system of ownership to a
justified level once and for all. Following such a rectification, however, Nozick
believes that redistribution can never again be justified, since people own the
Normative Frameworks 45
fruits of their labor mixed with their legitimately held property. Nonetheless,
one need not think of Nozick as embracing the current status quo, since that
status quo may be built on a foundation of unjust property claims. But once
such problems are addressed, Nozick believes the state must take a minimal
role—basically just protecting property rights—in order to respect people’s
self-ownership.
TRADE-OFFS
Another potential problem for a libertarianism grounded in an uncompro-
mising commitment to self-ownership (though not a libertarianism that is
derived from utilitarianism) is that it does not admit much in the way of trade-
offs. One can imagine situations in which small increases in coercion (say,
taxation for the purpose of providing education) might yield social benefits
well in excess of social costs. Yet the committed libertarian would reject such
policies, no matter how large the benefit, because forcible taxation for the
purpose of transferring resources to others (as opposed to taxation for, say,
the purpose of national defense, which would be permissible) is a violation
of the principle of self-ownership. Such is the nature of deontological commit-
ments of this sort.
1.6 Takeaways
• We’ve looked at several ways people think about how to evaluate or
justify the goals of public policy. Each of these various normative frame-
works has arguments to recommend it and each also has implications or
conceptual limitations that might leave you somewhat uncomfortable.
My goal was not to convince you of some particular normative position.
Rather, I hope this discussion has, at least to some extent, added a bit of
nuance to your normative thinking.
• Various normative frameworks are often in conflict with one another.
There are trade-offs in life. For instance, increasing equality through
redistribution may require diminishing freedom from coercion. Maxi-
mizing overall utility may also sometimes require reducing freedom by
engaging in physical coercion (remember the transplants example).
• The same term is often used to mean different things. When this
happens, serious deliberation over policy goals becomes difficult. For
instance, freedom-as-autonomy and freedom-from-coercion are often
both simply called freedom. But they are very different things and if
you don’t know which your opponent is referring to, you are unlikely
to make arguments she finds persuasive.
46 Chapter 1
• Anyplausible normative framework has good arguments in its favor and
good arguments against it. As such, consensus on the proper normative
framework is not a workable goal. Reasonable people can disagree.
• Indeed, I would go further. Arriving at a coherent framework that
accounts even just for all of your ownpersonal normative commitments
probably isn’t a reasonable goal. Sometimes you will be motivated by a
concern for freedom. Other times you will be motivated by a concern
for overall utility. Deep down, these two normative frameworks may
contradict each other. But so what? Physics has unanswered (perhaps
unanswerable) questions deep down. Must political philosophy be on
firmer footing than physics? That said, in your more self-righteous
moments, youmight want to remember that lack of deep foundations.
• Normative frameworks are often presented as the answer to a set of
moral questions. This is nonsense. As we’ve seen, there are lots of
trade-offs and contradictions—not all good things go together all the
time. Normative frameworks are better seen as models—conceptual
frameworks that help you think through one aspect of a problem. It
might be helpful to think of them as all-else-equal claims. All else equal,
more freedom is better than less, more utility is better than less, more
justice is better than less, and more equality is better than less. But all
else is never held equal. So, in coming to a normative judgment on
some policy issue, you must weigh the trade-offs. How much do you
care about equality versus freedom in this case? Your position, then, will
not be right everywhere and always, but rather will reflect the particular
trade-offs you happen to be willing tomake. Reasonable people can and
will disagree about those trade-offs.
1.7 Further Reading
Of course, the political philosophy literature is vast. Peter Singer’s Practical
Ethics is a classic, thoughtful introduction to ethics and its application to policy
problems. Adam Swift’s Political Philosophy: A Beginners’ Guide for Students and
Politicians is a nice, accessible primer on political philosophy. John Broome’s
Climate Matters: Ethics in a Warming World gives a moral philosopher’s take on
many of the same themes discussed in this chapter in a particular applied policy
context.
To my mind, the deepest formal treatment of the sort of issues discussed in
this chapter is John E. Roemer’s extraordinary Theories of Distributive Justice.
Some of the classic works discussed in this chapter are Kant’s Groundwork of
the Metaphysics of Morals, Rawls’s A Theory of Justice, Nozick’s Anarchy, State, and
Utopia, Cohen’s Why Not Socialism?, and Dworkin (1981a,b). Sen (1980) help-
fully asks “equality of what?” The veil-of-ignorance argument for utilitarianism
Normative Frameworks 47
is articulated inHarsanyi (1953) and in his book Rational Behavior and Bargaining
Equilibrium in Games and Social Situations.
1.8 Exercises
1. Suppose a car company produces a small, light, inexpensive, fuel efficient
car. Because the car is inexpensive and fuel efficient, it will be affordable for
relatively low-income people, who will use it to get to work, take their
children to school, and so on. However, because the car is so small and light,
it also turns out not to be as safe as larger cars. Indeed, the manufacturer
discovers that the car does not performwell on several crash tests.
Addressing these safety issues would require modifications to the car that
would significantly increase its cost, making it inaccessible to many
low-income potential users.
Ignoring regulatory issues (i.e., is the manufacturer allowed to sell such a
car), use different normative frameworks to make a pro and con argument
for each of the following two positions:
(a) The car company should disclose the safety flaws, but sell the car at the
affordable price without alteration.
(b) The car company should either modify the car and increase the price or
not sell the car at all.
2. Consider the proposition that the United States should reduce barriers to
immigration, allowingmanymore people to emigrate from poor countries
where they lack opportunity. Take as given that the kind of people who
immigrate tend to be low skill, but smart and ambitious.
(a) Focusing only on the U.S. population and the immigrants themselves,
evaluate this proposal from a utilitarian, egalitarian, and libertarian
perspective.
(b) Now expand your analysis to also consider the populations of the
immigrants’ home countries. Does this alter any of your evaluations?
3. In a recent set of influential articles Sunstein and Thaler argue for a
normative position which they call libertarian paternalism (Sunstein and
Thaler, 2003; Thaler and Sunstein, 2003). Drawing on insights from
psychology and behavioral economics, they start with the premise that, left
to their own devices, people oftenmake choices that are not in their own
interest (e.g., eatingmore than they would like to eat, saving less for
retirement than they would like to save). That is, people are irrational in
certain predictable ways. This, in their view, is an argument for a certain
48 Chapter 1
kind of paternalism—because policymakers are aware of these systematic
biases in people’s behavior, in some circumstances, the policymaker can
make decisions that are better for a person than the decisions the person
wouldmake him or herself.
However, Sunstein and Thaler are also interested inmaintaining certain
libertarian principles. In particular, while they want to help people make
better choices, they don’t want to coerce people. Thus, they suggest
“nudging” people towards better choices—for example, making the default
choice the “right” one, while always leaving people with the option to act
differently.
For instance, they would like companies to have the default be that all
employees make the full contribution to a retirement plan (nudging people
towards saving), while allowing people the option to opt out of the
program. One systematic bias in people’s behavior is an overwillingness to
stick with the status quo. So, they argue, making the default option the
good choice, while leaving people the option to change their decision, has
the dual virtues of using people’s behavioral biases to push them towards
the better choice (paternalism), while not forcing them tomake that choice
(libertarianism).
(a) To what extent do you think libertarian paternalism in fact fulfills the
goals of libertarianism in Nozick’s sense of the term?
(b) What would a utilitarian think about libertarian paternalism? Think
about this from two perspectives:
i. Assuming the policymaker really does knowwhat is in the interest of
individuals better than they do, what would a utilitarian think about
using behavioral methods to nudge people towards better decisions?
ii. Is the notion that people don’t know their own true interests (in the
sense that they are unable to act on those interests) conceptually
problematic for defining utilitarianism?
4. In a provocative essay, O’Hare (2015) argues that major art museums should
sell off some of their art. Here’s the essence of his argument:
Any top-rank museum exhibits no more than a twentieth of its collec-
tion, often much less. There is some rotation in and out of storage but,
as a rule of thumb, consider the least distinguished object in a gallery,
and you can be sure that there are one or two just a teeny bit inferior,
and a dozen nearly as good, in a warehouse or the basement. The Met,
for example, shows 27 of its 41 Monets, but only three out of its 13
Eugène Boudins.. . .
Normative Frameworks 49
Selling just 1 percent of the collection by value—much more than
1 percent by object count—would enable the AIC [Art Institute of
Chicago] to endow free admission forever.
. . . selling another percent of the museum’s collection would pay for
30 percent more exhibition space (either where it is now, or in a big
satellite somewhere), to actually show us more art. Let’s go crazy and
sell another percent—that would endow $17million a year of operating
budget, a fifth of the institute’s current “instructional and academic”
staff costs, which would enable it to hire something on the order of 200
more full-time researchers, educators, designers, and people studying
the audience to understand what really goes on when people get up
close to art. All this, and the AIC would still be sitting on 97 percent
of the value of its current stockpile, but showing a third more of it, and
better.
Adopting two different normative frameworks, make an argument for and
against this proposal.
5. In 1991 Lawrence Summers (a Harvard economist who was then chief
economist at theWorld Bank and later became secretary of the treasury)
wrote the followingmemo:
Just between you and me, shouldn’t the World Bank be encouraging
MORE migration of the dirty industries to the LDCs [Less Developed
Countries]? I can think of three reasons:
1) Themeasurements of the costs of health impairing pollution
depends on the foregone earnings from increasedmorbidity and
mortality. From this point of view a given amount of health
impairing pollution should be done in the country with the lowest
cost, which will be the country with the lowest wages. I think the
economic logic behind dumping a load of toxic waste in the lowest
wage country is impeccable and we should face up to
that.
2) The costs of pollution are likely to be non-linear as the initial
increments of pollution probably have very low cost. I’ve always
thought that under-populated countries in Africa are vastly
UNDER-polluted, their air quality is probably vastly inefficiently
low [sic] compared to Los Angeles or Mexico City. Only the
lamentable facts that so much pollution is generated by
non-tradable industries (transport, electrical generation) and that
the unit transport costs of solid waste are so high prevent world
welfare enhancing trade in air pollution and waste.
50 Chapter 1
3) The demand for a clean environment for aesthetic and health
reasons is likely to have very high income elasticity. The concern
over an agent that causes a one in amillion change in the odds of
prostate cancer is obviously going to bemuch higher in a country
where people survive to get prostate cancer than in a country where
under 5 mortality is 200 per thousand. Also, much of the concern
over industrial atmosphere discharge is about visibility impairing
particulates. These discharges may have very little direct health
impact. Clearly trade in goods that embody aesthetic pollution
concerns could be welfare enhancing. While production is mobile
the consumption of pretty air is a non-tradable. The problemwith
the arguments against all of these proposals for more pollution in
LDCs (intrinsic rights to certain goods, moral reasons, social
concerns, lack of adequate markets, etc.) could be turned around
and usedmore or less effectively against every Bank proposal for
liberalization.
One at a time, briefly evaluate Summers’s argument from the perspective of
any two of our normative frameworks. Do not dispute Summers’s factual
assertions (e.g., that the marginal cost of pollution is increasing), but rather
offer a normative evaluation, assuming his factual assertions are true.
6. Consider a person of above-average wealth who believes strongly in
government redistribution of wealth, but does not give personally to charity.
Evaluate the reasonableness of holding these two positions simultaneously
from the perspective of utilitarianism and Kant’s Categorical Imperative.
2
Collective Goals
We’ve seen that there are lots of reasonableways to normatively evaluate policy.
This multiplicity of potentially mutually exclusive normative criteria creates
something of a problem for our standard discourse about good policy.We often
want to say that goodpolicy serves the public interest. But howdowedetermine
what the public interest is if we can’t agree on a normative framework?
An alternative approach is to think of these (and other) normative frame-
works as reflecting the opinions of individuals within a society. That is, none
of them defines the public interest. Rather, they may describe what a particular
individual believes the public interest to be. And when we speak of the public
interest we mean a set of goals or standards that a society—made up of people
with their individual opinions—collectively agrees on.
What does it mean for a society of individuals, who disagree on the right set
of goals, to nonetheless collectively agree on a notion of the public interest?
One possibility is that we might all agree on some procedure for aggregating
our individual opinions and then define the public interest for our society as
the outcome of that aggregation procedure.
For instance, consider a choice between two policies, which I’ll call x and y.
The individuals in a society might disagree over which of those two policies is
best or right. But theymight agree to define the public interest as whichever of x
or y a majority prefer. I’m not saying this is a particularly good definition of the
public interest. But it is a plausible procedure that takes as inputs contradictory
individual opinions and returns as output a vision of the public interest,
without asking the individuals to agree with one another as to which of x or y is
the better choice.
This notion of the public interest being defined through the aggregation of
individual interests is one way of understanding what Rousseau had in mind
when he wrote of the “general will” in The Social Contract:
There is often a great deal of difference between the will of all [what all
individuals want] and the general will; the general will studies only the
common interest while thewill of all studies private interest, and is indeed
no more than the sum of individual desires. But if we take away from
these same wills, the pluses andminuses which cancel each other out, the
balance that remains is the general will.
52 Chapter 2
So we have arrived at a potential way forward. We cannot all agree on a
normative standard by which to evaluate policies. However, perhaps we can all
agree on an aggregation procedure that will take our heterogeneous preferences
and turn them into a set of collective goals that we can define as the public
interest. This approach, of course, depends on our finding an aggregation
procedure that we can all agree on and that will in fact generate meaningful
collective goals. In what follows, we explore whether this approach will work.
To do so, we first need to develop a little bit of apparatus to formalize the ideas
of individual and collective preferences.
2.1 Rational Individuals
Let’s start with a model of individual preferences. We assume that each person
in our society has preferences over a set of alternatives, A. The elements of this
set of alternatives could be a variety of things, but for concreteness, let’s think
of them as policies.
Consider an individual named i facing a choice between two policies (call
them x and y) from the set of alternatives. Person i’s preferences indicate
whether she likes x at least as much as y (denoted x �i y) or likes y at least as
much as x (denoted y �i x). If she likes x at least as much as y but not vice versa,
then she strictly prefers x to y (denoted x �i y). If she likes x at least as much as y
and y at least as much as x, she is indifferent between them (denoted x ∼i y).
We say that a person is rational if her preferences satisfy two simple
conditions:
1. Completeness: For any two policies in the set of alternatives
(i.e., x, y ∈ A) person i has a preference (i.e., x �i y, y �i x, or x ∼i y).
2. Transitivity: Consider three policies in the set of alternatives
(i.e., x, y, z ∈ A). If x �i y and y �i z, then x �i z.
Completeness simply says that i always has an opinion. She can say she likes
x better than y, y better than x, or is indifferent between them. What she can’t
say is that she is wholly unable to compare x to y.
Transitivity says that if a person likes x at least as much as y and y at least as
much as z, then she likes x at least as much as z. (Transitivity of the weak pref-
erence implies transitivity of both the strict preference and indifference.) This
is a minimal condition for rationality. A person with intransitive preferences—
say, x �i y �i z �i x—might constantly cycle in her choices. If she was offered
y or z she’d choose y. If offered x or y, she’d choose x. If offered x or z she’d
choose z, ending up right where she started. Such a personwould potentially be
unable to make coherent decisions and, as the following example shows, could
be exploited by clever tricksters.
Collective Goals 53
EXAMPLE 2.1.1 (THE MONEY PUMP)
Paul has intransitive preferences over three fruits: apples (a), bananas (b),
and oranges (o). In particular, Paul’s preferences are such that a �P b, b �P o,
and o �P a. Moreover, Paul values each of these preferences at one dollar and
ten cents. That is, if you ask Paul how much he’d be willing to pay to trade a
banana for an apple, the answer is $1.10. If you ask Paul how much he’d be
willing to pay to trade an orange for a banana, the answer is $1.10. Finally, if
you ask Paul howmuch he’d be willing to pay to trade an apple for an orange,
the answer is $1.10.
Suppose Paul has an orange and $10. Sally is a fruit seller. One day, Paul
enters Sally’s storewith his orange andhis $10. Sally offers to trade Paul one of
her bananas in exchange for Paul’s orange plus a dollar. Paul would be willing
to pay all the way up to $1.10 to trade his orange for a banana, so he eagerly
takes the deal. Now Paul has a banana and $9.
Sally, crafty business person that she is, now offers Paul another trade. She
will give Paul an apple in exchange for Paul’s banana and a dollar. Paul would
be willing to pay all the way up to $1.10 to trade his banana for an apple, so he
once again eagerly takes the deal. Now Paul has an apple and $8.
Sally offers Paul yet another trade. She will give Paul an orange in exchange
for Paul’s apple and a dollar. Paul would be willing to pay all the way up to
$1.10 to trade his apple for an orange, so he once again eagerly takes the deal.
Now Paul has an orange and $7.
Recall that Paul entered Sally’s store with an orange and $10! Sally has
turned Paul into a money pump. And notice, Sally can keep doing this until
Paul runs out of money.
An important point here is that, as we’ve defined it, rationality has nothing
to do with the normative content of preferences. A rational person can think
any crazy thing she likes about which policies are better and which policies
are worse, as long as those preferences are complete and transitive. This is
important because the content of your preferences may well be a function
of the normative frameworks to which you are committed. (It may also be a
function of other things like your wealth, life experience, or what have you.)
And the whole point of our current enterprise is that we lack any principled
way to choose among a variety of plausible normative frameworks. Thus, we
don’t want to label certain kinds of preferences as irrational simply because we
happen to disagree with them.
2.2 Aggregation Procedures
For the purposes of our analysis, a society is a collection of rational individuals.
That society has to make a decision over some set of alternatives, A. Each
54 Chapter 2
individual has preferences over those alternatives. Define an issue as a set
of alternatives and the collection of each individual’s preferences over those
alternatives.
Remember, our goal is to find an aggregation procedure that, for any issue,
takes individual preferences and returns a social preference, so that we can all
agree that the outcome of that aggregation procedure yields something we will
accept as the public interest on that issue.
What exactly is an aggregation procedure? It is a function that takes as
inputs all of the individual preferences and returns as output a social preference.
A social preference, just like an individual preference, is simply a rank ordering
of all the alternatives in the set A. For concreteness, let’s consider one particular
aggregation procedure: pairwise majority rule.
Pairwise majority rule aggregates preferences as follows. For any two alterna-
tives, x, y ∈ A, say that society prefers x to y if amajority of individuals in society
prefers x to y, society prefers y to x if a majority of individuals prefers y to x, and
society is indifferent between x and y if the same number of people prefers x to
y as y to x. A simple example will fix ideas.
EXAMPLE 2.2.1 (MAJORITY RULE AGGREGATION)
A society with three members—Beth (B), Charles (C), and Dana (D)—is
considering tax policy. There are four possible taxes: None, Low,Medium, and
High. That is, the set of alternatives is A = {N,L,M,H}.
The three members of society have different views about the appropriate
tax rate. In particular, their preferences are
H �B N �B L �B M
M �C H �C L �C N
M �D H �D N �D L.
Suppose they agree to define the public interest as the preference ordering
determined by pairwise majority rule. What will that social preference be?
Let’s denote the social preference under majority rule by �maj. Comparing
High taxes to Medium taxes, we find that a majority (Charles and Dana)
prefers Medium taxes. From the perspective of society, under majority rule
aggregation, M �maj H. Comparing High taxes to Low or No taxes, we find
that there is unanimous agreement in favor of High taxes. Thus,H �maj L and
H �maj N. While there is not unanimity in support of Medium compared to
Low or No taxes, a majority (Charles and Dana) does prefer Medium taxes to
either of these alternatives. Thus,M �maj L andM �maj N. Finally, comparing
(Continued on next page)
Collective Goals 55
Low to No taxes, a majority (Beth and Dana) prefers No taxes to Low taxes. So
this analysis gives us the full social preference for this society under pairwise
majority rule aggregation:
M �maj H �maj N �maj L.
Of course, we might have used a different aggregation procedure, such as a
scoring rule like theBorda count. Under this procedure, if there are k alternatives,
each person’s first choice gets k − 1 points, each person’s second choice gets
k − 2 points, and so on, with each person’s last choice getting 0 points.We then
sum the total points for each policy and rank order policies by their scores. Let’s
redo our example under the Borda count.
EXAMPLE 2.2.2 (BORDA COUNT AGGREGATION)
Consider the same society as in Example 2.2.1. Under the Borda count
aggregation procedure, point totals are as follows:
• H: 3 + 2 + 2 = 7
• M: 0 + 3 + 3 = 6
• L: 1 + 1 + 0 = 2
• N: 2 + 0 + 1 = 3
Let’s denote the social preference under the Borda count by�bor. Under this
aggregation procedure, we have the following social preferences:
H �bor M �bor N �bor L.
The examples highlight two key points. First, there are multiple potentially
reasonable aggregation procedures for determining social preferences. Second,
different aggregation procedures can give rise to different notions of the public
interest. For instance, the social preference in our example is different under
majority rule than under the Borda count. Given this, we need to look for a
principled argument to choose among potential aggregation procedures.
2.3 Evaluative Criteria for Aggregation Procedures
There are a huge number of potential aggregation procedures. So choosing
among them is a daunting task. The key approach to narrowing down the set is
56 Chapter 2
to start by identifying some intuitively appealing features of social preferences
and eliminating aggregation procedures whose outputs (i.e., the social prefer-
ences the rule produces) do not have those features.
Before jumping into this task, however, there is an important subtlety to be
highlighted. An aggregation procedure is basically just a machine that takes a
collection of individual preferences as an input and spits out a social preference
as an output. The social preference that an aggregation procedure produces,
therefore, depends on the individual preferences that are fed in. Suppose we
identify some intuitively appealing feature that we want the social preference
produced by an aggregation procedure to have. In trying to figure out whether
the social preference produced by an aggregation procedure will or will not
have that feature, the answer may well depend on the particular individual
preferences with which we started. So what do we do?
Typically, we say that we want an aggregation procedure to satisfy some
intuitively appealing criterion for any possible collection of rational individual
preferences we feed in. This requirement is called universal domain.1 Let me be a
little more concrete to fix ideas.
Here’s an intuitively appealing criterion. Suppose absolutely everyone in
society prefers x to y. Then you might think that any sensible aggregation pro-
cedure should say that society prefers x to y. This criterion is called unanimity.
The universal domain requirement, applied to unanimity, says the following:
No matter what issue—that is, set of alternatives and collection of individual
preferences—themembers of our society happen to face, a sensible aggregation
procedure will respect unanimity. If everyone agrees about the ranking of two
alternatives, the social preference will share that ranking.
We care about universal domain because, when we choose an aggregation
procedure, we don’t knowwhat issuesmight arise in the future.We are going to
use this same aggregation procedure, nomatter the issue. So we want to be sure
that the aggregation procedure will behave sensibly in any setting.
Given this, let’s start looking at some fairly basic criteria to see which aggre-
gation procedures they rule out.
2.3.1 Transitivity of Social Preferences
The first criterion we will impose is transitivity. Transitivity is a minimal
requirement for coherent social preferences, just as it is for individual
preferences. If an aggregation procedure returns intransitive social preferences,
then it really isn’t useful in identifying the public interest. If our social prefer-
ences rank x over y, y over z, and z over x, then what exactly do we prefer?
1The term universal domain refers to the fact that the domain of the aggregation procedure is
the set of all profiles of individual preferences.
Collective Goals 57
Remember, for any criterion (like transitivity), the principle of universal
domain says that an aggregation procedure should satisfy the criterion for any
issue with which it is presented. If we can find even one example where a
candidate aggregation procedure violates transitivity (or any of the other cri-
teria we will discuss) we will throw it out of contention, since that aggregation
procedure is not guaranteed to always yield something that could be sensibly
called the public interest.
Strikingly, demanding transitivity of social preferences rules out what, for
many people, is the most intuitively appealing aggregation procedure: pair-
wise majority rule. To see this, consider the following example, known as the
Condorcet Paradox.
EXAMPLE 2.3.1 (CONDORCET PARADOX)
There are three alternatives A = {x, y, z} and three members of society
(person 1, person 2, and person 3). Individual preferences are
x �1 y �1 z
y �2 z �2 x
z �3 x �3 y.
A majority (1 and 3) prefers x to y. A majority (1 and 2) prefers y to z. And
a majority (2 and 3) prefers z to x. Hence, under pairwise majority rule, the
social preference is intransitive:
x �maj y �maj z �maj x.
Example 2.3.1 implies that if we want to use an aggregation procedure that
is guaranteed to return transitive social preferences, we cannot use pairwise
majority rule.
2.3.2 Unanimity
The next criterion we will impose is one mentioned earlier, unanimity. Recall
that an aggregation procedure satisfies unanimity if, whenever everyone prefers
some alternative x to another alternative y, the aggregation procedure says that
society prefers x to y as well.
It might seem impossible that any sensible aggregation procedure doesn’t
respect unanimity. But this is not the case. For instance, consider a procedure
inspired by amendment rules in the U.S. Congress.
58 Chapter 2
Suppose there are n alternatives. First randomly label all of the alternatives
with letters: a, b, . . . ,n. Now begin round 1. Compare a against b by majority
rule, the winner against c by majority rule, the winner against d by majority
rule, and so on through n. Call the final winner of round 1 the most preferred
alternative. Nowbegin round 2 and do the same procedure on all the remaining
alternatives (i.e., on all those other than the alternative that won round 1). Call
the winner of round 2 the second most preferred alternative. Continue this
process until all alternatives are ranked. Label the social preference under this
aggregation procedure �amend.
To see that the amendment procedure does not respect unanimity, consider
the following example. There are threemembers of society (1, 2, and 3), and five
alternatives: (a, b, c, d, and e). Individual preferences are
b �1 a �1 d �1 c �1 e
c �2 b �2 a �2 d �2 e
e �3 a �3 d �3 c �3 b.
Suppose the random procedure places the alternatives in alphabetical order. In
the first round, here is what happens:
• b defeats a (it is preferred by 1 and 2)
• c defeats b (it is preferred by 2 and 3)
• d defeats c (it is preferred by 1 and 3)
• d defeats e (it is preferred by 1 and 2)
Thus, d is themost preferred alternative under the social preferences defined by
the amendment procedure.
We can stop here. A problem is already evident. The amendment procedure
identifies d as society’s most preferred alternative. Whatever the rest of the
social preferences, we know d �amend a, b, c, e. But notice, themembers of society
unanimously prefer a to d! This example implies that if wewant our aggregation
procedure to always respect unanimity of opinion when forming the social
preference, then we cannot use the amendment procedure.
2.3.3 Independence of Irrelevant Alternatives
Our third criterion is called independence of irrelevant alternatives (IIA, for
short). IIA is slightly more subtle than transitivity or unanimity, but still intu-
itively appealing. IIA says that the social preference between two alternatives,
x and y, should depend only on people’s preferences over x and y. That is,
whether society likes x better than y or y better than x should depend on what
people think about x versus y. But it should not depend on what people think
about some irrelevant alternative, z.
Collective Goals 59
The intuitive appeal of such a criterion is perhaps clearest when thinking
about what it would mean for an individual to violate IIA. Imagine you are
at a restaurant and the waiter tells you that there are two choices: chicken
or beef. You choose the chicken. Then the waiter informs you that he’s just
remembered, there is also fish. Upon hearing this, you change your mind and
order the beef.
This is strange behavior. You compared chicken to beef and preferred
chicken. Then you heard that there was fish—a fact irrelevant to your evalua-
tion of the relative merits of chicken and beef—and changed your preference
from chicken to beef. This is a violation of IIA. Your preference for chicken or
beef was affected by the presence of an irrelevant alternative. The IIA require-
ment says that we don’t want social preferences to behave in this strange way.2
The IIA criterion rules out another kind of aggregation procedure that
we’ve already seen—scoring rules like the Borda count. To see this, consider
the following example. There are 4 members of society and 3 alternatives,
A = {x, y, z}. Preferences are
x �1 y �1 z
x �2 y �2 z
y �3 z �3 x
y �4 x �4 z.
The Borda count gives first choices 2 points, second choices 1 point, and third
choices 0 points. Point totals are
• x: 2 + 2 + 0 + 1 = 5
• y: 1 + 1 + 2 + 2 = 6
• z: 0 + 0 + 1 + 0 = 1.
The social preference under the Borda count is
y �bor x �bor z.
Now suppose a fourth alternative, w, is introduced. The new preferences are
x �1 w �1 y �1 z
x �2 w �2 y �2 z
y �3 z �3 x �3 w
w �4 y �4 x �4 z.
2There are other justifications for the IIA criterion as well. In particular, IIA is closely related
to the procedure not being strategically manipulable, for instance, by people introducing new
alternatives that do not win, but alter the outcome.
60 Chapter 2
Notice that no individual’s preferences among x, y, and z changed, so w is an
irrelevant alternative with respect to x, y, and z.
The Borda count now gives first choices 3 points, second choices 2 points,
third choices 1 point, and fourth choices 0 points. Point totals are
• w: 2 + 2 + 0 + 3 = 7
• x: 3 + 3 + 1 + 1 = 8
• y: 1 + 1 + 3 + 2 = 7
• z: 0 + 0 + 2 + 0 = 2.
In this case, the social preference under the Borda count is
x �bor w ∼bor y �bor z.
In the first scenario, ywas strictly preferred by society to x. Adding the irrele-
vant alternative,w, flipped the social preference; xbecame strictly preferred to y.
Thus, if we want our aggregation procedure to always respect the independence
of irrelevant alternatives when forming the social preference, we cannot use
scoring rules like the Borda count.
2.4 Arrow’s Theorem
We could continue adding more criteria and ruling out more aggregation
procedures. But, it turns out, at this point we’ve done enough. We’ve been
listing criteria and using them to rule out possible aggregation procedures.
Kenneth Arrow (1950) provides a sweeping result that bypasses this laborious
exercise.
Arrow asks whether we can characterize all aggregation procedures that
satisfy some appealing set of criteria. It turns out that the answer is yes. And
there is even more good news. There is exactly one aggregation procedure that
satisfies universal domain, transitivity, unanimity, and IIA. So, assuming you
want social preferences determined by a procedure that satisfies these criteria,
Arrow’s theorem pins down exactly the procedure you should use. There is,
however, a little bit of bad news. Here’s the theorem.
Theorem 2.4.1 (Arrow’s Theorem). Suppose a society has at least
2 people considering at least 3 alternatives. Then there is exactly one
kind of aggregation procedure that satisfies universal domain, transitivity,
unanimity, and independence of irrelevant alternatives. Those procedures
are dictatorships—that is, rules that identify one individual and define
the social preference as being identical to that individual’s preference
regardless of what anyone else thinks.
Collective Goals 61
A proof of Arrow’s theorem is beyond the scope of this book. I provide
references at the end of the chapter.
2.5 Social Decisions Instead of Social Preferences
Arrow’s theorem provides a striking impossibility result—there is no non-
dictatorial aggregation procedure that is guaranteed to satisfy three minimal
requirements (transitivity, unanimity, IIA) for every issue society might con-
front (universal domain). But it does so for a pretty demanding notion of
what it means for an aggregation procedure to tell us the public interest. In
particular, the framework on which Arrow’s theorem is built involves searching
for (and showing we can’t find) an aggregation procedure that returns a full
social preference over all the possible alternatives.
We don’t necessarily need our aggregation procedure to do quite so much
to have a notion of the public interest on which we can base public policy
decisions. For that purpose, we might make do with knowing what the best
alternative or alternatives are. We don’t really care whether our aggregation
procedure yields incoherent social preferences with respect, say, to which alter-
natives are rankedfifth, sixth, or seventh.We justwant it to do a good job telling
us which alternative or alternatives are ranked first. This raises a question:
does there exist an aggregation procedure that satisfies minimal normative
requirements and always identifies an alternative (or set of alternatives) that
is the best from a social perspective? If so, we might yet resurrect a procedural
notion of the public interest.
Unfortunately, the answer is still no. Under minimal conditions, we can’t
even find an aggregation procedure that reliably identifies the best alterna-
tive(s). The conditions needed to rule out this possibility are somewhat stronger
than those needed for Arrow’s theorem, but still pretty weak.
The first two requirements are familiar—independence of irrelevant alterna-
tives and unanimity. We can, of course, weaken the transitivity requirement,
since we are no longer looking for a social preference over all alternatives, we
just want to ensure that the aggregation procedure identifies at least one most
preferred alternative. But we will require that an aggregation procedure satisfy
a new condition called positive responsiveness. Suppose we have some collection
of individual preferences such that, under our aggregation procedure, society is
indifferent between two alternatives, x and y. Now suppose we hold everyone’s
preferences fixed except that at least one individual who preferred y to xmoves
x up relative to y in her preference ranking (i.e., so that now she is at least
indifferent between x and y). We say that the aggregation procedure is positively
responsive if such a change breaks the social indifference, so that society now
strictly prefers x to y. One can think of positive responsiveness as a sort of
representativeness requirement. It says that, if society is indifferent between
62 Chapter 2
two alternatives, if we leave everyone else the same, any individual choosing
tomove x up relative to y in her rankings should break the indifference.
Let’s see howpositive responsivenessmatters for our ability to identify amost
preferred alternative or alternatives. Consider an aggregation procedure that we
will call the unanimity-or-indifference rule, defined as follows.
• If every individual at least weakly prefers an alternative x to an alter-
native y and at least one individual’s preference is strict, then society
strictly prefers x to y.
• If at least one person strictly prefers x to y and at least one person strictly
prefers y to x, then society is indifferent between x and y.
This rule satisfies Arrow’s unanimity and IIA requirements. Moreover, it is not
a dictatorship. It does not always produce a transitive social preference (if it
did, it would have been a counter-example to Arrow’s theorem). However,
it does always identify a most preferred alternative or alternatives. Indeed, it
will often produce a huge set of alternatives that are ranked at the top of the
social preference, since as long as two people disagree about two alternatives,
society is indifferent between them. But the unanimity-or-indifference rule is
not positively responsive. To see this, consider a society with three individuals
who rank two alternatives as follows:
x �1 y
y �2 x
y �3 x.
Under the unanimity-or-indifference rule, this society is indifferent between
x and y. If persons 1 and 2 do not change their preferences, but person 3
changes her mind so that x �3 y, positive responsiveness says that the social
indifference should be broken in favor of x. But since person 1 and person 2 still
strictly disagree, the unanimity-or-indifference rule continues to yield social
indifference.
Now that we understand positive responsiveness, we are almost in a position
to state a result about identifying most preferred alternatives that is analogous
to Arrow’s theorem for full social preferences. Before doing so, we need one last
concept. An individual is a weak dictator if when that individual strictly prefers
some alternative x to another alternative y, then it must be that society at least
weakly prefers x to y.
With that concept in hand, we can state a result, due to Mas-Colell and
Sonnenschein (1972), on the impossibility of finding an aggregation procedure
that identifies the socially most preferred alternative(s).
Collective Goals 63
Theorem 2.5.1 (Mas-Colell and Sonnenschein’s Theorem). Sup-
pose a society has at least three people considering at least three alter-
natives. Then any aggregation procedure that always identifies at least
one socially most-preferred alternative and satisfies universal domain,
unanimity, independence of irrelevant alternatives, and positive respon-
siveness is a weak dictatorship.
2.6 The Public Interest?
Arrow’s andMas-Colell and Sonnenschein’s theorems are quite upsetting, given
the project we set for ourselves—defining a coherent procedural notion of the
public interest. It appears that looking for such procedures is a fool’s errand.
None exist, save dictatorship.
So what are we to do? I see a few ways forward.
First, we might abandon this whole notion of the public interest. There are
many possible motivations for making public policy. The public interest is only
one of them. Anoption open to us is to dispensewith the idea that public policy
is about serving some public interest that can be coherently and consistently
defined. But in so doing, we lose a powerful motivation for policymaking and
are left somewhat adrift in terms of evaluating our policy goals.
Another approach is to weaken our ambitions a bit more. There is a sense
in which Arrow’s and Mas-Colell and Sonnenschein’s theorems are very strong
results. They rule out all aggregation procedures, save dictatorship, with appeal
to only minimal criteria. There is no need, in generating these impossibility
results, to delve into controversial criteria like equality of opportunity, respect
for freedom, or other such contested normative standards. But there are also
ways inwhich these theorems are quite weak. Let’s explore three ways wemight
relax the theorems’ requirements to make progress.
2.6.1 Only Two Alternatives: May’s Theorem
Both impossibility theorems assume that societymust choose among at least
three alternatives. But there may be policy settings in which the issue boils
down to a choice among two options. What can we say about social preference
in such settings?
Following our usual approach, we can answer this question by identifying
some intuitively appealing normative criteria that we would like our aggrega-
tion procedure to satisfy. Here we consider three. The first two criteria are that
people and alternatives should be treated equally. People are treated equally
if the procedure satisfies anonymity—if the preferences of two members of
society are switched with one another and nothing else changes, the rank
ordering of the alternatives under the aggregation procedure shouldn’t change.
Alternatives are treated equally if the procedure satisfies neutrality—if the
64 Chapter 2
preferences of all members of society flipped between the two alternatives, the
rank ordering of the alternatives under the aggregation procedure would flip.
The final requirement is positive responsiveness, whichwe’ve already discussed.
These criteria are related to those from Arrow’s theorem. In particular, if
an aggregation procedure satisfies anonymity, it clearly is non-dictatorial. If a
procedure satisfies neutrality, it respects the independence of irrelevant alter-
natives. And if a procedure is positively responsive, then it respects unanimity.
Hence, onemight beworried that no aggregation procedurewill satisfy all three
criteria. But, because we have restricted attention to a situation in which the
choice is between only two alternatives, this is not the case. Instead, we can
state our first positive result about the notion of the public interest, due to May
(1952).
Theorem 2.6.1 (May’s Theorem). Suppose society has at least two
people considering exactly two alternatives. The only aggregation proce-
dure that satisfies universal domain, anonymity, neutrality, and positive
responsiveness is simplemajority rule—if a plurality of individuals strictly
prefer one alternative to the other, then so does society and otherwise
society is indifferent between the two alternatives.
2.6.2 Ruling Out Some Collections of Preferences: The Median Voter Theorem
May’s theorem suggests the desirability of majority rule as a way of defining
the public interest, but only when there are exactly two alternatives. If we
are willing to relax another of Arrow’s criteria, we can construct a different
argument for majority rule, even when society is faced with many alternatives.
For this argument, the key is to relax universal domain—the idea that an
aggregation procedure should satisfy the normative criteria for all possible
collections of individual preferences.
Let’s be clear about what is at stake here. Our impossibility theorems do
not say that there are no circumstances in which we can aggregate individual
preferences into a coherent notion of the social preference. Indeed, there
are many such instances. One possible such scenario is an issue on which
every member of society agrees. In such a circumstance, majority rule, the
Borda count, and many other aggregation procedures will all yield completely
sensible social preferences. But we don’t actually need universal agreement to
get a coherent social preference or decision out of some particular aggregation
procedure. For instance, recall Example 2.2.1. That fictional example about tax
policy had considerable disagreement among the individuals. Yet majority rule
did a perfectly good job of identifying a coherent social preference.
Our theorems say we can’t be sure that some aggregation procedure that
works for one issue will continue to yield coherent social preferences when the
next issue arises. If, on that next issue, we end upwith the right (or is it wrong?)
Collective Goals 65
collection of preferences, an aggregation procedure that worked fine in the past
might now yield incoherent or bizarre social preferences.
But perhaps we don’t need to worry about every possible issue emerging. Per-
haps some issues are exceedingly unlikely, so that we can reasonably restrict the
domain of collections of preferences our aggregation procedure has to work for.
I will consider one particular such restriction. First, notice that on any given
issue, we can line up all the alternatives in any order we like. It will be helpful
to describe such an order in terms of an ideological dimension. That is, we can
say alternative 1 is to the left of alternative 2 which is to the left of alternative 3,
and so on. A little notation is useful here. Consider two alternatives, a1 and a2.
If alternative a2 is to the right of (or more conservative than) alternative a1, we
write a1 < a2.
For any set of alternatives, there are many possible ideological orders. For
instance, suppose we have three alternatives, A = {a1, a2, a3}. One ideological
order is a1 < a2 < a3. Another ideological order is a2 < a1 < a3. Another is
a3 < a1 < a2. And so on.
Once we have an ideological order of the alternatives, we can try to de-
scribe individuals as more liberal or conservative than one another. What do
I mean by this? Say that individual i ismore conservative than individual j under
a given ideological order if the following holds: Consider two alternatives,
a1 < a2. If i is more conservative than j, then a2 �j a1 implies a2 �i a1. That is,
i is more conservative than j if whenever j likes the more conservative of two
alternatives at least as much as the more liberal alternative, then so does i. We
then say that individual i is strictly more conservative than individual j if i is more
conservative than j and j is not more conservative than i. We can define one
person beingmore liberal than another analogously.
Whether we can describe people ideologically as ranging from liberal to con-
servative depends on the individual preferences and on the ideological orderwe
choose for the alternatives. To see what I mean let’s consider an example.
EXAMPLE 2.6.1
A society with 3 members—Beth (B), Charles (C), and Dana (D)—is con-
sidering tax policy. There are three possible tax rates: Low (L), Medium (M),
and High (H). The three members of society have different views about the
appropriate tax rate. Their preferences are
H �B M �B L
M �C H �C L
L �D M �D H.
(Continued on next page)
66 Chapter 2
There aremany possible ideological orders on the alternatives. One natural
order is descending tax rates, so that the highest tax rate is identified with
the most liberal position and the lowest tax rate is associated with the most
conservative position. That is,H < M < L.
Under this order, Beth is strictly more liberal than Charles or Dana. To see
that Beth is more liberal than Charles, notice that whenever Charles prefers
the more liberal option (M over L and H over L), so too does Beth. To see
that Beth is strictly more liberal than Charles, notice that there is an instance
where Beth prefers the more liberal option while Charles does not (H vs. M).
To see that Beth is more liberal than Dana, notice that Dana never prefers
the more liberal option, while Beth always does. A similar set of comparisons
shows that Dana is strictly more conservative than Beth or Charles. Thus, we
can describe these three individuals from liberal to conservative under this
ideological order.
If we had chosen a different ideological order, we might not have been
able to describe the individuals ideologically. For instance, consider the order
M < H < L. Here, Charles is strictly more liberal than Beth or Dana. But Beth
and Dana are not ranked ideologically. In particular, comparingM toH, Beth
prefers themore conservative alternative, whileDana prefers themore liberal.
However, comparing M to L, Beth prefers the more liberal alternative, while
Dana prefers the more conservative. Thus, Beth and Dana cannot be ranked
ideologically under this order.
In Example 2.6.1, we see an issue where if we choose the right ideological
order, then the preferences of the individuals can be described ideologically.
There are, however, also issues where, no matter what ideological order we
choose, individual preferences cannot be described ideologically. To see this,
recall Example 2.3.1.
EXAMPLE 2.6.2 (EXAMPLE 2.3.1, REVISITED)
There are three alternatives A = {x, y, z} and three members of society
(person 1, person 2, and person 3). Individual preferences are
x �1 y �1 z
y �2 z �2 x
z �3 x �3 y.
(Continued on next page)
Collective Goals 67
There are six possible ideological orders. Nomatter which order we choose,
we cannot describe the individuals in ideological terms. Consider all six
possible ideological orders:
1. x > y > z: Person 3 prefers x (the most conservative alternative) to y,
while person 2 prefers y to x. But person 2 prefers y to z (the most
liberal alternative), while person 3 prefers z to y. Hence, 2 and 3
cannot be ranked ideologically under this order.
2. x > z > y: Person 1 prefers x (the most conservative alternative) to z,
while person 3 prefers z to x. But person 3 prefers z to y (the most
liberal alternative), while person 1 prefers y to z. Hence, 1 and 3
cannot be ranked ideologically under this order.
3. y > x > z: Person 2 prefers y (the most conservative alternative) to x,
while person 1 prefers x to y. But person 1 prefers x to z (the most
liberal alternative), while person 2 prefers z to x. Hence, 1 and 2
cannot be ranked ideologically under this order.
4. y > z > x: Person 1 prefers y (the most conservative alternative) to z,
while person 3 prefers z to y. But person 3 prefers z to x (the most
liberal alternative), while person 1 prefers x to z. Hence, 1 and 3
cannot be ranked ideologically under this order.
5. z > x > y: Person 2 prefers z (the most conservative alternative) to x,
while person 1 prefers x to z. But person 1 prefers x to y (the most
liberal alternative), while person 2 prefers y to x. Hence, 1 and 2
cannot be ranked ideologically under this order.
6. z > y > x: Person 3 prefers z (the most conservative alternative) to y,
while person 2 prefers y to z. But person 2 prefers y to x (the most
liberal alternative), while person 3 prefers x to y. Hence, 2 and 3
cannot be ranked ideologically under this order.
I will say that an issue is described by an ideology if we can find some ideolog-
ical order on the alternatives such that individuals can be rank ordered from
liberal to conservative.3 The domain restriction I want to consider is to restrict
attention only to issues that are described by an ideology.
Example 2.6.2 shows that restricting attention to issues that are described
by an ideology does in fact rule out some cases. But it also has a substantive
interpretation that explains why it is useful. To get some intuition for what
it means for an issue to be described by an ideology, consider redistribution.
3The term used in the academic literature is that preferences are single crossing or satisfy order
restriction. This condition is distinct from the single peakedness assumption used in Black’s (1958)
famous median voter theorem. But it yields a more powerful median voter theorem.
68 Chapter 2
Suppose people’s preferences for redistribution are driven by their personal
wealth—the richer you are, the less you like redistributive policies. Then the
issue of the level of redistribution is described by an ideology. Line people up
from poorest to richest. Now consider two levels of redistribution, a lot and
a little. Suppose a relatively poor person prefers a little redistribution to a lot of
redistribution. Then any person who is richer than her also prefers a little to
a lot. But a person who is poorer than her may prefer a lot to a little. Hence,
with respect to redistribution, we can order people from more liberal to more
conservative by their level of wealth.
What does being able to describe an issue by an ideology buy us? Consider
two alternatives, a1 > a2, such that at least one individual prefers a1 and at least
one individual prefers a2. If preferences are described by an ideology, then we
can identify some individual i such that peoplewho aremore conservative than
i prefer a1 and people who are more liberal than i prefer a2. To see this, suppose
person i is just indifferent between a1 and a2. Then, by definition, any person
who is more conservative than i prefers a1 at least as much as a2 and any person
who is more liberal than i prefers a2 at least as much as a1.
An immediate implication of this fact is that if an issue is described by an
ideology, thenwe can be sure thatmajority rule will yield coherent preferences.
For instance, imagine a society with five individuals considering an issue that
is described by an ideology. Suppose the ideology is such that person 5 is more
conservative than person 4, person 4 ismore conservative than person 3, and so
on. Notice that person 3 plus the individuals who are more conservative than
her make up a majority of this society. The same is true of person 3 plus the
individuals who are more liberal than her. We refer to person 3 as the median
voter. The median voter is a member of society who (herself included) has a
majority to her left and to her right. (Notice, if society has an even number of
people, there is not a uniquemedian voter.)
If we compare two alternatives, x > y, themajority rule winner will always be
whichever is preferred by themedian voter. To see this, suppose person 3 prefers
x to y. Since person 4 and person 5 are more conservative than person 3, they
must also prefer x to y, so x wins a majority vote. Now suppose person 3 prefers
y to x. Since person 2 andperson 1 aremore liberal than person 3, theymust also
prefer y to x, so y wins a majority vote. Thus, when an issue is described by an
ideology, majority rule always yields coherent social preferences—in particular,
majority rule induces social preferences that are identical to the median voter’s
preferences, as stated in the next result, due to Gans and Smart (1996).
Theorem 2.6.2. (Gans and Smart’s Median Voter Theorem). Sup-
pose society has an odd number of people and is considering an issue that
is described by an ideology. Then social preferences under majority rule
are identical to the preferences of themedian voter. That is, society prefers
Collective Goals 69
an alternative x to an alternative y if and only if the median voter prefers
x to y.
Let’s notice a couple of things about themedian voter theorem. First, the fact
that the majority preference is identical to the median voter’s preference does
notmean thatmajority rule is a dictatorship. The identity of themedian voter is
not fixed; it can change from issue to issue.Consider some societywith 3people.
On one day it may face an issue on which person 1 is more conservative than
person 2 who is more conservative than person 3. On this issue, majority rule
induces social preferences that are identical to person 2’s preferences. But on the
next day societymay face an issue onwhich person 2 ismore conservative than
person 1 who is more conservative than person 3. On this issue, majority rule
induces social preferences that are identical to person 1’s preferences. While,
on any given issue, the social preference undermajority rule corresponds to the
median voter’s preference, there is no dictator because different issues can have
different median voters.
Second, assuming that issues are described by an ideology yields coherent
social preferences through majority rule by relaxing the assumption of uni-
versal domain. That is, we are no longer allowing for the possibility than any
future issue (with any collection of individual preferences) might arise—we
are assuming that only issues that can be described by an ideology will arise.
Example 2.6.2, which illustrated an issue not described by an ideology, shows
why this is important. The preferences in Example 2.6.2 were precisely those
that we used in Example 2.3.1 to show thatmajority rule didn’t necessarily yield
transitive social preferences. It is exactly these sort of preferences that are ruled
out by the restriction to issues that are described by an ideology.
We’ve now seen two results that give us two conditions underwhichmajority
rule will do a good job of identifying social preferences. If there are only two
alternatives, May’s theorem shows that majority rule is the unique aggregation
procedure that satisfies some minimal, normatively desirable conditions. And
if there are more than two alternatives, the median voter theorem shows that
majority rule will at least yield coherent social preferences if society faces issues
that can be described by an ideology.
2.6.3 Intensity of Preferences
So far, in searching for a procedure for aggregating individual preferences
into social preferences, we’ve made another very restrictive assumption, this
one on the sort of information that is available about individual preferences.
In particular, we have only been using information about individuals’ rank
orderings of alternatives. We have not spoken about how intensely individuals
feel about the relative merits of various alternatives or about how strongly one
individual feels relative to another. Without going into details (which are quite
70 Chapter 2
technical), it is worth noting that if we allow for the possibility of using more
information about relative preferences and intensity of preferences, thenwe can
saymore about social preferences.
Roemer (1998) shows the following two results. If we allow for information
that informs us about the relative well-being of each individual under given
alternatives (i.e., I can say person 1 is better off than person 2, but can’t
say how much better off), then conditions similar to Arrow’s criteria (plus
a minimal equity condition) yield a unique rule for aggregating individual
preferences into social preferences. The unique aggregation procedure will
correspond, loosely, to Rawls’s difference principle—one alternative is preferred
to another if and only if it is preferred by the person who is worst off. If we
allow for evenmore information—in particular, if we can compare the intensity
of individuals’ well-being under various alternatives—then conditions similar
to Arrow’s criteria are consistent only with an aggregation procedure that is
identical to utilitarianism.
2.6.4 Agreement
A final approach we might take is to look for situations in which it is likely
that any sensible rule will yield the same social choice. The most obvious
such situation is one in which we all agree. In such circumstances, it seems
uncontroversial to say that there is a public interest. (Though we’ll reconsider
whether this claim is really uncontroversial in Chapter 3.6.) Of course, for this
to be a useful thought, opportunities to enact policies that induce outcomes
that we could all agree are improvements over the status quo must arise in the
world with some frequency.
In what follows, we develop a conceptual framework for thinking about how
andwhen such circumstancesmight arise. Thiswill be important because Part II
is devoted to showing a variety of common social dilemmas in which this may
indeed be the case—good policymight get us to a situation that everyonewould
agree is an improvement over the status quo.
2.7 Takeaways
• One can approach defining the idea of the public interest procedurally
instead of substantively. That is, it is conceivable that people could
agree to a procedure that aggregates disparate, individual views into a
collective view such that each individual would accept the output of
the aggregation procedure as representing the public interest even if it
turned out contrary to that individual’s particular views.
• Arrow’s theorem and Mas-Collel and Sonnenschein’s theorem show
that if we want the aggregation procedure to be guaranteed to satisfy
Collective Goals 71
some minimal normative standards regardless of what issue a society
ends up confronting, then we are stuck with dictatorship.
• Majority rule is a particularly appealing aggregation procedure in at
least two settings. First, May’s theorem shows that, when there are only
two alternatives from which to choose, majority rule is the unique
procedure that satisfies minimal normative criteria. Second, regardless
of the number of alternatives, the median voter theorem shows that
if society only faces issues that can be described by an ideology, then
majority rule yields coherent social preferences.
• The key results in this chapter suggest that, in many circumstances, it
is not feasible to define a procedural notion of the public interest that
everyone will accept and that will always yield a coherent answer.
2.8 Further Reading
My dissertation advisor Ken Shepsle’s classic book Analyzing Politics: Rationality,
Behavior, and Institutionsprovides another introductory take onmuchof thema-
terial found in this chapter. The definitive source for the technically motivated
student is David Austen-Smith and Jeffrey S. Banks’s Positive Political Theory I:
Collective Preference, while Amartya Sen’s Collective Choice and Social Welfare is
the classic overview. Geanakoplos (2005) provides three straightforward proofs
of Arrow’s theorem.
Myerson (2013) discusses a variety of results from social choice theory and
tells us how to think about them. Sen (1970b) offers results linking social choice
and notions of individual rights.
Black (1958) is the original formulation of themedian voter theorem, though
the version discussed here is due to Gans and Smart (1996). While not the
primary approach I take in the remainder of this book, a long tradition, follow-
ing on Anthony Downs’s An Economic Theory of Democracy, makes use of the
median voter theorem to study elections, legislatures, committees, and other
aspects of democratic politics. Keith Krehbiel’s Pivotal Politics is a particularly
nice application of this approach.
2.9 Exercises
1. Answer true or false as to whether each of the following statements is an
implication of Arrow’s theorem. In each case, briefly justify your answer.
(a) Under no circumstances is there a preference ordering which we could
sensibly call the public interest.
(b) Consider the aggregation procedure pairwise majority rule. Now
consider some particular society made up of individuals with
72 Chapter 2
preferences over some set of alternatives. For that society, majority rule
violates at least one of transitivity, unanimity, or IIA.
(c) Consider some arbitrary aggregation procedure that is not dictatorship.
There exists a real society in the world (i.e., an actual country, city, or
what have you) in which that aggregation procedure violates at least one
of transitivity, unanimity, or IIA.
(d) Consider some arbitrary aggregation procedure that is not dictatorship.
You can imagine a society (i.e., a collection of individuals with
preferences over alternatives), though it may not actually exist in the
world, such that the aggregation procedure violates at least one of
transitivity, unanimity, or IIA.
2. Consider a society made up of three people—Dan (D), Erin (E), and Fred (F).
The society must choose between three immigration policies—Closed
Borders (C), Open Borders (O), and Regulated Immigration (R). Suppose
preferences are as follows:
R �D C �D O
C �E R �E O
O �F R �F C.
(a) Write down an ideological ordering on the alternative such that this
issue is described by that ideology.
(b) What is the preferred policy of the median voter under that ideology?
(c) Use this fact to make an argument for why pursuing that policy might be
considered serving the public interest in this setting.
(d) Make an argument for why youmight nonetheless reject the idea that
this policy is clearly in the public interest or explain why you think there
is no such argument.
3. At this point, given our discussion in Chapters 1 and 2, do you find the
notion of “the public interest” to be useful for thinking about policy
evaluation?Why or why not? (There isn’t a right answer here. You should
simply try to say something thoughtful.)
4. Consider a society with three workers. Each worker, i, has a wage wi. Assume
w1 > w2 > w3. Society is choosing a tax rate, τ ∈ [0, 1]. If the tax rate is τ ,
then worker i pays taxes τwi, so total government revenues are
R(τ ) = τw1 + τw2 + τw3. The revenues are redistributed back to each worker
equally. That is, each worker receives a transfer of T = R(τ )3 . So worker i’s
Collective Goals 73
overall income, given a tax rate, τ , is
Ui(τ ) = (1 − τ)wi +
R(τ )
3
.
(a) Show that worker 1’s income is decreasing in τ .
(b) Show that worker 3’s income is increasing in τ .
(c) Themedian wage isw2. Themean wage is
w1+w2+w3
3 . Show that worker 2’s
income is increasing in τ if the mean wage is greater than themedian
wage. Show that worker 2’s income is decreasing in τ if the mean wage is
less than themedian wage.
(d) Show that, in either case, this issue is described by the ideology where we
order taxes from lowest to highest.
(e) If the mean wage is greater than themedian wage, what is the majority
preferred tax rate? If the mean wage is less than themedian wage, what
is the majority preferred tax rate?
(f) When themean wage is much higher than themedian, we typically
think there is a lot of inequality (the highest paid worker has very high
wages). Given this interpretation, provide a substantive explanation of
the meaning of your answer to the previous subquestion.
3
Pareto Concepts
Our quest to preserve a notion of the public interest in the face of the negative
results fromChapter 2 endedwith the thought that a policy interventionmight
uncontroversially be thought of as in the public interest if everyone agrees it is
beneficial. The question, then, is whether such unanimity ever actually exists.
That is, are there any policies that make everyone better off, or at least make
some people better off withoutmaking anyone worse off? And, if so, how dowe
identify them?
The classic problem for finding such policies is that many interventions
that make people better off on average also have significant distributional
consequences—making some people better off and other people worse off.
Think of free trade. The 1993 North American Free Trade Agreement (NAFTA)
created a trilateral trading bloc betweenCanada,Mexico, and theUnited States.
The goal of NAFTA was to reduce barriers to trade and investment in North
America, including the virtual elimination of tariffs, reductions in non-tariff
trade barriers, protection of intellectual property, establishment of transporta-
tion corridors, and so on.
The idea underlying NAFTA, like any such trade agreement, is that free
trade encourages competition and prosperity. Because products canmove easily
across borders, workers and resources are used in industries for which they have
comparative advantage. Increased efficiency and lower input prices yield lower
prices for consumers.Overall, the result should be increasedwealth and growth.
And, indeed, the evidence suggests thatNAFTAdid improve overall economic
prosperity in North America. Caliendo and Parro (2015) find that, from 1993–
2005, trade within the NAFTA bloc increased by 118% for Mexico, 11% for
Canada, and 41% for the United States. As a consequence, they report, Mexico
experienced a large, net welfare gain, while the United States and Canada
experienced a small net welfare gain and loss, respectively.
As Canada’s trading loss highlights, even a policy that has large benefits on
average may create winners and losers. We can see the same pattern within
countries. When trade is liberalized, some industries benefit, but other indus-
tries suffer as production and jobs move to other locations. In the case of
NAFTA, Americans working in industries in which Mexico had comparative
advantage, but that had been protected by trade barriers, were likely to suffer
as a result of increased trade openness. Indeed, as McLaren and Hakobyan
(2010) point out, so too were people who did not work in such industries but
Pareto Concepts 75
lived in locales dominated by those industries. They give the example of an
American worker living in a small town dominated by apparel manufacturing,
butworking in an industry that does not face pressure from increased trade (e.g.,
a waiter in a restaurant). Even such a person, McLaren and Hakobyan argue,
suffered following NAFTA. Increased trade decreased employment in apparel
manufacturing, leading to decreased demand for restaurant food and increased
competition for restaurant jobs, leading to a reduction inwaiters’ wages. And, of
course,matters are evenworse for aworker in apparelmanufacturing, who faces
job loss, a shift of industry, and heightened competition. Overall, McLaren and
Hakobyan find that, even as the overall economy benefited, people who lived in
localities dominated by NAFTA-vulnerable industries experienced slower than
average wage growth, particularly for working-class jobs. Further, wages in the
most protected industries fell sixteen percentage points relative to unprotected
industry wages as a consequence of NAFTA.
And so we see a major challenge for trying to create unambiguously good
public policy. Even policies that do a fair bit of overall good, create winners
and losers. To get to unambiguously good policy, we have to find a way tomove
beyond just creating benefits on average.
3.1 Pareto Concepts
A group of related concepts will help us think through these issues. All
these concepts are named after the nineteenth-century Italian economist and
philosopher Vilfredo Pareto.
We will assume that the value of a policy to a particular individual, call her
i, is given by a utility function Ui. Although we’ve already discussed the idea of
utility, it will be useful to be a little more formal at this point.
A utility function represents preferenceswithnumbers.We say that person i’s
utility function represents her preferences if it satisfies the following properties:
1. If person i prefers a policy x to another policy y, then Ui(x) > Ui(y).
2. If person i is indifferent between a policy x and another policy y, then
Ui(x) = Ui(y).
Given this, we can now define our Pareto concepts.
Definition 3.1.1. A policy x Pareto dominates another policy y if two
conditions are satisfied:
1. No one strictly prefers y to x—that is, for all i, Ui(x) ≥ Ui(y).
2. At least one person strictly prefers x to y—that is, for at least one
person, i, we have Ui(x) > Ui(y).
Pareto dominance formalizes our notion of a choice on which everyone can
agree. If some policy y is Pareto dominated by some other policy, then we
definitely should not choose y. Moreover, if the status quo policy is y and it is
76 Chapter 3
Pareto dominated by some alternative policy x, then we would all agree that
moving from y to x serves the public interest. Of course, there may be policies
that some of us prefer even above x, but that is a separate question. All we are
saying is that the move from y to x is unambiguously good.
We give this notion of a policy change that is unambiguously in the public
interest its own name.
Definition 3.1.2. Themove from a policy y to an alternative policy x is a
Pareto improvement if x Pareto dominates y.
Finally, we can also define the set of policies from which no unambiguously
good policy change is possible.
Definition3.1.3. Apolicy x isPareto efficient if no other policy Pareto
dominates it.
An equivalent definition is that x is Pareto efficient if moving from x to any
other policy makes at least one person worse off. I refer to any policy that is not
Pareto efficient as Pareto inefficient. The notion of Pareto efficiency is important
for two reasons. First, the set of Pareto efficient policies is the set of policies
from which there are no policy changes that unambiguously serve the public
interest, in the sense of making no one worse off. Second, social scientists
believe that they know a lot about identifying the set of Pareto efficient policies.
3.2 From Pareto Efficiency to Pareto Improvements
Given that social scientists claim to know a great deal about how to identify
Pareto efficient policies, it is unfortunate that our normative benchmark is
Pareto improvements rather than Pareto efficiency. The distinction is important
because it is entirely possible to move from a Pareto inefficient to a Pareto
efficient policy without achieving a Pareto improvement. To see this, consider
the following example.
EXAMPLE 3.2.1
A society made up of three people (1, 2, and 3) is choosing between three
policies (x, y, and z). The three people have the following utility functions:
U1(x) = 5 U1(y) = 2 U1(z) = 4
U2(x) = 1 U2(y) = 3 U2(z) = 7
U3(x) = 4 U3(y) = 1 U3(z) = 1.
(Continued on next page)
Pareto Concepts 77
The policy y is Pareto inefficient. In particular, everyone is at least as well
off under the policy z as under the policy y and both person 1 and person 2
are strictly better off. The other two policies, x and z, are both Pareto efficient.
Any move from either of these policies to some other feasible policy leaves at
least one person strictly worse off. So we have two Pareto efficient policies, x
and z, and one Pareto inefficient policy y.
A policy change that moves from the Pareto inefficient policy to a Pareto
efficient policy need not be unambiguously in the public interest—that is,
need not be a Pareto improvement. For instance, consider the move from the
policy y to the policy x. This is a move from a Pareto inefficient to a Pareto
efficient policy. However, this policy shift leaves person 2 strictly worse off.
Hence, it is not a Pareto improvement.
The disconnect between Pareto efficiency and Pareto improvements presents
a challenge for us. We have good reason to believe Pareto improvements are
good policy. We believe we know some things about how to achieve Pareto
efficiency. But, on its own, Pareto efficiency is not obviously normatively com-
pelling.
3.3 A Model of Policies and Preferences
Pareto concepts are only useful in the search to define unambiguously good
policy if we think it is in fact plausible to identify opportunities for Pareto
improvements. As we saw in Example 3.2.1, simply identifying Pareto efficient
policies is not enough. In this section, we develop a framework to help us think
about how wemight use our knowledge about how to achieve Pareto efficiency
to construct Pareto improving policy changes. We do so by building a model of
people’s preferences over policy that allows us to separate two potential effects
of a policy change—the effect on efficiency and the effect on distribution.
3.3.1 Actions and Transfers
Think of all policies as having two components: an action and a monetary
transfer scheme. The action representswhich policy lever is pulled— for example,
free trade or protectionism, CAFE standards or a carbon tax, high-stakes testing
or an extended school day. The transfer scheme represents redistribution of
money from some people to other people.
Suppose our society has n people in it. The set of possible actions is A. For
instance, in the case of trade we might have A = {Free Trade, Protectionism}.
A transfer scheme consists of a transfer to or from each individual. A transfer
scheme is represented by t = (t1, t2, . . . , tn). The transfer to person i is ti. If ti
xiafm
Highlight
78 Chapter 3
is negative, then the transfer scheme takes money away from person i. If ti is
positive, then the transfer scheme gives money to person i. If ti is zero, then the
transfer scheme neither takes money away from nor gives money to person i.
We will say that a transfer scheme has a balanced budget if
n∑
i=1
ti = 0.
No money is created or lost through a balanced budget transfer scheme. Any
transfer to one person must be fully paid for by transfers away from other
people. Since money can not be manufactured out of thin air, we will focus on
balanced budget transfer schemes. Thus, a policy (a, t) is a pair consisting of an
action (a ∈ A) and a budget balanced transfer scheme (t). Consider an example
motivated by our opening discussion of NAFTA.
EXAMPLE 3.3.1
A society made up of two people, Capital and Labor, has to decide between
two actions, Free Trade and Protectionism. A policy for that society would
be something like this: (Free Trade, tC = −10million, tL = 10million). That is,
the society implements free trade and transfers 10million dollars fromCapital
to Labor.
Notice, this framework is flexible. It allows for the possibility that society
might pull a policy lever (i.e., choose an action) without making anymonetary
transfers. Such a policy is represented by an action coupled with a transfer
scheme in which everyone receives a transfer of zero.
3.3.2 Quasi-Linearity: A Bridge from Pareto Efficiency to Pareto Improvement
Our model of policy and preferences needs one more piece if we are to
construct a bridge between Pareto efficiency and Pareto improvements. The
key assumption is that the value of each additional dollar is the same to each
person.
To formalize this idea, let the value to player i of an action a (e.g., free trade
or protectionism) be given by a function vi. That is, the value of some action a
to person i is vi(a). Further, let the value of a transfer of dollars, ti, to person i be
exactly ti. This implies that one dollar is worth exactly one unit of utility to any
person. Person i’s overall utility (or payoff) from an action a and a transfer ti is
given by the following quasi-linear utility function:
Ui(a, t) = vi(a) + ti.
Pareto Concepts 79
We call these preferences quasi-linear because the utility function is linear in
money but need not be linear in the action. (I haven’t said anything about how
the function vi behaves.)
Quasi-linearity is a useful starting point for building a bridge between Pareto
efficiency and Pareto improvements and clarifying the relationship between
these two concepts. (Later we will look at what happens if people do not have
quasi-linear utility.) This is because the quasi-linearmodel of preferences neatly
separates efficiency concerns from distributional concerns. Let me illustrate by
continuing Example 3.3.1.
EXAMPLE 3.3.2 (EXAMPLE 3.3.1, CONTINUED)
Suppose Capital and Labor both have quasi-linear preferences. Capital’s
payoffs from the actions are given by vC(FT) = 12 and vC(P) = 4. Labor’s
payoffs from the actions are given by vL(FT) = 2 and vL(P) = 9. SoCapital likes
free trade and Labor likes protectionism.
Payoffs from a policy (FT, (tC, tL)) are
UC(FT, (tC, tL)) = vC(FT)+ tC = 12+ tC and UL(FT, (tC, tL)) = vL(FT)+ tL = 2+ tL.
Payoffs from a policy (P, (tC, tL)) are
UC(P, (tC, tL)) = vC(P)+ tC = 4+ tC and UL(P, (tC, tL)) = vL(P)+ tL = 9 + tL.
Since the budget is balanced, it must be that tC + tL = 0. Hence, between
the two players, the total amount of utility under a policy (FT, (tC, tL)) is 14,
whereas the total amount of utility under a policy (P, (tC, tL)) is only 13. This
implies that if we start at protectionism and move to free trade, we can find a
way tomake both players better off using transfers.
For instance, suppose we start at the policy (P, (tC = 0, tL = 0)). Under this
policy, Capital’s payoff is 4 and Labor’s payoff is 9. If we then move to the
policy (FT, (tC = 0, tL = 0)), Capital’s payoff is 12 and Labor’s payoff is 2. This
is not a Pareto improvement because Labor was made worse off. But now
suppose we also change the transfers, implementing the policy (FT, (tC =
−7.5, tL = 7.5)). Under this policy, Capital’s payoff is 4.5 and Labor’s payoff
is 9.5. Both players are strictly better off than under (P, (tC = 0, tL = 0)).
Example 3.3.2 shows how quasi-linearity splits the policy problem into two
components. First, we identify the efficient action—i.e., the action that creates
the most total utility—in this case, free trade. Then we use transfers to create a
Pareto improvement by moving utility among individuals, compensating any
losers from free trade with transfers from the winners.
80 Chapter 3
The conceptual value of this division of policy problems into efficiency
and distributional concerns is not purely theoretical. It directly influences
government thinking about, among other matters, trade policy. For instance,
a report of the Congressional Research Service states:1
Congress created Trade Adjustment Assistance (TAA) in the Trade Expan-
sionAct of 1962 tohelpworkers andfirms adjust to dislocation thatmaybe
caused by increased trade liberalization. It is justified now, as it was then,
on grounds that the government has an obligation to help the “losers” of
policy-driven trade opening.
Under TAA, American workers who lose their jobs as a consequence of free
trade agreements receive relocation assistance, subsidized health insurance,
and extended unemployment benefits (or wage insurance for older workers)
while they are enrolled in retraining programs.
Extensions of presidential authority to negotiate free trade agreements have
typically been coupled in various ways with trade adjustment assistance. TAA
was a key condition for ratification of the Tokyo Round of the General Agree-
ment on Tariffs and Trade in the late 1970s. And, while it was scaled back
through the 1980s, in the 1990s, President Clinton insisted on TAA expansion
as part of the negotiations over NAFTA. In 2002, President Bush sought Con-
gressional approval of Trade Promotion Authority (known as “fast track” or
TPA).Under TPA, the president is authorized tonegotiate trade agreementswith
a guarantee of an expedited, up-or-down Congressional vote on ratification.
Democrats in Congress opposed fast track authorization and only granted it
after reaching a deal on expansion of TAA.
A similar debate recurred in 2015, when President Obama sought Trade
Promotion Authority to negotiate the Trans-Pacific Partnership—a free trade
deal focused on U.S. relations with the Asia Pacific region. It was commonly
understood that TPA was a non-starter without an expansion of TAA. Indeed,
at one point, in an attempt to derail trade expansion, Congressional Democrats
voted down a bill extending TAA. The eventual compromise again coupled new
TAA protections with fast track authority.
Example 3.3.2 also highlights the fact that quasi-linearity creates an equiv-
alence between Pareto efficiency and utilitarianism. Recall that under utilitari-
anism, we evaluate a policy based on the sum of utilities. When preferences are
quasi-linear, the set of Pareto efficient policies is exactly the same as the set of
policies that maximize the sum of utilities. Indeed, it is straightforward that, in
the example, free trade is the utilitarian optimal action—total utility under free
1See J. F. Hornbeck. August 5, 2013. “Trade Adjustment Assistance (TAA) and Its Role in U.S.
Trade Policy.” Congressional Research Service R41922. https://www.fas.org/sgp/crs/misc/R41922.pdf.
https://www.fas.org/sgp/crs/misc/R41922.pdf
Pareto Concepts 81
Figure 3.1. Any division of a Small pie is Pareto
dominated by that same division of a Large pie.
Here, the left hand pie is Small and divided 3:1
while the right hand pie is Large and divided
3:1. Both people receive a larger amount of pie
under the Large pie scenario.
trade is 14, while it is 13 under protectionism. Hence, any policy involving the
action free trade is Pareto efficient.
To see the equivalence between Pareto efficiency and utilitarianism a little
more clearly, consider a society with twomembers making a policy choice. The
society has only two actions available to it, but can choose any budget balanced
transfer scheme it likes. People have quasi-linear utility.
One of the two actions is the unique utilitarian optimum (e.g, free trade in
our example). That is, it results in more total utility in society. The other action
is not the utilitarian optimum (e.g., protectionism in our example). It results in
less total utility in society. Let’s represent the total amount of utility in society
by a pie. If society takes the action that is the utilitarian optimum, it ends up
with a Large utility pie. If it takes the other action, it ends up with a Small utility
pie.
I want you to see two things. First, any policy that involves an action that
yields a Smallpie, regardless of the division of that pie (i.e., the transfer scheme),
is Pareto dominated by some other policy. To see this, consider the policy that
results in a Small pie with share p going to person 1 and share 1 − p going to
person 2. To find a Pareto improvement, simply move to the action that results
in a Large pie and choose transfers that keep the shares at p and 1 − p. Both
people are now strictly better off. This is illustrated in Figure 3.1.
Of course, one doesn’t have to keep the shares fixed to create a Pareto
improvement when moving from a Small pie to a Large pie. All one has to do
is make sure that no one’s piece of pie shrinks.
The fact that any policy involving a Small pie is Pareto dominated by at least
one policy involving a Large pie implies that a policy can only be Pareto efficient
if it involves a Large pie—that is, if the action taken is a utilitarian optimum.
The next thing I want you to see is that all policies involving the action that
produces a Large pie are Pareto efficient. To see this, notice that once the pie
is Large, all we can do is redistribute shares of the pie between the two people
through transfers. Any redistribution of shares, of course, makes one person
better off and the other worse off.
The points above are general. They do not depend on there being only two
people or only two actions. Whenever people have quasi-linear preferences
and transfers are possible, a policy is Pareto efficient if and only if the action
82 Chapter 3
Figure 3.2. The move from a Small pie divided
25% to Person 1 and 75% to Person 2 to a Large
pie divided 100% to Person 1 and 0% to Person
2 is not a Pareto improvement.
involved in that policy is a utilitarian optimum. Moving to a utilitarian opti-
mum increases aggregate utility. And, when transfers are possible and money
is worth the same amount to everyone, once you’ve created extra utility, you
can always divvy it up in a way that makes everyone better off. These facts are
recorded in the following theorem. (For interested readers, the proof is in the
appendix of this chapter.)
Theorem3.3.1. Assumepeople have quasi-linear preferences andbudget
balanced transfers are feasible.
1. If x ∈ A is a utilitarian optimum, then for any budget balanced
transfer scheme, t, the policy (x, t) is Pareto efficient.
2. If the policy (x, t) is Pareto efficient, then x is a utilitarian
optimum.
Now it is straightforward that quasi-linearity allows us to build a bridge
between Pareto efficiency and Pareto improvements in two steps. First, we
choose an action that increases the total amount of utility in society—ideally
choosing an action that is a utilitarian optimum. Second, if that action had
distributional consequences such that some people are worse off than they
previously were, we use transfers to compensate those people. We know that
doing so is possible because there is more total utility to share. This is precisely
what we did to construct a Pareto improvement in Example 3.3.2.
Let’s return to our pies to see this two-step procedure in action. Suppose that
our society has two actions available. The two different actions have different
implications for the total amount of utility in society (i.e., the size of the pie)
as well as for the distribution of that utility (i.e., the division of the pie). In
particular, one action results in Person 1 getting 25% and Person 2 getting
75% of a Small pie. The other action results in a Large pie going exclusively to
Person 1. If no transfers aremade, themove from the Small pie to the Large pie is
a move from a Pareto inefficient to a Pareto efficient policy, but it is not a Pareto
improvement. This is illustrated in Figure 3.2.
The problem is that the change in action that yields Pareto efficiency—
that is, the change in action that increases the size of the utility pie—also
has distributional consequences that make Person 2 worse off. Importantly,
Pareto Concepts 83
Figure 3.3. The move from a Small pie divided 25% to Person 1 and 75% to Person 2 to
a Large pie divided 100% to Person 1 and 0% to Person 2 is not a Pareto improvement
even though the latter alternative creates more overall utility in society. However, by
transferring 75% of a Small pie back to Person 2, we create a Pareto improvement. That is,
the right hand cell is a Pareto improvement over the left hand cell.
Figure 3.4. The move from a Small pie to a Large pie, with properly chosen transfers, can
make both people strictly better off.
though, there ismore overall utilitywhen the pie is Large, sowe canuse transfers
to create a Pareto improvement. Imagine that we start at the policy (Small, t1 =
0, t2 = 0). We create a Pareto improvement by switching to the action Large and
choosing transfers appropriately. In particular, wemust use transfers to take pie
away from the beneficiary of the action change (Person 1) and give it to the
person harmed by the action change (Person 2).
Suppose we choose a policy that yields a Large pie and has transfers that
give Person 2 exactly the amount of pie she had under the previous policy of
(Small, t1 = 0, t2 = 0). Then she is indifferent between the two policies. More-
over, it must be that Person 1 now has strictly more pie than he did under the
previous policy (since the total pie is bigger), so he is strictly better off. Hence,
we have a Pareto improvement. This idea is illustrated in Figure 3.3.
Of course, this isn’t the only way to construct a Pareto improvement after
increasing the size of the pie. Indeed,we could choose transfers so that everyone
ends up strictly better off, as illustrated in Figure 3.4.
These results offer reasons for optimism. I’ve told you, and will show you in
what follows, that social scientists have some ideas about how to use policy to
achieve utilitarian improvements. Normatively, however, we want to achieve
Pareto improvements. Not every utilitarian improvement is a Pareto improve-
ment. But the discussion above shows that, when transfers are possible and
people have quasi-linear preferences, one can turn a utilitarian improvement
84 Chapter 3
into a Pareto improvement by choosing transfers correctly. In particular, when
changing actions in a way that simultaneously increases total utility in society
and also creates winners and losers, one creates a Pareto improvement by
transferring money from the winners to the losers.
3.4 A Bridge Too Far?
Quasi-linearity is a useful model. Treating the efficiency and distributional
consequences of a policy change separately is conceptually clarifying. And, as
we’ve discussed, this insight in fact affects the way we think about and build
actual policies.
That said, I don’t want you to get too optimistic. We’ve used this model
to build a bridge between Pareto efficiency and Pareto improvements. But
recall, before we make use of the implications of a model, we should probe
their robustness. The bridge we’ve built between Pareto efficiency and Pareto
improvements rests upon two critical assumptions—that preferences are quasi-
linear (so that efficiency anddistribution canbe separated) and that appropriate
transfers will in fact be made. If either of these assumptions is false, a focus
on actions that yield utilitarian improvements need not result in a Pareto
improvement. Let’s see why.
3.4.1 Limited Transfers and Distributional Concerns
The bridge between Pareto efficiency and Pareto improvements depends on
the necessary transfers actually being made.2 But there might be lots of reasons
to worry that this will not happen. Technological constraints can get in the way
of transfers—compensating losers from a policy shiftmight provemore difficult
than themodel suggests. Indeed, according to a Congressional Research Service
report, one of the reasons that trade adjustment assistance declined in the
1980s was because of a series of studies showing that TAA programs were
failing in their mission to help displaced workers transition to new jobs.3
Informational constraintsmightmake it difficult for the government to identify
the people entitled to compensation. Economic constraints might also pose
an obstacle to compensatory transfers—collecting and redistributing resources
requires significant government infrastructure andmay create a variety of other
distortions that could make the transfer scheme itself very costly. And, perhaps
2I don’t want to push this transfer point too far. There are ways of compensating for distribu
tional effects that don’t involve direct transfers. For instance, a well known result in trade theory
shows that one can achieve Pareto improvements moving from protectionism to free trade without
direct transfers by increasing taxes on goods that become cheaper as a result of trade (Dixit and
Norman, 1986). Still, the point stands, some policy shift that addresses distributional consequences
is necessary to achieve Pareto improvements.
3See J. F. Hornbeck. August 5, 2013. “Trade Adjustment Assistance (TAA) and Its Role in U.S.
Trade Policy.” Congressional Research Service R41922. https://www.fas.org/sgp/crs/misc/R41922.pdf
https://www.fas.org/sgp/crs/misc/R41922.pdf
Pareto Concepts 85
most importantly, political constraints often prevent transfers—for instance, if
the losers from some policy change are relatively weak or underrepresented,
then political leadersmight not have incentives tomake the transfers necessary
to achieve a Pareto improvement.
If we are to use Pareto efficiency as a normative benchmark, we must
take these constraints seriously. Policy actions can have distributional conse-
quences. Without properly chosen transfers, there is no reason to believe that
moves toward Pareto efficiency are unambiguously in the public interest, a fact
that is often hidden in both political debate and traditional policy analysis—
where the fragility of the bridge between Pareto efficiency and Pareto improve-
ments is often left unmentioned.
3.4.2 Non Quasi-Linear Preferences
The other assumption on which the bridge between Pareto efficiency and
Pareto improvements rests is quasi-linearity. When people do not have quasi-
linear preferences, a dollar to one person may be worth less than a dollar to
another person. As such, transfers of money are not equivalent to transfers
of utility. Hence, we cannot necessarily neatly separate policy problems into
efficiency concerns to be solved with policy levers and distributional concerns
to be solved with transfers.
The most obvious substantive objection to quasi-linearity is that it is in-
consistent with diminishing marginal utility from money. Under quasi-linear
preferences, no matter how much money you have, the next dollar is worth
exactly the same to you as the previous dollar—one unit of utility. Typically,
however, we think that an extra dollar is worth more to a poor person than
to a rich person. Thus, we assume people have diminishing marginal utility in
money.
Example 3.4.1 shows that sometimes, when people have diminishing mar-
ginal utility from money, one cannot create a Pareto improvement by moving
to a utilitarian optimum and choosing transfers carefully. In the example, the
losers from the policy change are also the people who value money the least.
Thus, to compensate the losers, wemust transfermoney frompeoplewho care a
lot aboutmoney to peoplewho care very little aboutmoney. And thatmeanswe
have to transfer so much money that we are taking more utility away from the
winners (through the negative transfer) than they got from the action change.
EXAMPLE 3.4.1 (THE IMPORTANCE OF QUASI-LINEARITY)
Suppose there are two people: Rich and Poor. Rich has wealth wR =
$1,000,000 and Poor has wealthwL = $1,000.
(Continued on next page)
86 Chapter 3
Each player gets utility from policy and from money. People have dimin-
ishingmarginal utility frommoney. In particular, if the action is a and person
i receives transfer ti, then person i’s payoff is
Ui(a, t) = vi(a) +
√
wi + ti.
(I use the square-root because it is a simple functional form that exhibits
diminishingmarginal returns.)
There are two possible actions: x and y. Rich prefers action x. Her payoffs
from the two actions are
vR(x) = 5 vR(y) = 0.
Poor prefers action y. His payoffs from the two actions are
vP(x) = 0 vP(y) = 10.
Suppose the status quo policy is xwith no transfers. So, under the status quo,
Rich is making a payoff of
vR(x) +
√
1,000,000
and Poor is making a payoff of
vP(x) +
√
1000.
The action that maximizes the size of the utility pie is y. Suppose we adopt
y and the balanced budget transfer scheme that takes t dollars from Poor and
gives t dollars to Rich, in order to compensate Rich for the policy change. Can
we achieve a Pareto improvement?
In exchange for the action change from x to y, Poor is willing to transfer
any amount, t, that satisfies
vP(x) +
√
1000 ≤ vP(y) +
√
1000 − t.
This means themost that Poor is willing to transfer is tP given by
0 +
√
1000 = 10 +
√
1000 − tP.
A little computation shows that Poor iswilling to transfer up to approximately
$532 in exchange for a shift from x to y.
(Continued on next page)
Pareto Concepts 87
Howmuchwould Richhave to be transferred in order for the action change
from x to y not to leave her worse off? She would need an amount, t, that
satisfies
vR(x) +
√
1,000,000 ≤ vR(y) +
√
1,000,000 + t.
Thus, the least that Rich must be transferred to leave her no worse off is tR
given by
5 +
√
1,000,000 = 0 +
√
1,000,000 + tR.
Again, computation shows that Rich must be transferred at least $10,025 to
compensate her for the change from x to y.
Given that Poor is only willing to pay up to $532 and Rich must be paid
at least $10,025, there is no way to make the move from x to y a Pareto
improvement, even though y maximizes vR + vP. The problem is that players
have diminishing marginal utility in money. On the margin, money is worth
less to Rich than it is to Poor. The change from x to ymakes Poor better off and
Rich worse off. So, although Poor would be willing to transfer enough utility
to compensate Rich, Poor isn’t willing to transfer enoughmoney to do so.
3.5 Relationship to Cost-Benefit Analysis
At some point in your policy education, you will likely learn about cost-
benefit analysis. Loosely speaking, cost-benefit analysis is a process for trying
to systematically measure and compare the costs and benefits of some policy
or project. It is used both to assess whether a given project is a good idea
and to compare the merits of multiple projects. In the United States, cost-
benefit analysis is a mandatory component of much of the regulatory process.
As Sunstein (2014, p. 170) explains, under Executive Order 13,563, an agency
can only proceed with a regulatory action “if the benefits justify the costs and
only if the chosen approach maximizes net benefits (unless the law requires
otherwise).”
The model underlying cost-benefit analysis is more flexible and robust than
a model with quasi-linear preferences, but it is particularly easy to see the
relationship between Pareto concepts and cost-benefit analysis when people
have quasi-linear preferences.
Here’s onemodel of cost-benefit analysis based on a concept calledwillingness
to pay. Consider two possible projects: x and y. Individual i, who has quasi-
linear preferences, has payoffs from the two projects given by vi(x) and vi(y),
88 Chapter 3
respectively. Given quasi-linear preferences, vi(x) − vi(y) is person i’s willingness
to pay (in both utility and monetary terms) for a change from y to x. A person
with a negative willingness to pay for a project prefers the status quo to that
project, while a person with a positive willingness to pay for a project prefers
that project to the status quo.
Theoretically, all we need to do to carry out a cost-benefit analysis on some
project is to measure each person’s willingness to pay and sum these up. If the
sum is positive, then the benefits of the project outweigh the costs, relative to
the status quo. Thus, it should be clear, with quasi-linear preferences, that there
is a close connection between cost-benefit analysis, utilitarianism, and Pareto
efficiency. In particular, a project will only satisfy cost-benefit analysis if it is a
utilitarian improvement over the status quo. Moreover, the only situations for
which there is no new project that survives cost-benefit analysis is one inwhich
the status quo is Pareto efficient.
While I won’t go into any detail here, this type of claim extends beyond
the environment with quasi-linear preferences. Indeed, quite generally, if a
project does not survive cost-benefit analysis, then the project cannot result
in a Pareto improvement. Importantly, however, all our earlier caveats about
Pareto efficiency still hold. The fact that a project looks good in terms of cost-
benefit analysis tells us nothing about whether that project will result in a
Pareto improvement. Many projects can perform well with respect to cost-
benefit analysis and, yet, make some people much worse off as a result of the
distributional consequences. Having larger benefits than costs is a necessary
condition for a project generating Pareto improvements. But it is by no means
sufficient.
It is also worth noting that there may be times when you wish to pursue a
project even though it fails a cost-benefit test. For instance, some project might
achieve a distributional goal that you find desirable, albeit in a manner that is
not cost effective. Nonetheless, if outside constraints—for instance, politics—
prevent you from achieving the distributional goal in a more efficient way, you
may be willing to accept the costs of the project to achieve your goals. (We will
explore many such issues in Part III.)
The practice of cost-benefit analysis is a field unto itself, with lots of nuance.
The simple model based on quasi-linear preferences and willingness to pay
that I’ve just given you certainly does not capture everything that is going
on in cost-benefit analysis. However, it does raise what I believe are some
important questions about cost-benefit analysis as a normative standard for
policy analysis. Whenever a cost-benefit argument is presented, regardless of
the methodology used, it is valid and important to ask whether the resulting
conclusions are informative relative to the normative standard by which you
have chosen to judge policy changes.
Pareto Concepts 89
3.6 Are Pareto Improvements Unambiguously in the Public Interest?
Having spent this chapter arguing for the virtues of Pareto improvements, let
me now briefly take the opposite position. The argument for Pareto improve-
ments goes like this: a policy change that is a Pareto improvement makes some
people better off while leaving no one worse off, who could dislike that? The
implied answer is “no one.” But the actual answer is “lots of people.” Let’s see
why.
When we say that a Pareto improvement is good because it leaves no one
worse off and makes some people better off, we are already accepting the
proposition that the way one evaluates policies is by their effects on welfare.
We’ve snuck in consequentialism. Perfectly reasonable non-consequentialist
normative frameworks might, therefore, reject certain Pareto improving poli-
cies because those policies are deemed undesirable on some dimension other
than individual welfare.
An example will help to illustrate what I have in mind. Suppose it were the
case that banning possession of any gun that holds more than one bullet at a
time would eliminate all gun violence in the United States. (I’m not saying it
would and I’mnot advocating that policy. It’s just an example. Please don’t send
me hate mail.) Since gun violence is so socially costly, it seems likely that, were
that the case, the utility surplus generated by massive gun control would be
more than sufficient to compensate all the gunowners out there for taking away
their weapons, creating a Pareto improvement. However, many people would
nonetheless object to such a policy, not on consequentialist grounds, but from
a rights-based or liberty-based perspective. That is, they would argue that the
right to keep and bear arms is absolute and that any policy that abridges that
right is bad, regardless of its welfare consequences.
A similar kind of tension between consequentialist and rights-based norma-
tive frameworks can be seen in various historical debates about the protection
of civil liberties during times of national crisis (e.g., Lincoln’s suspension of
habeas corpus, increased surveillance provisions in the Patriot Act, and so on).
A reasonable person could make a consequentialist argument on behalf of
such policies—curtailing rights during a time of crisis might increase security,
making everyone better off. But an equally reasonable person could make a
rights-based argument against such policies, even while accepting that such a
policy is a Pareto improvement.
Yet another species of this kind of tension comes from the tradition of
virtue ethics. Those who subscribe to various notions of virtue ethics also reject
pure consequentialist reasoning, instead arguing that there are certain types of
behavior and pursuits that are (or are not) consistent with virtue—that is, with
proper human living—regardless of thewelfare consequences. Perhaps themost
90 Chapter 3
interesting place where this type of argument has been influential in modern
policy discussions is in the debates over stem cell research.
Most informed people would concede the consequentialist argument—stem
cell therapies have the potential to treat huge numbers of diseases and eliminate
an immense amount of suffering. In an important consequentialist sense,
massive investment in stem cell research wouldmake us all better off. Nonethe-
less, serious voices in medical ethics have objected to stem cell research on
non-consequentialist grounds. Perhaps most prominent among them is Leon
Kass, a former University of Chicago professor and chair of President Bush’s
Council on Bioethics. While acknowledging the consequentialist benefits of
stem cell research, Kass categorically opposes such work on the grounds that it
is “repugnant” and, thus, inconsistent with human dignity. Here is an example
of what he has to say:
In crucial cases, however, repugnance is the emotional expression of deep
wisdom. . . . Can anyone really give an argument fully adequate to the
horror which is father-daughter incest, or having sex with animals, or
mutilating a corpse, or eating human flesh. . . . The repugnance at human
cloning belongs in this category.We should declare that human cloning is
unethical in itself . . . . This still leaves the vexed question about laboratory
researchusing early embryonic human clones. . . . There is noquestion that
such research holds great promise . . . that might be used, say, in treating
leukemia or in repairing brain or spinal cord injuries. . . . As a matter of
policy and prudence, any opponent of themanufacture of cloned humans
must, I think, in the end oppose also the creating of cloned human
embryos.4
We will proceed for the rest of this book by assuming that Pareto improve-
ments are in fact good policy. And there are strong arguments for doing so. But
it is important to see that even this very restrictive normative standard does not
really, in the end, get us out of the problemswe’ve encountered throughout this
part of the book—reasonable people can, andwill, disagree about even themost
seemingly uncontroversial normative positions.
3.7 Takeaways
• Pareto improvements are (sort of) unambiguously in the public interest,
at least if you are willing to embrace amild version of consequentialism.
• The quasi-linear model of preferences suggests that we think about
achieving Pareto improvements in two steps. First, look for a policy
action that increases total utility. Second, address any distributional
4Leon Kass. “TheWisdom of Repugnance.” The New Republic 1997.06.02:17 26.
Pareto Concepts 91
concerns by transferring utility from people who benefited from the
policy change to people who were harmed.
• The quasi-linear analysis requires a few caveats. First, since utility is
not actually directly transferable, one has to think hard about what
kinds of transfers are possible and whether they justify a focus on
policy actions that achieve utilitarian improvements. Second, a focus
on utilitarian improvements is not justified if transfers are not made—
for technological, informational, economic, or political reasons.
• The Paretian normative framework is only useful insofar as plausible
situations exist where there are Pareto improvements to be achieved.
• There may well be a variety of reasons to support policies that would
not result in Pareto improvements. First, you may be willing to stake
out a stronger normative position than simply advocating for Pareto
improvements. Second, sometimes the efficient policymaynot be polit-
ically feasible, but an inefficient policy that achieves similar goals may
be. Thus, advocating for policies that are not Pareto improving may be
a fine thing to do. But an important lesson is that, when you do so,
you should be cognizant of the fact that you are not on unassailable
normative ground.
3.8 Further Reading
Edith Stokey andRichard Zeckhauser’sAPrimer for Policy Analysis introduces the
classic approach to policy evaluation in an accessibleway. Sunstein (2005, 2014)
provides a thoughtful argument about the benefits of cost-benefit analysis. For
an outsider’s deep, and surprisingly sensitive, take on the normative founda-
tions of economic policy analysis, you should read Michel Foucault’s The Birth
of Biopolitics.
3.9 Exercises
1. Consider a society made up of three individuals: Alice, Bob, and Cathy.
Currently, this society has a policy (x, (tA = 0, tB = 0, tC = 0)) in place, but it
is considering the possibility of a new policy. In particular, the society has to
choose whether to implement action y, action z, or stick with the status quo
action x. The three individuals in the society have quasi-linear preferences,
with valuations for the three actions given by the following:
vA(x) = 120 vA(y) = 30 vA(z) = 220
vB(x) = 75 vB(y) = 170 vB(z) = 40
vC(x) = 100 vC(y) = 110 vC(z) = 90.
92 Chapter 3
(a) Suppose that transfers are not possible so that the only policies available
are (y, (tA = 0, tB = 0, tC = 0)), (z, (tA = 0, tB = 0, tC = 0)), or the status
quo of (x, (tA = 0, tB = 0, tC = 0)). Which policies are Pareto efficient?
Which policies involve actions that are utilitarian optima? Are they the
same?
(b) Continue to assume transfers are not possible. Suppose wemove from
action x to the action that is the utilitarian optimum. Is this move a
Pareto improvement?Why or why not?
(c) Suppose, now, that it is possible to use any budget balanced transfer
scheme. Starting from a status quo policy of (x, (tA = 0, tB = 0, tC = 0)),
suggest a policy change that is a Pareto improvement.
(d) Is it possible, starting from (x, (tA = 0, tB = 0, tC = 0)), to suggest a policy
that is a Pareto improvement but is not Pareto efficient? If yes, do so.
If no, why not?
2. Imagine a society made up of two kinds of people—theXs and the Ys. There
are an equal number ofXs and Ys. The society is considering three policy
actions: a, b, and c. Each individual in the society cares only about his or her
personal wealth.
• Under action a, all members of society have wealth 10.
• Under action b, theXs each have wealth 11 and the Ys each have
wealth 12.
• Under action c, theXs each have wealth 15 and the Ys each have
wealth 9.
(a) Define a policy as an action and a budget balanced transfer scheme. All
budget balanced transfer schemes are feasible. People have quasi-linear
preferences. Which policies are Pareto efficient?
(b) Call the transfer scheme where no one gets any transfer t0. Which of the
following is true:
i. (a, t0) Pareto dominates (b, t0).
ii. (b, t0) Pareto dominates (a, t0).
iii. Neither of these two policies Pareto dominates the other.
(c) Identify a normative framework that would be in favor of the move from
(b, t0) to (c, t0) and explain why.
(d) Identify a normative framework that would be opposed to themove
from (b, t0) to (c, t0) and explain why.
3. Explain whymoving from a Pareto inefficient to a Pareto efficient policy
need not be an unambiguously good policy decision. Give a policy example
that you think illustrates your point.
4. I argued that allowing for utility transfers and quasi-linear preferences “built
a bridge” between Pareto efficiency and Pareto improvements—that is, made
Pareto Concepts 93
it possible to think about setting Pareto efficiency as a key goal of public
policy.
(a) Explain how transferable utility builds this bridge.
(b) Do you find this to be a compelling argument for why Pareto efficiency is
an important goal for public policy? Briefly explain your answer.
5. For the purposes of this question, a policy is a pair that includes an action (a)
and a budget balanced transfer scheme (t). Assume people have quasi-linear
preferences and that any budget balanced transfer scheme is possible.
(a) True or False? Consider two actions: a1 and a2. Also consider some
particular budget balanced transfer scheme (t′). Suppose a1 is a
utilitarian optimum and a2 is not. Then the policy (a1, t′) definitely
Pareto dominates the policy (a2, t′).
(b) True or False? Again assume that a1 is a utilitarian optimum and a2 is
not. The policy (a1, t′) is Pareto efficient and the policy (a2, t′) is not.
(c) Suppose (a2, t) is not Pareto efficient. Could there be a policy (a3, t′) that
is Pareto dominated by (a2, t)?
(d) In words (3 sentences or less), what do wemean when we say that Pareto
improvements are “unambiguously good policies”? How convincing is
that argument?
(e) Suggest an example (4 sentences or less) of a situation in which there
might be a policy change that is a Pareto improvement and yet would
still be viewed as a bad policy decision by one of our normative
frameworks (be specific about what normative framework and why).
3.10 Appendix: Proof of Theorem 3.3.1
Theorem 3.3.1. Assume people have quasi-linear preferences. Suppose
the set of policies is any pair including an action drawn from the set A and
a budget balanced transfer scheme. If x ∈ A is a utilitarian optimum, then
for any budget balanced t, the policy (x, t) is Pareto efficient. If the policy
(x, t) is Pareto efficient, then x is a utilitarian optimum.
Proof. The proof of the first claim is by contradiction. To get a contradiction,
assume that some action x is a utilitarian optimum, but that (x, t) is not Pareto
efficient. The fact that x is a utilitarian optimum implies that
n∑
i=1
vi(x) ≥
n∑
i=1
vi(y), (3.1)
for all y ∈ A. The fact that (x, t) is not Pareto efficient means that there is
some (y, t′) that Pareto dominates (x, t). For this to be true, it must be that
94 Chapter 3
vi(y) + t ′i ≥ vi(x) + ti for each i and vi(y) + t ′i > vi(x) + ti for at least one i. This
implies that
n∑
i=1
[vi(y) + t ′i] >
n∑
i=1
[vi(x) + ti].
Since t and t′ have balanced budgets, this implies
n∑
i=1
vi(y) >
n∑
i=1
vi(x),
which contradicts Condition 3.1. This completes the proof of the first claim.
To prove the second claimwe will show that if x is not a utilitarian optimum,
then (x, t) is not Pareto efficient. This implies that if (x, t) is Pareto efficient, then
x is a utilitarian optimum. If x is not a utilitarian optimum, then there exists a y
such that
n∑
i=1
vi(y) >
n∑
i=1
vi(x). (3.2)
Nowfixanarbitrary budget balanced transfer scheme t anddefine anew transfer
scheme T such that Ti = vi(x) − vi(y) + ti. All people are indifferent between
(x, t) and (y,T):
Ui(y,T) = vi(y) + Ti
= vi(y) + vi(x) − vi(y) + ti
= vi(x) + ti
= Ui(x, t).
But T is not budget balanced, on net it makes negative transfers:
n∑
i=1
Ti =
n∑
i=1
[vi(x) − vi(y) + ti]
=
n∑
i=1
vi(x) −
n∑
i=1
vi(y) +
n∑
i=1
ti
=
n∑
i=1
vi(x) −
n∑
i=1
vi(y) < 0,
where the final inequality follows from Condition 3.2. Hence, we can define
a new, budget balanced transfer scheme, T ′, that gives each person T ′i =Ti +k
with k =
∑n
i=1 vi(y)−
∑n
i=1 vi(x)
n > 0 (i.e., that gives everyone a little share of themoney
not distributed by T). Since everyone is indifferent between (y,T) and (x,T),
everyone strictly prefers (y,T ′) to (x,T). Hence, (x,T) was not Pareto efficient.
Summing Up Normative Foundations
The next section focuses on trying to identify situations where Pareto im-
provements can be achieved. Before getting there, let’s remember why we are
doing this. Our discussion of normative frameworks and various impossibility
theorems taught us that we are unlikely, through argument or aggregation,
to find a set of criteria that uncontroversially describe a general notion of
the public interest. We want to avoid the conclusion that the merits of any
policy goal we might set are simply a matter of personal opinion, without any
normative foundation. So we’ve adopted a very limited notion of the public
interest on which we can all agree (almost)—achieving Pareto improvements.
Then, in order to make this useful, we pointed out that under some extra
assumptions (in particular, quasi-linear preferences and feasible transfers), a
utilitarian improvement can be turned into a Pareto improvement, if transfers
are chosen properly. This allows us to usefully divide the process of finding good
policy into two steps. First, identify a policy that increases the size of the utility
pie. Then use transfers to compensate anyonewhose welfare was harmed by the
distributional impact of that change. To paraphrase my colleague Chris Berry:
“Youwanted to learn how tomake theworld a better place.We’re going to teach
you how tomake it more efficient.”
PART II
Social Dilemmas
The social world is a strategically interdependent place. Virtually every outcome
you or I care about depends not only on our own actions, but on the actions of
others as well. This is why game theory is so valuable. It provides us with a set of
analytic tools to simplify and study some of the most fundamental issues that
arise in social interactions.
One of the things that taking strategic interdependence seriously does is
highlight some fundamental social dilemmas. A social dilemma, as I will use
the term, is a situation in which every individual is acting rationally and yet
the outcome is suboptimal. That is, a social dilemma is a situation in which
individually rational behavior leads to a Pareto inefficient outcome. In such
situations, we could all be better off if we could find a way to behave differently.
But, left to our own devices, we can’t find a way to behave differently because
the way we are behaving is an equilibrium—none of us individually regrets his
or her actions, given what everyone else did.
These social dilemmas are ubiquitous—in our economies, schools, govern-
ments, communities, bureaucracies, and so on. As such, they constitute amajor
opportunity for policies that we can all agree are in the public interest—policies
that implement Pareto improvements. If you learn to spot these social dilemmas
wherever they arise, you will be strongly positioned to find opportunities to
make the world a better place through policy. It is my hope that by mastering
some simple models, you will begin to view the world through the lens of these
social dilemmas—seeing them, and the opportunities they present for good
policy, all over the place.
4
Externalities
In 2014, theWorldHealthOrganization (WHO)warned of the growing problem
of antibiotic resistance. Adaptation and natural selection have given rise to
bacteria that are immune to most of the world’s antibiotics.1 The WHO report
raises the specter of a future in which diseases that were easily treated in
the twentieth century once again become life threatening. One key cause
of antibiotic resistance is a combination of doctors prescribing unnecessary
antibiotics and patients failing to take the full course of treatment.
Why might physicians overprescribe antibiotics? In interviews with doctors
in Britain, Butler et al. (1998) identify several factors. Doctors face pressure from
patients, who believe antibiotics will speed their recovery. For instance, Butler
et al. (1998, p. 638) report:
A typical clinician’s opinion was, “You can’t just say, ‘It’s viral, you don’t
need antibiotics, go away,’ because they feel they’re being fobbed off. They
feel that their illness is not being taken seriously.”
Patients’ desire for antibiotics creates real costs—in terms of time and repeat
business—for clinicians who resist overprescribing or attempt to educate their
patients. For instance, Butler et al. (1998, p. 639) quote one practitioner saying:
You spend 15 minutes trying to educate them, when they will go out
disillusioned, come back the next day and see someone else, making you
feel 5 minutes would be better spent just giving them a prescription and
getting rid of them.
Doctors see benefits to prescribing antibiotics and costs to not doing so. Still,
one might expect them to resist the temptation to overprescribe. Indeed,
admonitions against overprescription are routine in both medical education
and official statements of medical best practices.2 But the diffuse and abstract
benefits to society in general that underlie these ethical mandates can seem
less than compellingwhen compared to the immediate and personal benefits to
1http://www.who.int/mediacentre/news/releases/2014/amr report/en/
2For example, see Cooper et al. (2001); Barnett and Linder (2014).
http://www.who.int/mediacentre/news/releases/2014/amrreport/en/
100 Chapter 4
the doctor and his or her patient. One of Butler et al.’s interviewees articulates
precisely this tension:
In a way it would be better for the community that so many people would
not take antibiotics, but I have a feeling that for the individual it is better
for him or for her to take antibiotics. So here is a little bit of conflict
of interest in a way. . .now antibiotics are cheap and no harm is done if
antibiotics are prescribed once or twice a year for an upper respiratory tract
infection or a little bronchitis. Now why should I deprive my patients?
(p. 639)
The result of these incentives is massive overprescription. Barnett and Linder
(2014) estimate that the rate of antibiotic prescription for sore throats in the
United States is six times the appropriate level and has been since the early
2000s despite “decades of effort” to curtail it.
This example illustrates a ubiquitous feature of social interactions—one indi-
vidual’s behavior has spillover effects on the welfare of others. Your actions—be
it driving a car, studying hard for an exam, building a factory, vaccinating your
children, joining a political protest, prescribing antibiotics, or what have you—
impact not just your own well-being, but the well-being of those around you.
Situations in which one person’s actions directly affect another person’s
welfare are called situations with externalities. In particular, if person A’s ac-
tion positively affects person B’s well-being, we say that person A imposes a
positive externality on person B. If person A’s action negatively affects person
B’s well-being, we say that person A imposes a negative externality on person
B. Situations with externalities (negative or positive) constitute our first social
dilemma.
Rational individuals, when choosing their actions, ignore the externalities
they impose on others—by definition, the externalities an individual imposes
on others don’t affect her individual payoffs, so they don’t affect her best
responses. We have a linguistic shorthand for describing the fact that rational
people do not take externalities into account when making decisions. We say
that people don’t internalize their externalities. The doctor above who wondered
“why should I deprive my patients?” despite acknowledging that doing so
“would be better for the community” was failing to internalize his or her
externalities.
As the example highlights, externalities can be very important from a social
perspective because they affect the overall size of the utility pie. So the fact that
externalities are ignored in individual decision making is a serious problem. In
particular, it implies that, relative to the social optimum, actions that impose
positive externalities are typically done too little and actions that impose nega-
tive externalities are typically done too much. Prescribing antibiotics imposes
negative externalities. Thus, we have overprescription. By way of contrast,
Externalities 101
vaccination imposes positive externalities—a vaccinated child is less likely to
spread disease to others. Thus, we have under-vaccination.
A policymaker facing a situation of externalities—be they positive or
negative—can improve everyone’s well-being by getting people to internalize
their externalities. Often, policy does so by taxing or fining actions that impose
negative externalities and subsidizing actions that imposepositive externalities.
For instance, a carbon tax is a way of making consumers of fossil fuels internal-
ize their negative environmental externalities. And medical research grants are
a way of making scientists internalize the positive externalities created by new
medical discoveries.
Of course, such policy interventions sometimes comewith problems of their
own—for instance, the taxes needed to fund a subsidy might distort other
economic decisions—that must be taken into account when formulating a
policy response. In this chapter, we look at several models of situations with
externalities. Doing so will allow us to get a sense of some of the ways in which
externalities matter in the world, as well as to explore the possibilities and
challenges of using policy to mitigate the problems they create.
4.1 Collective Action
A thriving society requires teamwork. Holding a government accountable,
providing for the common defense, and cleaning up a neighborhood park all
depend on costly contributions from a lot of people. As anyone who has ever
lived in an apartment with messy roommates or worked in a problem set group
with slacker study partners knows, teamwork is not always easily achieved.
The problem is each individual’s effort may make only a small contribution to
achieving the desired outcome, but impose a sizable personal cost. Thus, each
individual, acting rationally, may find it optimal to shirk. But an individual’s
contribution to the collective mission has sizable externalities, since his small
contribution benefits all themembers of the group.Hence, even if the individual
costs of effort exceed the individual benefits, they may not exceed the social
benefits. When this is the case, individuals contribute too little.
Think of a protest. A protest aims to achieve some goal. How likely is the
protest to succeed? That depends on how many people show up. The more
people who show up, the more powerful the protest and the more likely it is
to achieve its goal—be that toppling a government, forcing a policy change,
expressing solidarity over some issue, generatingmedia attention, or what have
you.
Actually, this is a reasonable description of a lot of things. Think of regional
theater or the arts. How likely is it that the new dance troupe in your city
will survive? That depends how many people show up for the first season of
performances. Think of trade sanctions imposed by the United Nations. How
102 Chapter 4
likely is it that such sanctions will lead the target to change its behavior? That
depends on howmany countries choose to enforce the embargo. I invite you to
think of examples in your own area of interest.
To get ahandle on these issues, let’s examine amodel of participation in some
collective activity in the presence of positive externalities.
Consider a group of N > 1 people. They share a goal in common—
overthrowing the government, supporting a particular cause, forcing a policy
change, etc. The individuals must decide, simultaneously, whether or not to
participate in some activity that will increase the likelihood that the goal will
be achieved. This could be turning out for a protest, making donations, writing
letters to political leaders, and so on. The cost of participating is c > 0.
Each individual benefits if the goal is achieved. The value to an individual of
having the goal achieved is B > c. An individual gets to enjoy the benefit of the
goal being achieved whether or not she participated in the activity.
Theprobability that the goal is achieved is a functionof thenumber of people
who mobilize. To keep things simple, assume that if n people participate, the
probability that the goal is achieved is nN . That is, the probability of success is
equal to the fraction of the population that participates. If everyone partici-
pates, they succeed for sure. If no one participates, they fail for sure. If half of
the population participates, they succeed with probability one-half.3
Suppose a player, i, believes that n other people will participate. Her expected
utility from participating is
n + 1
N
× B − c.
The first term represents the probability of the goal being achieved when n + 1
people participate (Player i plus the n others she believes will participate) times
the benefit to Player i of the goal being achieved. The second term represents
Player i’s private costs of participating. Player i’s expected utility from not
participating is
n
N
× B,
which is simply the probability of the goal being achieved without Player i’s
participation times the benefit to Player i of the goal being achieved.
Player i’s best response is to participate if and only if
n + 1
N
× B − c ≥ n
N
× B,
3This is one of those instances in which I’m choosing the simplest possible model. Nothing
about the results I’m going to discuss depends on this particular functional form for probability of
success.
Externalities 103
which can be rewritten
Incremental Benefit
︷ ︸︸ ︷[
n + 1
N
− n
N
]
B ≥
Incremental Cost
︷︸︸︷
c .
The term
[
n+1
N − nN
]
is critical. It is the difference between the probability
the goal is achieved with Player i’s participation versus without. That is, it
constitutes Player i’s personal contribution to the collective goal. Call the left-
hand side of this inequality Player i’s incremental benefit of participating—the
increase in probability of achieving the goal times the benefit of achieving
the goal. The right-hand side is Player i’s incremental cost of participating.
Player i participates if and only if her incremental benefit is greater than her
incremental cost.
For most collective goals like this, the presence or absence of any one indi-
vidual is of essentially no consequence. In the model, if N is reasonably large,
an individual has almost no impact on the probability of a good outcome—
that is,
[
n+1
N − nN
] = 1N is very close to zero. As such, the incremental benefit
is miniscule. However, the costs of participation, in terms of time, money, or
personal risk can be quite large. Hence, it is typically a best response not to
participate. If this is the case, then in equilibrium no one participates.
Let’s do an example to see how this works. Suppose our society has ten
million people in it—that is, N = 10,000,000. Further, suppose the goal is very
important. Say achieving it is worth onemillion dollars to each individual.Will
an individual participate to achieve such an important goal?
According to our calculations above, it is a best response to participate if
1
10,000,000
× $1,000,000 ≥ c
which is the same as
$
1
10
≥ c.
Everyone agrees that the goal is extremely important—the value of achieving it
is $1,000,000 per person. Yet, a rational individual is only willing to participate
if the cost of doing so is less than ten cents! As you can see from this example,
in a model like this, if participation is at all costly, it is virtually certain that no
one will participate. And even the cheapest of collective actions—for example,
cleaning up the local park,making a donation toNPR—costs something in time
or money.
104 Chapter 4
4.1.1 The Social Dilemma
The example illustrates how pathological situations with externalities can
be. Continue the example above and imagine the cost of participating is just
one dollar. In equilibrium, no one participates. So payoffs are zero for each
individual. If, instead, everyone participated, then the goal would be achieved
for certain. As a result, every single individual (and there are ten million of
them) would gain a benefit worth one million dollars and bear a cost of only
one dollar. Thus, the total extra social value created would be
10,000,000
(
$1,000,000 − $1) = $9,999,990,000,000.
If everyone would participate, this society would create a social surplus of
almost ten trillion dollars! That’s a lot of utility pie. Yet, in equilibrium, no
one participates. This is what I mean by a social dilemma.With each individual
acting rationally, society leaves trillions of dollars in social surplus on the table.
A policy intervention that got everyone to participatewould be amassive Pareto
improvement. Imagine if you could fix even just one such problem in your
career.
Mynumbersmayhave been chosen to be a bit dramatic. (What can you think
of that you value at onemillion dollars, other than onemillion dollars?) But the
basic point stands. Rational individuals fail to participate even though everyone
would be better off if everyone participated. This is a bit of a puzzle, since being
rational means doing what is best for you. So what is going on?
In this model, people don’t participate because each individual’s partici-
pation has very little effect on the probability of success, so an individual’s
expected benefits from participating don’t exceed his or her costs from partic-
ipating. But there are a lot of individuals out there. Individual i’s participation
benefits each of them a small amount. So if we think about the social, rather
than individual, benefit of Player i participating, it is quite large. In particular,
it is her small contribution to the probability of success times the benefit of
success times the large number of people who enjoy the benefit if success is
achieved: 1N × B × N = B. The fact that the individuals don’t internalize these
positive externalities is the source of the social dilemma. Each individualmakes
her decision with respect to her personal well-being, ignoring her impact on
everyone else’s well-being. Hence, participation is lower than is socially opti-
mal.
4.1.2 Interpretations
We’ve already discussed a variety of interpretations of this model. It is a
stylized representation of incentives that exist whenwe think aboutmany areas
of society. As such, I hope it can serve as a kind of template you keep in the
back of your mind and compare to real-world situations. Whenever you see a
Externalities 105
situation in which a large group of people must each individually take a small,
but costly, action to achieve a collective goal, you should worry. This might
include many everyday situations. For instance, the decision to support local
arts, attend a public or community meeting, donate blood, join the governing
board of a non-profit organization or neighborhood association, or work hard
on a group project might all be subject to collective action problems. On a
societal level, collective action problems affect people’s incentives to join a
volunteer army, register as an organ donor, turn out to vote, or protest policies
they dislike.
This is not to say that groups never find ways to overcome these incentives
and act collectively. But the incentives to shirk (or “free ride” as we sometimes
say)—and thus the likelihood of socially suboptimal outcomes—are there and
must be actively overcome. Being cognizant of these incentives may help
you identify situations where interventions facilitating collective action would
create Pareto improvements.
4.2 Public Goods
Some of what makes life good we must, by necessity, share in common. If the
air is clean for me, it is clean for you as well. If the country is safe from foreign
threats for me, it is safe for you as well. If NASA develops a technology to detect
and deflect asteroids that might end life as we know it for me, it does so for you
as well. (That one is a bit of a personal nightmare of mine. Why aren’t more
people working on this? Did we learn nothing from the dinosaurs?) Scientific
discoveries that become available to me, also become available to you.
A public good (not to be confused with the public good) has two defining
characteristics:
1. It is non-excludable: My having access to it means you have access to it
as well.
2. It is non-rival: My using the good does not reduce your access to the
good.
Clear air, national defense, not dying in an asteroid-induced mass extinction
event, and scientific knowledge are all examples of public goods.
If you understood Section 4.1, on collective action, you might already see
where we are going. Situations where people have the opportunity to create
public goods are situations with positive externalities. Left to our own devices,
we typically underprovide public goods, relative to the social optimum. (This
may well be why we are not prepared to avoid mass extinction from space. You
heard it here first.) This under-provision of public goods is another example of
Pareto inefficiency caused by people not internalizing their externalities.
106 Chapter 4
Here we will consider a model of public goods being provided through the
joint efforts of a group of people working as a team. In Chapter 9 we will
consider the problem of a government directly trying to provide a public good
whose value is uncertain.
Suppose there are N > 1 people. Each chooses how hard to work on creating
a public good. Call Player i’s effort ei.
The total public good created (G) is simply the sum of all the efforts. That is,
G = e1 + e2 + . . . + eN .
This is a simple functional form that captures the idea that the amount of public
good which we each get to enjoy depends on each of our individual efforts.
Individuals find effort costly. The cost to Player i of effort ei is given by e2i .
A player’s payoff is the total public goods provided minus the costs of her
individual effort:
ui(e1, e2, . . . , eN) = e1 + e2 + . . . + eN − e2i .
To put some substance to the model, think of a group of people each
individually deciding howmuch of their travel to do by car versus public trans-
portation. You can interpret effort as the amount of personal inconvenience
a person chooses to endure to take public transportation. Some people may
do a lot, others may do very little. The more effort you put into taking public
transportation, the greater your personal costs. This is represented by the cost
term e2i . But, the more effort you put into taking public transportation, the
cleaner is the air in your locality. Clean air is non-rival and non-excludable.
Thus, the public good G is increasing in your effort directed at taking public
transportation and in everyone else’s effort as well.
Let’s think about a Nash equilibrium of this game. Suppose Player i believes
the efforts by everyone else are given by e−i = (e1, . . . , ei−1, ei+1, . . . , eN). Thenher
best response solves the followingmaximization problem:
max
ei
e1 + e2 + . . . + ei + . . . + eN − e2i .
To find her best response, we differentiate with respect to ei and set the first
derivative equal to zero:
1 − 2e∗i = 0. (4.1)
The first term in the first-order condition in Equation 4.1 represents her
marginal benefit from effort—increasing ei increases the level of public goods
she enjoys in a one-for-one manner. The second term represents her marginal
cost from effort. At the optimum, marginal benefits equal marginal costs.
Externalities 107
Rearranging, we have that Player i’s optimal effort is
e∗i =
1
2
.
In this simple model, a player’s best response is to choose effort of one-half,
regardless of what everyone else is doing. This implies that there is a unique
Nash equilibrium—all players choose effort e∗i = 12 .
The total amount of public goods created in this equilibrium is N2 . Hence,
each player’s equilibrium payoff is
ui
(
1
2
, . . . ,
1
2
)
= N
2
−
(
1
2
)2
= 2N − 1
4
.
4.2.1 Comparison to the First Best or Utilitarian Optimum
Youwill not be surprised to learn that this equilibrium is not Pareto efficient.
This public goods game is a situation with positive externalities, so people con-
tribute too little, relative to the utilitarian optimum. Before showing you how
much better players could do if they behaved differently, I want to introduce
onemore piece of terminology, whichwill becomeuseful later whenwe analyze
optimal policy interventions.
The term is the first best, which is just another name for the utilitarian
optimum. I will sometimes refer to the first-best actions, by which I mean
the action profile that maximizes the utilitarian welfare. Having defined this
terminology, let’s solve for the first best to see howmuch better off players could
be in our public goods game.
Suppose that the society produces a total amount of public goods, G, with
each player contributing an equal share: ei = GN . (This is precisely what is hap-
pening in equilibrium, with G = N2 .) How much would be socially optimal to
produce?4
In such a situation, each individual’s payoff is G − (GN
)2
. So the total utilitar-
ian payoff for the society is
N
(
G −
(
G
N
)2
)
.
To find the first best wemaximize this utilitarian payoff:
max
G
N
(
G −
(
G
N
)2
)
.
4It is, in fact, socially optimal for each individual to take equal effort.
108 Chapter 4
Differentiating and setting the first derivative equal to zero, we find that the
first-best level of public goods provision (denotedGFB) satisfies
N
(
1 − 2G
FB
N2
)
= 0 ⇒ GFB = N
2
2
.
The first best involves each individual contributing N2 , which, in a large group,
is a lot more than the equilibrium contribution of 12 .
Why does the utilitarian optimum require people to contribute so much
more than they do in equilibrium? As we’ve already seen, in equilibrium, a
person contributes until her personal marginal benefit equals her personal
marginal cost. She ignores the benefit of her effort forN − 1 other people—that
is, she doesn’t internalize her externalities. At the utilitarian optimum, each
person internalizes her positive externalities. She keeps contributing until the
marginal benefit of her effort to the whole society equals her effort’s marginal
cost. This means she internalizes the fact that N people benefit from each
increment of effort, not just one person. And, consequently, to achieve the first-
best level of public goods, each individual worksN times harder.
If individuals are working harder at the utilitarian optimum, why are they
better off? The key is that each individual benefits from the fact that everyone
else is also working harder. If everyone contributes N2 to providing the public
good, each individual’s payoff is
N × N
2
−
(
N
2
)2
= N
2
4
,
which is greater than the payoff to an individual under the Nash equilibrium
(2N−14 ). Players are better off if everyone does the socially optimal level of effort,
rather than the equilibrium level of effort. Moreover, the more people there
are, the larger the gap between the two payoffs. These facts are illustrated in
Figure 4.1.
4.2.2 Interpretation
A few examples will hopefully highlight the ubiquity of the incentives that
lead to the under-provision of public goods. Governments expending effort
to fight a transnational threat such as terrorist groups, drug traffickers, global
warming, or the spread of a disease may fail to internalize their positive exter-
nalities on other countries. Similarly for individuals and corporations taking
costly actions to reduce pollution. Scientific research leading to knowledge
with broad benefits for humanity is likely to be under-provided because the
individual researchers do not fully internalize the benefits of their research for
others. Some individuals are inclined to turn down access to vaccination, de-
worming, or other health improving actions. Those individuals typically justify
Externalities 109
2500
2000
1500
1000
500
20 40 60
N
U
ti
li
ty
80 100
Individual payoff if everyone
does equilibrium effort
In
div
idu
al
pa
yo
ff i
f e
ve
ryo
ne
do
es
fir
st-
be
st
eff
ort
Figure 4.1. Each individual’s payoff is higher if everyone does the first best level of effort
rather than the equilibrium level of effort. This becomes increasingly true as society gets
large so that externalities loom large.
their choice in terms of their individual rights, but are failing to internalize
the externalities generated by vaccines and the like—when an individual is
treated, it benefits others by reducing their exposure to disease. Members of
corporate boards are supposed to monitor the behavior of executives. While
board members have some incentives to do so, those incentives are unlikely
to be strong enough to fully internalize the positive externalities generated for
shareholders when executive behavior is closely monitored.
4.2.3 Concentrated vs. Diffuse Interests
The collective action and public goods problems are particularly important
for understanding how the politics of special interests impact policy outcomes.
Because of failure to internalize externalities, it is difficult to organize support
for a policy that benefits a large, diffuse group of people. In a setting with diffuse
interests, each individual has trouble imagining that his or her contribution
matters. By contrast, it is relatively easy to organize support for a policy that
strongly benefits a small group of people. In a setting with concentrated interests,
there are fewer externalities and each individual’s participation is more impor-
tant. Hence, the logic of externalities suggests that concentrated interests will
be overrepresented, relative to diffuse interests, in the policymaking process.
There are many examples of this phenomenon. Public sector unions are
better organized and more influential in debates over pension reform than are
citizens’ groups. The financial industry was more influential in banking reform
than were consumers. It is difficult to curtail pork-barrel spending in Congress
110 Chapter 4
because each individual congressperson is willing to work hard on behalf of his
or her individual district, but not against pork barreling in general. And so on.
The relationship between urban planning and the construction of the
interstate highway system in the United States provides a particularly strik-
ing example of the advantages concentrated interests have relative to diffuse
interests.5 In 1956, President Eisenhower approved construction of a national,
interstate highway system. This was an exceptionally ambitious public works
project that ultimately resulted in the construction of over 42,000miles of road,
crisscrossing the country. Interstate highways set the course for patterns of eco-
nomic development, internalmigration, housing, urban policy,manufacturing
and shipping, andmuch else that characterized the secondhalf of the twentieth
century in the United States.
A major issue for highway planners was the relationship between the inter-
states and urban centers. The population and retail decline of industrial cities
had taken hold by the 1950s. One problem the highway system had to address
was how to meet the ever-increasing demand to move workers efficiently from
the suburbs into the city and back. The solutionwas the familiar hub-and-spoke
pattern of inner- and outer-belt highways that connected suburbs with the
urban core.
But this issuewas intimately tied upwith the racially fueled politics of “urban
revitalization.” In the three decades that followed World War II, millions of
southern African Americansmigrated to northern andmidwestern city centers.
The combination of middle-class suburbanization, racial housing segregation,
and massive migration created urban ghettos and slums which were of great
concern to urban political leaders, as well as business and real estate developers.
Highway advocates seized on this “urban blight” problem as a key argument
for the construction of the interstates. They claimed that strategic placement of
expressways would facilitate urban redevelopment by forcing the destruction
of low-income housing and tenements. In particular, they proposed running
highways through the middle of poor, residential districts in the inner city,
using the government’s land acquisition rights to force out poor residents and
make room for high-rise and retail development.
Of course, such a policy had both winners and losers. Urban politicians,
real estate owners and developers, and various industries benefited from the
construction of the interstates. These are classic examples of concentrated
interests. Urban real estate owners and developers were represented by the
Urban Land Institute (ULI). According to Rose and Mohl (2012), p. 101, “The
ULI’s Central Business District Council focused on freeways as ‘the salvation of
the central district, the core of every city.’ ” Road builders, the concrete industry,
5This discussion is based on Rose andMohl (2012).
Externalities 111
and automobile manufacturers also all participated in lobbying. For instance,
Rose andMohl, p. 101–102 report:
As early as 1949, in a letter to President Truman, the ARBA [American Road
Builders’ Association] defended the use of highway construction in slum
clearance. Urban express highways, the ARBA contended, were necessary
to alleviate traffic congestion, but through proper right-of-way planning
they also could “contribute in a substantial manner to the elimination of
slum and deteriorated areas.”. . .
[T]he American Concrete Institute, which had an obvious interest in
highway construction, championed the use of urban expressways in “the
elimination of slums and blighted areas.” Build highways through the
city slums, urged the ARBA and the ACI, and solve the problems of urban
American.. . .
[T]he Automotive Safety Foundation assured readers that freeways were
desirable, beneficial, and beautiful; they stimulated rising land values and
prevented “the spread of blight and. . . slums.”
On the losing side were poor, African American, city residents—a classic
example of a diffuse interest. These communities did not successfully organize
in opposition to the interstate highways in the 1940s and 1950s, when the
system was planned. As a consequence, Rose and Mohl, p. 96, report that “[b]y
the 1960s, federal highway constructionwas demolishing 27,000urbanhousing
units each year.” It was not until the massive costs of these highways became
clear that organized opposition emerged, primarily under the auspices of the
civil rights movement. But by then it was too late to changemuch.
Nashville’s Interstate 40 is a case in point. As Rose andMohl, p. 105, describe:
[H]ighway planners went out of their way to put a “kink” in the urban
link of Interstate-40 as it passed through the city. The expressway route
gouged a concrete swath through the North Nashville black community,
destroying hundreds of homes and businesses and dividing what was left
of the neighborhood. The decision for the I-40 route had been made
quietly in 1957 at a nonpublic meeting of white business leaders and state
highway officials. By 1967, after years of denying that the expressway
would adversely affect the community, the state highway department
began acquiring right of way, displacing residents, and bulldozing the
route.
Residents eventually organized in opposition to the highway, gaining a tem-
porary restraining order, but ultimately losing in federal court. The highway
was constructed as planned. Similar stories played out in cities throughout the
country. Andwhile some highway construction was halted and some highways
were rerouted, the overwhelmingmajority of the stories endwith the interstates
112 Chapter 4
following precisely the plans established by the concentrated interests starting
in the 1940s.
Let’s look at amodel to see that externalities can lead to the differential power
of concentrated versus diffuse interests.
Imagine a setting inwhich, say, a factory owner ismaking profits by polluting
the water supply of a town. A regulator must decide whether to regulate the
factory. Both the factory owner and the citizens of the town can invest in
lobbying the regulator. Each hour of lobbying costs $100. The regulator can
be influenced through lobbying. If the citizens do C hours of lobbying and the
factory owner does F hours of lobbying, the probability that the regulator sides
with the citizens and factory owner are
C
C + F and
F
C + F ,
respectively. If the two sides spend equally, they winwith equal probability. But
the more one side spends relative to the other, the more likely it is to win.
There are N citizens in the town. If the factory stops polluting, each citizen
experiences a benefit of b > 0. Polluting allows the factory owner (who lives
elsewhere) to make an extra profit of π . Assume that b < π < Nb, so that
the factory owner values polluting more than any individual citizen, but the
utilitarian outcome is for the regulator to prevent pollution.
The citizens and factory owner each choose an amount to contribute towards
lobbying. The factory owner (being only one person) is a concentrated interest,
while the citizens are a diffuse interest. As we will see, even though the utilitar-
ian outcome is for the factory to be regulated, in equilibrium the factory owner
will yield more influence than the citizens and, as a result, almost certainly will
not be regulated.
Consider a citizen, i, who believes that each of her fellow citizens will con-
tribute enough to purchase c hours of lobbying and that the factory owner will
buy F hours of lobbying. Citizen ibelieves that if she contributes enoughmoney
to purchase ci hours of lobbying, then the total amount of lobbying in support
of regulation will be C = ci + (N − 1)c. Hence, she believes the probability of
regulation will be ci+(N−1)cci+(N−1)c+F . Given this, citizen imakes a contribution, ci, that
solves
max
ci
(
ci + (N − 1)c
ci + (N − 1)c + F
)
b − 100ci.
Taking the first-order condition and rearranging, citizen i’s best response is
BRi(c, F) =
√
bF
10
− F − (N − 1)c.
Externalities 113
Since the citizens are identical, focus on the case in which eachmakes the same
contribution (given F). Call this contribution BRi(F). Since all citizensmake the
same contribution, it must satisfy
BRi(F) =
√
bF
10
− F − (N − 1)BRi(F).
Rearranging, each citizen’s contribution purchases the following number of
hours of lobbying:
BRi(F) =
√
bF − 10F
10N
. (4.2)
If the factory owner believes that the citizens will purchase a total of C hours
of lobbying, he solves
max
F
(
F
C + F
)
π − 100F. (4.3)
Maximizing this function, the factory owner’s best response is
BRf (C) =
√
Cπ − 10C
10
.
Equations 4.2 and 4.3 give us the two best responses. If we substitute the
right-hand side of Equation 4.3 for F in Equation 4.2, we find the Nash
equilibrium:
c∗ = b
2π
100(b + π)2N and F
∗ = bπ
2
100(b + π)2 .
What does this imply aboutwhich side’s lobbying efforts are likely to prevail?
Total lobbying by the citizens is
C∗ = Nc∗ = b
2π
100(b + π)2 ,
while total lobbying by the factory owner is
F∗ = bπ
2
100(b + π)2 .
Since π > b, it is straightforward that the factory owner’s investment in lobby-
ing is larger than the sum total of the citizens’ investments. Thus, the factory
owner is more likely to prevail. In particular, the probability that the citizens
114 Chapter 4
win and pollution is stopped is
C∗
C∗ + F∗ =
b2π
100(b+π)2
b2π
100(b+π)2 + bπ
2
100(b+π)2
= b
b + π < 1/2. This outcome is inefficient. As a group, the citizens value stopping the pollution more than the factory owner values polluting. For instance, suppose b = 1000, N = 100, 000, and π = 1, 000, 000. The citizens’ total value of stop- ping pollution is $100,000,000. The factory owner’s value of polluting is only $1,000,000. Yet the probability that the regulator stops the pollution is tiny: 1000 1000 + 1,000,000 = 1 1001 . Because the citizens are a diffuse interest, their efforts to organize are hampered by an externalities problem. Each individual benefits only a small amount from her individual contribution. But that contribution also benefits all the other citizens. Hence, each citizen under-contributes. They all would be better off if they could find a way to all contribute more to the cause. 4.3 The Tragedy of the Commons In February of 2009, an American commercial communications satellite (Irid- ium33) and adefunct Russianmilitary communications satellite (Kosmos 2251) collided in low earth orbit traveling over 42,000 km/hour. Both satellites were destroyed on impact. According to the European Space Agency, the collision and destruction of the satellites generated 2200 trackable fragments of space debris.6 In 2012 one such fragment passed close enough to the international space station that astronauts were forced to take refuge in “life boats” as a precaution against a collision. All told, the international space station has had to reposition itself to avoid space debris at least fifteen times.7 Though dramatic, this story is in some sense not surprising. Low earth orbit (approximately 200 to 2000 kilometers above the earth) is the least costly part of space to access. Moreover, because of its close proximity to earth, communications can be achieved with relatively low power. However, because objects in low earth orbit circle the globe quite quickly (relative to the rotation of the planet), they do not stay over a fixed position on earth. A constellation of interconnected satellites is, thus, required to provide uninterrupted coverage. As a consequence of these facts, an enormous number of objects—scientific 6http://www.esa.int/Our Activities/Operations/Space Debris/About space debris 7http://www.esa.int/Our Activities/Operations/Space Debris/FAQ Frequently asked questions http://www.esa.int/OurActivities/Operations/SpaceDebris/Aboutspacedebris http://www.esa.int/OurActivities/Operations/SpaceDebris/FAQFrequentlyaskedquestions http://www.esa.int/OurActivities/Operations/SpaceDebris/FAQFrequentlyaskedquestions Externalities 115 equipment, satellites used for communications, spying, global positioning, weather and environmental monitoring, and so on—have been sent into low earth orbit. While several international treaties regulate space, the underlying legal framework leaves the peaceful use of space as a right of sovereign nations. As the example of space debris highlights, this creates externalities problems. Space in low earth orbit is a finite resource. When one country or firm launches a satellite into orbit, it reduces available space for others. This is a situation of negative externalities—countries and firms suffer only a small portion of the costs associated with crowding space with debris. Thus, we should expect there to be toomuch space debris, relative to the social optimum. And, indeed, the European Space Agency estimates that there are over 600,000 pieces of debris of at least 1 cm in size orbiting the earth. This debris is the result of thousands of satellites, rockets, and instruments launched into orbit since the space age began. In fact, prior to the collision, the defunct Kosmos 2251was itself space debris. A related issue arises for satellites in geostationary orbit at much higher altitude (almost 36,000 kilometers above the earth). Objects in geostationary orbit circle the globe directly above the equator, at the same speed as the earth rotates on its access. As a consequence, they stay above a fixed position on earth at all times. This stationarity is particularly valuable for communications, since a single satellite can guarantee continuous coverage of a particular part of the globe. The problem for geostationary orbit is not primarily debris. It is limited space. Because the radio frequencies used by such satellites can interfere with one another, they must be spaced appropriately. As a result, there are a very limited number of spots, especially above desirable parts of the globe.Moreover, satellites must stay in a very narrow altitude band to remain geostationary (if they fall out of that band, they cease to remain over a fixed location). Hence, satellites must reposition relatively frequently, a process which can again interfere with signals sent by nearby satellites. While there is an international registry to coordinate positioning of satellites in geostationary orbit, the right to launch and to reposition satellites again rests with sovereign nations. As with space debris in low earth orbit, then, there are significant externalities problems. Individual countries and firms fail to internalize the full costs of putting a satellite in orbit or of repositioning that satellite. As a consequence, we expect inefficient overuse. In the previous section we explored externalities in the context of public goods—goods that are neither excludable nor rival. The problem of overcrowd- ing in space illustrates an externalities problem that is very closely related, but arises with another type of good—the commons. The commons (sometimes also called a common-pool resource) is a good that is non-excludable, just like a public good, but is rival, unlike a public good. As you’ll recall, a non-excludable 116 Chapter 4 good is one that has the property that if anyone has access to it, everyone has access to it. A rival good is a good where my use of it diminishes the supply of the good left for you—that is, the resource in question can be depleted. Other classic examples of the commons include fish stocks within a fishery, grazing land, space on the road, internet bandwidth, water, and so on. Because of its rivalrous nature, the commons presents a situation with nega- tive externalities. If I use a lot of bandwidth to stream movies to my TV in the evening, I slow down everyone else’s internet connection. But I don’t take those negative externalities into accountwhenusing the commons. As such, typically people use too much of the commons, relative to the social optimum. Hence, the tragedy of the commons. Think about that next time you are downloading movies from BitTorrent. The real crime isn’t stealing intellectual property. It’s the negative externalities you are imposing on my internet speed as I try to streamNetflix legally. To be a little more precise, let’s consider a simple model of a commons that is a little more down to earth than geostationary orbit, a fishery. The fishery is small enough that, no matter how much fishing is done, it does not affect the price of fish on the market. The price per fish is $2. There are two firms running boats in thefishery: firm1andfirm2. Thefirms simultaneously choose how many fishing boats to run: b1 and b2. It costs $20 to run a boat. We will assume that, if they want to, firms can run partial boats, so that b1 and b2 are real numbers rather than integers. (This is just for technical convenience.) Fish are a depletable resource. So the more boats out fishing, the lower the density of fish in the fishery and the fewer fish caught per boat. In particular, if the total number of boats in the water is B = b1 + b2, then the number of fish caught per boat is 100 − B. The firms care about profits. If a firm runs bi boats, then its profits are $2(100 − B)bi − $20bi. The first term represents revenues: two dollars per fish times (100 − B) fish per boat times bi boats. The second term represents costs: $20 per boat. How many boats will each firm run? Suppose firm i believes the other firm will run b−i boats. Then it chooses a number of boats to maximize profits: max bi 2(100 − bi − b−i)bi − 20bi. The optimal number of boats for firm i is given by BRi(b−i), which (if it is positive) satisfies the following first-order condition: 200 − 4BRi(b−i) − 2b−i − 20 = 0. Externalities 117 0 30 45 90 100 100 90 30 0 45 b 2 b1 BR1(b2) = 90 – b2— 2 BR2(b1) = 90 – b1— 2 Figure 4.2. Best response corre spondences in the Tragedy of the Commons game. Rearranging we have BRi(b−i) = ⎧ ⎨ ⎩ 90−b−i 2 if b−i ≤ 90 0 otherwise. (4.4) We can use these best response correspondences to find a Nash equilibrium. A profile (b∗1, b ∗ 2) is a Nash equilibrium if and only if the following conditions hold: b∗1 = BR1(b∗2) and b∗2 = BR2(b∗1). (4.5) Figure 4.2 draws both best response correspondences. The solid line is firm 1’s best response correspondence. For any number of boats run by firm 2 (on the y-axis), you find the best response for firm 1 bymoving horizontally to this line and then dropping down to the horizontal axis. The dash-dot line is firm 2’s best response correspondence. For any level of boats by firm1 (on the x-axis), youfindfirm2’s best response bymoving vertically to this line and thenmoving leftward to the vertical axis. The best response correspondences intersect at an equilibrium—each firm runs 30 boats. One can also see this algebraically. Substituting the best responses from Equation 4.4 into Equation 4.5, if the firms run fewer than 90 boats, then at an equilibriumwe have b∗1 = 90 − b∗2 2 and b∗2 = 90 − b∗1 2 . 118 Chapter 4 Substituting the second equation into the first we get b∗1 = 90 − 90−b∗12 2 . Rearranging yields b∗1 = 30 and b∗2 = 90 − 30 2 = 30. Given that each firm runs 30 boats, each firm’s equilibrium profits are $2(100 − 30 − 30)30 − $20 × 30 = $2400 − $600 = $1800. 4.3.1 A Pareto Improvement You won’t be surprised to learn, given the negative externalities, that the equilibrium involves overfishing. To see this, imagine that each firm ran 20 boats instead of 30. Under this scenario, profits are $2(100 − 20 − 20)20 − $20 × 20 = $2400 − $400 = $2000 > $1800.
By running 20 rather than 30 boats each, the firms actually keep revenues
exactly the same ($2400) but save the costs of running an extra 10 boats each.
This works because, by not running so many boats, the firms are able to catch
more fish per boat.
4.3.2 The First Best
It turns out that running 20 boats each is not the utilitarian optimum for
these firms. It was simply a convenient example to show that the firms could
do better by both fishing less. Let’s now figure out how many boats are socially
optimal.
Suppose that the total number of boats run is B and each firm runs an equal
number. Then the sum of the two profits is
$2
(
100 − B
2
− B
2
) (
B
2
+ B
2
)
− $20
(
B
2
+ B
2
)
.
We can find the B that maximizes this sum of profits (which we will call BFB for
the “first best”) by differentiating and setting the first derivative equal to zero:
$2
(
100 − 2BFB) − $20 = 0.
Rearranging, the first-best number of boats is
BFB = 45.
Externalities 119
4.3.3 Interpretation
We opened with an example of a tragedy of the commons in space. As the
model highlights, another famous setting typically viewed as a commons is
fisheries or grazing land. Perhaps the most famous such example is the collapse
of Canada’s Grand Banks cod fishery in the 1990s. Hutchings (1996) reports
that the Grand Banks fishery was once the world’s largest cod fishery. How-
ever, beginning in the 1960s, technological innovations (e.g., larger trawlers,
electronic navigation, sonar) increased the rate at which cod were caught. For
a while, this led to record catches. Eventually, however, the density of cod in
the fishery began to decline, leading to ever smaller catches. The annual catch
fell from over 800,000 tons in 1968 to under 200,000 tons by the late 1970s.
According to Hutchings, between 1962 and 1992, there was a 94% decrease in
the abundance of cod old enough to be commercially fished. In 1993, amid
concerns of permanent collapse, the fishery was closed down.
There are many other such examples in environmental policy. For instance,
deforestation due to overlogging is a classic example of a tragedy of the com-
mons which has played out in tropical forests throughout south Asia, Africa,
and South America.
Another particularly striking example is the Pacific trash vortex (also known
as the Great Pacific garbage patch). This enormous gyre of marine debris in
the Pacific Ocean is estimated by the U.S. Environmental Protection Agency
(EPA) to stretch from Hawaii to Japan and contain approximately 100 million
tons of garbage.8 The garbage patch is a source of significant environmental
problems. For instance, the EPA reports that concentratedmarine debris results
in degraded habitat, harm to coral reefs, accumulation and transport of high
levels of contaminants (including PCBs and pesticides), and direct damage to
animal life through ingestion and entanglement.
The vortex is the consequence of marine pollution that gets trapped and
consolidated by oceanic currents. The EPA reports that
[t]he primary source of marine debris is the improper waste disposal or
management of trash and manufacturing products, including plastics
(e.g., littering, illegal dumping). . . . Debris is generated on land atmarinas,
ports, rivers, harbors, docks, and storm drains. Debris is generated at sea
from fishing vessels, stationary platforms and cargo ships.
Such an outcome is not surprising. Clean and well-functioning oceans are a
common pool resource. The logic of the tragedy of the commons, then, implies
that, absent intervention, we should expect overpollution. And in this case,
8U.S. Environmental Protection Agency Pacific Southwest/Region 9, “Marine Debris in
the North Pacific A Summary of Existing Information and Identification of Data Gaps.”
http://www.epa.gov/region9/marine debris/pdf/MarineDebris NPacFinalAprvd.pdf
http://www.epa.gov/region9/marinedebris/pdf/MarineDebrisNPacFinalAprvd.pdf
120 Chapter 4
where there are so many possible ways for debris to flow into the sea, it may
be particularly difficult to solve the problem.
There are also applications outside the context of environmental policy. As
already mentioned, various forms of traffic—vehicular, internet, cell phone,
radio, satellite, and so on—share the strategic structure of a tragedy of the
commons. Anyone can get on the highway or the internet. But themore people
who use the highway or the internet, the slower the traffic moves. Hence, your
presence on the highway imposes a negative externality on me by depleting a
resource that we share—open road, as it were.
The metaphor can extend even further. For instance, Berry (2009) argues
that the structure of local government in the United States creates a tragedy of
the commons with respect to taxation. In many localities in the United States,
citizens are represented by a large number of overlapping, local governments—
a city, a county, a school district, a parks district, a water reclamation district, a
library district, amosquito abatement district, and so on.Manyof these districts
have independent taxation authority. Hence, they are all drawing government
revenues froma commonpool of the citizens’ depletable, taxable resources. The
consequence is overtaxation by local government in those areas where there are
many overlapping districts.
And, indeed, Berry finds precisely this effect in the data by studying how
taxation and service provision change in a county when the number of over-
lapping jurisdictions in that county changes. In the United States, increasing
jurisdictional overlap in a county from the 25th to the 75th percentile (this
is a move from 2 to 5 overlapping jurisdictions) leads to an 11% increase in
government revenue, about $130 per capita. Moreover, this increase in revenue
comes with no appreciable increase in government services, suggesting that it
really is the result of common pool incentives, rather than expanding service
provision.
4.4 Policy Interventions
All of ourmodels point to a commonpolicy prescription. If a policymaker could
get people to internalize their externalities, outcomes could be vastly improved,
making everyone better off. But how?
4.4.1 The Failure of Persuasion
A common intuition is that we could achieve a better outcome by simply ex-
plaining to people how much better off they would be if everyone internalized
their externalities. It is important to see that thiswill notwork. Let’s think about
the public goods model from Section 4.2.
The incentive for an individual to undercontribute to public goods
persists even if players believe everyone else will do the socially optimal thing.
Externalities 121
5000
4000
3000
2000
1000
20 40 60
N
U
ti
li
ty
80 100
Individual payoff if everyone
does equilibrium effort
In
di
vi
du
al
pa
yo
ff
if
ev
er
yo
ne
els
e d
oe
s fi
rst
-b
es
t e
ffo
rt
an
d
in
di
vi
du
al
ch
oo
se
s e
ffo
rt
1/
2
Ind
ivid
ual
pa
yof
f if
ev
ery
one
doe
s fi
rst-
bes
t ef
for
t
Figure 4.3. An individual’s payoff is higher if everyone else does the first best level of
effort and she does her individual best response.
In particular, if I believe that all other players will choose effort N2 , I still want to
choose effort 12 . Yes, I am better off with everyone (including me) choosing the
first-best level of effort (N2 ) than with everyone choosing the equilibrium level
of effort ( 12 ). But I am even better off if everyone but me chooses the first-best level
of effort and I get to free ride on them. In particular, my payoff if everyone but me
chooses N2 and I choose
1
2 is
(N − 1)N
2
+ 1
2
− 1
2
2
= 2N
2 − 2N + 1
4
,
which is even larger than the payoff under the first-best: N
2
4 . (Check if you want
to practice your algebra.) This point is illustrated in Figure 4.3.
The same is true in the tragedy of the commons. An agreement to each
run fewer than 30 boats is not self-enforcing. Indeed, if firm 1 knew that firm
2 would run, say, 20 boats, firm 1 would exploit the greater fish density by
running even more boats than in equilibrium. You can see that fact through
the following calculation:
BR1(20) =
90 − 20
2
= 35.
Even though both firms are better off under a deal where they each run fewer
than 30 boats, neither firm has an incentive to honor such a deal.
The point that players do not internalize their externalities, regardless of
what others do, is important for two reasons.
122 Chapter 4
First, as I’ve already indicated, a common reaction to this type of model is
to say, “This argument doesn’t make any sense. If everyone thought like this,
nothing would get done. So let’s just explain that to people and they’ll act
differently.” But that response doesn’t hold water. Suppose it was the case that
everyone didn’t “think like this.” Indeed, suppose you knew that everyone else
in your society would contribute a lot to producing a public good (or attending
a protest). Then it is still a best response for you to shirk.
Second, this logic highlights the challenge for policy interventions. It is not
enough for a leader to explain that everyone would be better off if everyone
would pitch in. True as that might be, if everyone else is pitching in, I still
don’t want to. And if everyone faces that same calculation, then we are right
back where we started—underproviding public goods, over-consuming the
commons, and so on. Some more active kind of policy intervention is called
for in these circumstances. Indeed, this is why we typically think of providing
public goods—national defense, environmental protection, scientific research,
roads, air traffic control, safety from enormous rocks falling from space, and so
on—as one of the essential roles of government.
4.4.2 Pigovian Subsidies and Taxes
Taxes and subsidies are the most direct way to induce people to inter-
nalize their externalities. When an activity imposes negative externalities, a
tax incentivizes people to do less of it. When an activity imposes positive
externalities, a subsidy incentivizes people to do more of it. These kinds of
subsidies or taxes are often referred to as Pigovian, after the economist Arthur
Cecil Pigou. Examples of such policies include carbon taxes—designed to curb
the use of fossil fuels, which impose negative externalities—or subsidies for
scientific research—designed to expand the creation of scientific knowledge,
which imposes positive externalities.
Let’s look at how a Pigovian subsidy works in a bit more detail in our public
goods model. (In the exercises you can explore a Pigovian tax in our Tragedy of
the Commonsmodel.)
Suppose a subsidy, σ , is paid to each player in our public goods game for
each unit of effort she contributes. We must collect revenue through taxation
to fund the subsidy. Unfortunately, taxation itself results in some inefficiencies.
This might be due to reduced incentives for work, distortions in behavior
to focus on less productive tasks that are taxed at a lower rate, the need to
build a bureaucracy to collect the taxes, or what have you. We will model this
inefficiency in as simple a way as possible. It costs taxpayers $τ > $1 for each
dollar of revenue the government requires. That is, to disburse $T in subsidies,
the government must collect $T × τ in revenues.
Assume that each member of society pays an equal share of the tax burden
to fund subsidies for everyone other than herself. For instance, suppose Player i
Externalities 123
earns a subsidy of ei × σ . Then each of theN − 1 other taxpayers must pay taxes
of ei×σ×τN−1 to fund Player i’s subsidy. This implies that, if tax revenues of T are
needed to fund the subsidies for all citizens other than Player i, then Player i
pays a total tax equal to T×τN−1 .
Suppose Player i believes everyone else will use the strategies given by e−i. If
the subsidy is σ , Player i’s best response solves
max
ei
Public Goods
︷ ︸︸ ︷
e1 + e2 + . . . + ei + . . . + eN +
i’s subsidy
︷︸︸︷
eiσ −
i’s costs
︷︸︸︷
e2i
−
i’s tax burden
︷ ︸︸ ︷
(e1 + e2 + . . . + ei−1 + ei+1 + . . . + eN)στ
N − 1 .
Taking the first-order condition, and labeling i’s best response given the subsidy,
BRi(e−i, σ), we have
1 + σ − 2BRi(e−i, σ) = 0.
This first-order condition looks much like the first-order condition without a
subsidy. (See Equation 4.1.) The key difference is that the marginal benefit of
contributing to the public good is now larger, reflecting the presence of the
subsidy.
Rearranging, an individual’s best response is now to contribute
BRi(e−i, σ) =
1 + σ
2
. (4.6)
If we set the subsidy at σ = 0, then people will each choose the level of effort
they did in our original model, 1/2. If we set the subsidy at σ = N − 1, then
people will choose the first-best level of effort:
BRi(e−i, σ) =
1 + N − 1
2
= N
2
.
The intuition is simple. The subsidy that induces players to choose the first-
best level of effort is the one that makes them fully internalize the positive
externalities of effort. The externalities from effort are the benefit given to
the N − 1 other people in society. Thus, the subsidy that fully internalizes the
externalities must provide Player i with the benefit that all the N − 1 other
people enjoy.
Importantly, σ is not the socially optimal subsidy. Because raising revenues
to pay for the subsidies is itself costly, the social welfare maximizing subsidy
balances the benefits of increased public goods that higher subsidies induce
and the costs of increased distortionary taxation that higher subsidies require.
124 Chapter 4
The socially optimal subsidy, therefore, lies somewhere between zero and σ . We
explore this in detail in Section 4.5.
4.4.3 Regulation
An alternative to a Pigovian subsidy or tax is to directly regulate the exter-
nality generating activity. If the government can mandate how much carbon
people can emit, how many fish a firm can catch, how much medical research
scientists must do, and so on, then it is straightforward to implement the
utilitarian optimum. Of course, problemsmay arise.
One problem with direct regulation is that the government must monitor
the relevant activities. It might be, for instance, much easier to impose a tax on
carbon at one or two points in the production process than to monitor all the
end uses of carbon.
A second problem is that the government may not know precisely what
the optimal level of activity is. Hence, it may not be certain exactly how to
regulate. This, of course, is also a problem for the Pigovian approach. If the
government doesn’t know the optimal level of activity, it is uncertain what
the right regulation or the right Pigovian subsidy or tax is. We will return to
the issue of what the government does when it lacks relevant information in
Chapter 9.
A third important downside to direct regulation, relative to the Pigovian
approach and related to the information problem, is flexibility. Suppose the
government wants to limit carbon emissions because of negative externalities.
At the time it decides to pursue this policy goal, perhaps the most efficient
way to do so is to shift to some mix of natural gas and renewable energy.
But, over time, there may be technological innovations that suggest even
better alternatives. One wants a policy that allows firms to switch to those
better solutions and, as importantly, gives firms incentives to look for such
innovations. If the government promulgates a regulation that simply says that
x percent of an industry’s energy needs must be met with natural gas and y
percent must be met with renewables, carbon emissions will be reduced. But
firms will not be able to flexibly shift to new alternatives as they become
available and, so, will not have incentives to look for such alternatives. By
contrast, if the government imposes a Pigovian tax on carbon, firms have
incentives to avoid carbon as inexpensively as possible and, so, have incentives
to innovate.
4.5 The Theory of the Second Best
No policy intervention is perfect. Any policy lever that the government pulls to
address some issue is likely to cause at least some new problems in some other
domain. Hence, the art of designing good policy involves balancing benefits
Externalities 125
and costs. It is this insight that leads to oneof themost important ideas in policy
analysis—the theory of the second best (Lipsey and Lancaster, 1956).
As we’ve already discussed, we use the term first best to describe the efficient
outcome. The secondbest, by contrast, is the best outcome that canbe achieved,
given all the constraints faced by the government. One of the most important
lessons that comes from the theory of the second best is the following. When
facedwith a situation inwhich there are constraints that imply thatmatterswill
not be efficient in one domain, it is not always the best policy to try to achieve
efficiency in some other domain.
To be a little less abstract, let me give you a famous example of the theory
of the second best. It is a well-known fact from basic microeconomics that
monopolies create inefficiency. A monopolistic firm has incentives to hold
productiondown, thereby raising prices andprofits. This is inefficient because it
creates a situation inwhich there are consumerswhowould behappy to buy the
monopolist’s product for more than the monopolist’s marginal cost of produc-
tion, butwho are left unserved. Forcinghigher production—through regulation
or increased competition—increases utilitarian social welfare. Hence, standard
policy advice is to break upmonopolies.
But now suppose there is a monopolist in an industry, say mining, that
imposes negative externalities through pollution. Moreover, suppose that this
particular type of mining is inherently polluting—there is simply no way to
do it without producing the pollution. Is it still a good idea to break up the
monopoly?
Here, there are two domains of concern for social welfare—the inefficiency
associated with monopolistic underproduction and the inefficiency associated
with externalities from pollution—and so there are competing effects of break-
ing up the monopoly. On the one hand, production goes up, prices go down,
and more consumers are served. This tends to increase social welfare. On the
other hand, production goes up, so the negative externalities from pollution go
up. This tends to decrease social welfare.
The optimal policy regarding how competitive the mining industry should
be must balance these costs and benefits of increased production. The second-
best policy optimally balances this trade-off. The key is that, because of the
constraint that says that matters will not be efficient in the pollution domain,
the second-best policy involves less competition (and, so, less production)
in the mining industry than would the first best (a completely competitive
market).
The theory of the second best is critical for thinking about the optimal use
of Pigovian taxes and subsidies. Pigovian taxes and subsidies offer a powerful
lever that policymakers can use to get decision makers to internalize their ex-
ternalities. However, like any policy intervention, they are not perfect. As we’ve
already discussed, the use of taxes to collect government revenue creates costs.
126 Chapter 4
We captured such costs in Chapter 4.4.2 by assuming that it costs taxpayers
$τ > $1 for each dollar of revenue the government requires. Let’s see this more
specifically in our public goods model.
4.5.1 The Second-Best Pigovian Subsidy
Given that taxes are distortionary, the theory of the second best implies that
the subsidize-and-tax plan that implements the first best, σ , is not the socially
optimal subsidize-and-tax plan. Inefficiencies on one dimension (distortionary
taxes) imply that the optimal policy does not achieve complete efficiency on
another dimension (the first-best level of public goods). This is a subtle and very
important point, so I want to spend a bit of time on it.
We call the level of public goods provided under the socially optimal
subsidize-and-tax plan the second best. Here, the first best is the socially optimal
level of public goods unconstrained by concerns about how you achieve it. The
second best is the level of public goods that is socially optimal, taking into
account the unfortunate inefficiencies created by the very policy interventions
meant to get us closer to the first best. The secondbest, then, is the best outcome
that society can actually hope to achieve.9 An important, and sometimes con-
fusing point given the terminology, is that the second-best policy yields higher
social welfare than the policy that induces the first-best action.
Definition 4.5.1. The second-best policy is the policy that maximizes the
utilitarian social welfare, taking into consideration all the various effects
of the policy. The second-best action is the action players are induced to take
when the second-best policy is implemented.
Let’s solve for the secondbest in our public goods game. Todo so,we are going
to engage in an analysis that is somewhat different than what we have done
previously. In Equation 4.6 we solved for the level of effort each individual will
take, in equilibrium, for any given subsidy σ . Our task now is the following:
1. We take that equilibrium effort as a function of the subsidy, σ , as given.
2. Given the equilibrium effort induced by a given subsidy, σ , we calculate
the utilitarian social welfare as a function of σ .
3. We find the σ that maximizes that social welfare. The σ that does so
is the second-best subsidy and the effort it induces is the second-best
effort.
9As we will emphasize in Part III, even achieving the second best is not a realistic goal, since
policymakers have their own incentives to pursue policies other than the social optimum.
Externalities 127
Recall, fromEquation 4.6, that for any level of subsidy, σ , each individual will
choose effort 1+σ2 . Let’s label that level of effort
e∗,σ = 1 + σ
2
.
To fund such a subsidy for theN − 1 other people, an individual must pay a tax
equal to
(N − 1) × e∗,σ × σ × τ
N − 1 = e
∗,σ × σ × τ .
Hence, for a given subsidy, σ , an individual i’s payoff is
Public Goods
︷ ︸︸ ︷
N × e∗,σ +
i’s subsidy
︷ ︸︸ ︷
e∗,σ × σ −
i’s cost
︷ ︸︸ ︷
(e∗,σ )2 −
i’s tax burden
︷ ︸︸ ︷
e∗,σ × σ × τ .
The first term is the payoff from the public goods created, the second term is
individual i’s personal subsidy, the third term is individual i’s cost of effort, and
the fourth term is individual i’s tax burden. Substituting for e∗,σ = 1+σ2 , this can
be rewritten:
N
(
1 + σ
2
)
+
(
1 + σ
2
)
σ −
(
1 + σ
2
)2
−
(
1 + σ
2
)
στ .
A total of N people make this same payoff. So, given the equilibrium effort
and taxes induced by a subsidy σ , the utilitarian social welfare as a function
of σ is
U(σ ) = N
[
N
(
1 + σ
2
)
+
(
1 + σ
2
)
σ −
(
1 + σ
2
)2
−
(
1 + σ
2
)
στ
]
.
To find the second-best subsidy, we maximize U by differentiating with respect
to σ and setting the derivative equal to zero (labeling the resulting subsidy
σ SB, for second best). Doing so, and rearranging, shows that for any τ < N, the
second-best subsidy is10
σ
SB = N − τ
2τ − 1.
This implies that the second-best level of effort is
e∗,σ
SB = 1 +
N−τ
2τ−1
2
= N − 1 + τ
2(2τ − 1) .
There are three points worth noting.
First, themore inefficient is taxation (higher τ ), the lower are the second-best
subsidy and effort.
10If τ ≥ N, then the inefficiency of taxes is so large that it swamps the benefits of internalizing
externalities, so it is optimal to offer no subsidy.
128 Chapter 4
400
300
200
100
10 20 30
N
τ = 1.25
τ = 1.5
U
ti
li
ty
40 50
Welfare under σSB
Welfare under σSB
Welfare with no subsidy
Welfare with no subsidy
Welfare under σ
Welfare under σ
150
100
50
10 20 30
N
U
ti
li
ty
40 50
Figure 4.4. For two different levels of tax inefficiency (τ = 1.25 and τ = 1.5), the figures
show individual welfare (as a function of the size of society) under the second best
subsidy, the subsidy that implements the first best effort, and no subsidy.
Second, for any τ that is greater than 1 and less than N, social welfare is
higher under the second-best subsidy than with no subsidy or with the subsidy
that implements the first-best effort. This fact is illustrated in Figure 4.4, which
shows individual payoffs under each of these policies for two different values
of τ . A point worth noting from the figure is that, as society gets large, such
that externalities matter a lot, it becomes particularly important to implement
a good subsidy policy.
Externalities 129
Third, for any τ > 1, the second-best subsidy is less than the subsidy that gets
people to choose the first-best effort:
σ
SB = N − τ
2τ − 1 < N − 1 = σ .
This straightforwardly implies that the second-best level of effort, and there-
fore the second-best level of public goods provided, is in between the no-
intervention equilibrium level of public goods and the first-best level of public
goods.
This is perhaps easier to see graphically. In the first panel of Figure 4.5, the
dotted line shows the subsidy that implements the first-best level of effort
for the case where society has 1000 people in it. As we have already seen,
this subsidy is σ = N − 1 = 999. The solid curve shows the second-best (i.e.,
optimal) subsidy as a function of how inefficient taxation is. When τ = 1,
taxation is not at all inefficient. That is, each dollar of taxes collected turns
into a dollar of subsidy. As you can see, in this case there is no trade-off, so the
second-best subsidy is the one that implements the first-best level of effort. But
as taxation becomesmore inefficient (i.e., τ gets larger), the second-best subsidy
gets smaller and smaller.
This logic carries through to the second panel of Figure 4.5. The dotted line
shows the first-best level of effort. As we’ve already seen, this is N2 = 500. The
solid curve shows the effort that will be chosen if the government imposes the
second-best subsidy. Again, as we saw above, this is e∗,σ
SB = N−1+τ2(2τ−1) . Finally, the
dashed line is the effort chosen in equilibrium if there is no subsidy, e∗ = 12 . The
figure shows that if taxation is not very inefficient, then the second-best effort
gets very close to the first-best effort. (Indeed, if τ = 1, so that taxation is not
at all inefficient, then second-best effort is equal to first-best effort.) However,
as taxation becomes more inefficient (i.e., τ gets big), this is no longer the
case. As we saw in the first panel, the subsidy gets smaller and smaller. And,
consequently, as we see in this panel, effort gets smaller and smaller. Indeed, as
τ gets very large, the second-best subsidy goes to zero and the second-best effort
approaches the equilibrium effort with no subsidy.
4.6 Alternative Responses
While regulation and Pigovian taxes or subsides are the most straightforward
policy solutions to externalities problems, they are not the only approach.
Below we consider various less direct ways of addressing externalities. Some
of these require intervention by the policymaker much earlier in the process.
Others suggest the possibility that society might, sometimes, be able to solve
these problems without a policy intervention, or at least with a less prescriptive
intervention.
130 Chapter 4
1000
800
600
400
200
0
1 2 3
τ
5 74 6 8
500
400
300
200
100
0
1 2 3
τ
5 74 6 8
Subsidy that implements first-best effort
σ– = N – 1
Second-best subsidy as a function of τ
σSB = N – τ—
2τ – 1
First-best effort: eFB = N—
2
Effort with no
subsidy: e* = 1—
2
Second-best effort as a function of τ:
e*,SB = N – 1 + τ—
2(2τ – 1)
E
ff
o
rt
Su
b
si
d
y
Figure 4.5. The upper panel shows the subsidy that implements the first best effort and
the second best subsidy as a function of τ , for the case of N = 1000. The lower panel
shows the first best effort, the second best effort, and the equilibrium effort with no
subsidy.
4.6.1 Altruism
We’ve seen that simple persuasion is unlikely to solve externalities prob-
lems. But that is not to say that things wouldn’t be better if people had a
greater sense of obligation to one another. In the models we’ve looked at,
people’s preferences are entirely focused on their own individual well-being.
Externalities 131
If people had direct concern for one another’s well-being, they would (at least
partially) internalize their externalities. So, if society can find ways to teach
or persuade people to feel more altruistically toward one another the situation
might improve.
Let’s see this in our model of collective action. Suppose that an individual
in that model values benefits to other people, as well as benefits to herself.
Let α ∈ (0, 1) be the amount she values benefits to another person relative to
benefits to herself. This change in preferences could have a big effect on her
behavior.
Consider an example with N people, each of whom values the outcome
at $100 and finds the cost of participating to be $10. A person, i, who be-
lieves n other people will participate has an expected payoff from participating
given by
n + 1
N
(
$100 + (N − 1) × α × $100) − $10.
The first term reflects the probability of success times the $100 benefit of success
directly enjoyed by person i plus the α-share of $100 per person (for all N − 1
people other than person i) that person i internalizes in terms of her concern
for the benefits to others.
Person i’s payoff from not participating is
n
N
(
$100 + (N − 1) × α × $100) .
Comparing, she participates if
α ≥ 1
10
(
N − 10
N − 1
)
.
The right-hand side is bounded above by 110 . Hence, in this example, even
with just 10% altruism, it is an equilibrium for everyone to participate. People
have less of an incentive to free ride when concern for others leads them to
internalize at least some of the positive externalities they impose on others.
Of course, it remains an open question whether you can actually educate
or persuade people to have this kind of altruistic view. You might not want to
count on it.
4.6.2 A Market in Externalities
Anotherway tomove toward efficiency in the face of externalities is to clearly
define property rights and facilitate private exchange. That is, assign someone
132 Chapter 4
the right to impose an externality and then make it easy for that person to
sell that right to the person (or people) who will bear the externality. Let’s
see how this works in the context of another famous example of negative
externalities.
Suppose that train tracks run through a neighborhood with one resident.
The railroad company gets a net benefit, B > 0, from running the trains. The
resident of the neighborhood suffers a cost,C > 0, from the trains running, due
to pollution (or what have you). Assume both the railroad and the resident have
quasi-linear preferences.
In this model, running trains imposes a negative externality on the resident
of the neighborhood. (Alternatively, we could say that the resident of the
neighborhood living in peace and quiet imposes a negative externality on
the railroad.) When the railroad decides whether to run trains, it ignores the
resident’s costs. Hence, the railroadmight make a socially suboptimal decision.
Indeed, the railroad alwayswants to run trains, sinceB > 0. But it is only socially
optimal to run trains if B > C.
Let’s do a little thought experiment. Imagine two property rights arrange-
ments:
1. The railroad owns the right to decide whether or not trains run.
2. The neighborhood resident owns the right to decide whether or not
trains run.
If the railroad and resident can negotiate costlessly, then the first best will be
achieved regardless of who owns the property right. To see this, we’ll break our
example up into two cases: (i) when it is socially optimal to run trains (B > C)
and (ii) when it is socially optimal not to run trains (B < C).
Start by assuming B > C, so running trains is socially optimal. Now, imagine
the railroad owns the property right. What will happen? The railroad makes a
profit of B from running the trains. The resident is willing to pay up to C not to
have the trains run. But B > C, so the resident is not willing to pay the railroad
enough to convince it not to run trains. Hence, trains run.
Now suppose the resident owns the property right.Whatwill happen?Again,
the railroad makes a profit of B from running trains and the resident bears a
cost of C. Since B > C, the railroad is willing to pay the resident more than C
to be allowed to run trains. The resident finds this deal worthwhile and sells
the railroad the right to run trains. Hence, just like when the railroad owns the
property right, trains run.
The same logic applies if running trains is inefficient (i.e., if B < C). If the
railroad owns the property right, the resident is prepared to pay the railroad
more than B not to run trains. Hence, the railroad won’t run trains. If the
resident owns the property right, the railroad is not willing to pay enough to
Externalities 133
convince the resident to let it run trains, so trains won’t run. Either way, trains
don’t run.
What havewe seen? If transactions between the railroad and the resident can
be made without cost, then trains run if it is socially optimal and don’t if it is
not, regardless of who owns the property right. Of course, the final individual
welfares depend on who owns the property right, since the property right is
valuable. So the point is not that the assignment of property rights is irrelevant
for individual welfare. It simply doesn’t affect whether or not trains run because
the socially optimal action maximizes the size of the pie. And with costless
transfers, the two sides always want the largest amount of total utility to split
between themselves.
The logic illustrated above is an example of an idea known as the Coase
theorem, after the economist Ronald Coase. If the right to impose an externality
can be bought and sold without transaction costs, and if the property right to
the externality is clearly defined and enforced, then bargaining between the
concerned parties leads to efficient outcomes.
It isworthnoting that the examplewe just analyzed exhibited two interesting
features:
1. The outcome is Pareto efficient.
2. The outcome (trains run or not) is invariant to the initial assignment
of property rights.
As I discussed in the introduction to this book, it is important, when thinking
about a model, to ask which features of it are robust and which might not
stand up to a small change in assumptions. It turns out that the first feature of
this model—that bargaining between parties without transaction costs yields
a Pareto efficient outcome—is pretty robust.11 However, the second feature of
the model—that the actual outcome is invariant to the assignment of property
rights—depends on some special assumptionswemade. In particular, this result
need not hold if players don’t have quasi-linear preferences.
To see this, suppose the resident has payoffs frommoney given by the square
root of her final wealth and that she starts with wealth w > C2. Let’s see when
she’d now be willing to buy the property right if the railroad owns it and when
she’d be willing to sell the property right if she owns it.
If the railroad owns the property right, the resident would be willing to buy
it from the railroad for an amount t if
√
w − t > −C + √w,
11Though there is an important caveat. Myerson and Satterthwaite (1983) show that if people
don’t know each other’s preferences (i.e., the railroad is uncertain ofC and the resident is uncertain
of B), then bargaining is not certain to yield an efficient outcome, even when transaction costs are
zero.
134 Chapter 4
which is true if
t < 2C
√
w − C2.
Assuming the railroad still has quasi-linear preferences, it is willing to sell for
t ≥ B. Hence, if the railroad startswith the property right, the outcomewill be:
• The railroad runs trains if B > 2C√w − C2.
• The resident pays the railroad to not run trains if B < 2C√w − C2.
Now suppose the resident owns the property right. She is willing to sell it to
the railroad for an amount t if
−C +
√
w + t > √w,
which is true if
t > 2C
√
w + C2.
The railroad is willing to pay any amount t < B. So, if the resident starts with
the property right, the outcome will be:
• The railroad pays the resident to allow trains to run if B > 2C√w + C2.
• The resident prevents trains from running if B < 2C√w + C2.
In all cases, the outcome is Pareto efficient—there does not exist another
outcome that makes at least one person better off and no one worse off. But
whether or not trains run is not invariant to the initial assignment of property
rights. If the railroad owns the property right, trains run if B > 2C
√
w − C2. If
the resident owns the property right, trains run if B > 2C
√
w + C2, which is a
more demanding requirement.
Leaving aside outcome invariance, the Coase theorem raises a provocative
question: given that allowing for buying and selling externalities gets us Pareto
efficiency, why are we worried about externalities at all? There are several
answers.
First, in many circumstances it may be infeasible or undesirable to define
property rights. What would it mean to give one person or another a property
right to clean air, the oceans, or the internet? How would we decide who owns
that right? Surely there are things which, because of our shared humanity, we
must actually share in common.
Second, even if we are prepared to dole out property rights to the air and
seas, how would one think about enforcing those property rights? If I own
one patch of sea and you own another, but fish can swim between them, who
Externalities 135
owns the right to catch the fish? If a river runs throughmultiple countries, and
each depends on it for drinking and agriculture, does it make sense to say one
country or another owns a property right to the water? (For a real example of
conflict over such a question, consider the Jordan River.) Similar problems exist
for oil reserves, clean air, and so on. Thus, technological feasibility is often a
constraint on establishing and enforcing property rights. If property rights can’t
be enforced or defined, how can they be traded?
Third, a key assumption of these efficiency results is that the railroad and
resident can reach agreements and transfer utility for free. In actuality, such
transactions require attorneys, loans, bankers, meetings, and so on. As a result,
it could well be that B > C and yet, if the resident owns the property right and
there are transaction costs (T) that are large (T > B − C), it is not worth it to
the resident and the railroad to reach a deal whereby trains are run. Hence, the
presence of transaction costs can prevent us from achieving efficiency.
A final issue involves the presence of multiple parties. The example we
looked at involved two parties reaching an agreement. Things become more
complicated when there are multiple parties, some winners and some losers
from a transaction. Imagine that instead of a railroad and a resident, there
was a railroad and a collection of many residents. Those residents might like
to negotiate with the railroad to reach a Coasean agreement, but they may
face an internal collective action problem. That is, as in our discussion of
diffuse interests in Chapter 4.2.3, theymay fail to organize to negotiate, leaving
opportunities for Pareto improvements between the residents and the railroad
unfulfilled.
For all of these reasons, while it is always important to think about these
sort of decentralized policy solutions, we cannot use the Coase theorem to
justify ignoring the problem of externalities and hope that clear assignment of
property rights will always solve the problems associated with them.
4.6.3 Ongoing Relationships and Self-Organization
In her classic book Governing the Commons, Elinor Ostrom tells the story
of water irrigation in the Spanish cities of Murcia and Orihuela. The Segura
River runs through these cities on its way to the Mediterranean. Water is scarce
in the region and so the river plays a critical role in local agriculture. This
creates an externalities problem akin to the tragedy of the commons. Individual
farmers can extract water from the river to irrigate their fields. But there is not
enough water for everyone. The social optimum involves sharing the water.
But upstream farmers have incentives to extract as much water as they need,
leaving too little for those downstream.
During the Middle Ages, no government authority regulated water use in
these cities. And, so, based on our analysis thus far, one might have expected
that terribly inefficient outcomes prevailed. But Ostrom reports otherwise.
136 Chapter 4
Defect
–1, 3
Cooperate
Player 2
Cooperate
Defect
Player 1
2, 2
0, 03, –1
Figure 4.6. Prisoner’s Dilemma.
The farmers of Murcia and Orihuela self-organized, creating norms of water
sharing whereby farmers had the right to irrigate their fields on a rotating
basis. The norms made it possible for everyone to have access to at least some
water.
There is a significant puzzle here.Our analysis suggests that upstream farmers
should not have been willing to follow the sharing norms. While such norms
create social efficiency, it is individually rational to defect from such an agree-
ment and, instead, extract all the water you need. But according to Ostrom, the
water-sharing norms worked successfully for hundreds of years.
As Ostrom explains, the farmers did more than simply reach an agreement.
They created informal institutions to enforce the agreement. Farmers were em-
powered to monitor one another’s water use. Farmers found to be taking water
to which they were not entitled could be reported to the larger community and
punished (with fines, social sanctions, and so on). While there was no formal
governmental authority to enforce the agreement, the farmers were able to
self-enforce.
The key difference between this story and themodels of externalities we have
studied thus far is the ongoing nature of the relationship among the farmers.
In our models, people interact once and then the game ends. In reality, people
often interact with one another repeatedly. In settings where this ongoing
relationship is valuable, groups may be able to self-organize into cooperative
agreements. In such an arrangement, each individual has an incentive to
engage in good behavior tomaintain relationswith the community. Something
like this seems to be at the root of the success of the farmers of Murcia and
Orihuela. They were a small and sufficiently tight-knit community that
they could monitor one another and coordinate on punishing people who
misbehaved. And, in this way, they were able to avoid the tragedy of the
commons.
Let’s look at a model that incorporates this idea of ongoing relationships to
see how self-organization might emerge. To do so, I’ll focus on a particularly
simple model of externalities called the prisoner’s dilemma (represented in
Figure 4.6). Two people interact. Each can either deal honestly with the other
(cooperate) or cheat the other (defect). There is a payoff to cheating the other
Externalities 137
player. And there is a cost to being cheated—if they both cooperate, they engage
in a productive interaction.12
The dilemma is this. It is a best response to play Defect regardless of what
the other player will do. Hence, the game has a unique Nash equilibrium,
(Defect, Defect), even though that outcome is Pareto dominated by (Cooperate,
Cooperate). The prisoner’s dilemma has negative externalities—if you play
Defect, youmakeme worse off. Thus, you can think of this inefficiency coming
from a failure to internalize externalities.
To get a handle on the logic of ongoing relationships, we will study a model
of people playing the prisoner’s dilemma over and over again, indefinitely. In
Appendix B.7, I explain how we model players thinking about the value of
payoffs in the future. Here I assume you know that material. Players discount
future payoffs according to the discount factor δ ∈ (0, 1).
Suppose players use strategies that call on them to behave differently depend-
ing onhow they have interacted in the past. One such strategy is called theGrim
Trigger:
• Begin the game playing Cooperate.
• If we have both always played Cooperate in the past, play Cooperate
today.
• If either of us has ever played Defect in the past, play Defect today.
The Grim Trigger creates a benefit to cooperating. If I cooperate today, then
I anticipate that we will both cooperate in the future. But if I defect today, then
I anticipate both defecting forever after. Thus, defecting today means forgoing
the benefits of cooperating in the future. The hope is that this concern about
future payoffs is sufficient to get us both to play cooperatively today. Let’s see.
First, notice that if both players play the Grim Trigger, then they will in fact
cooperate with each other forever. How do I know this? The strategy calls on
players to start the game cooperating. It then calls on them to keep cooperating
as long as they have both always cooperated in the past. If they in fact both
play the Grim Trigger strategy, they will have always cooperated in the past, so
they will never actually have to switch to defecting. So if both players playing
the Grim Trigger is a Nash equilibrium, then the players are able to overcome
the social dilemma through repeated interaction. We determine whether both
players playing the Grim Trigger is a Nash equilibrium as we always do in a
12The prisoner’s dilemma got its name from the story that originally motivated it. Two people
jointly commit a crime. The police put the two criminals in separate rooms and offer each the
following deal: If you confess and your partner does not, I’ll let you go and I’ll throw the book at
him. If neither of you confess, I’ll still prosecute, but you’ll be convicted of a somewhat lesser crime.
If neither confesses, you’ll likely both get off with aminor charge.
138 Chapter 4
game—by asking whether either player has a unilateral incentive to change her
behavior.
Suppose the two players are in some period in which both players have
always cooperated in the past. Let’s focus on Player 1 (Player 2 is exactly
symmetric). To see if Player 1 has a unilateral incentive to change her behavior,
we assume Player 2 is using the Grim Trigger strategy and then ask whether
Player 1 can make a higher payoff by using some strategy other than the Grim
Trigger.
If Player 1 sticks with the Grim Trigger, then the two players will continue
to cooperate forever. So Player 1 anticipates that, if she sticks with the Grim
Trigger, she will get a payoff of 2 in every period. That is, she will make a
payoff of
2 + δ × 2 + δ2 × 2 + δ3 × 2 + . . . = 2(1 + δ + δ2 + δ3 + . . .) = 2
1 − δ .
What if, instead, she changes behavior by defecting? Then she will make
a payoff of 3 today, which is a short-term benefit. But in the future, Player 2
(who is assumed to play the Grim Trigger) will always defect. Thus, in all future
periods, Player 1willmake payoffs of atmost 0 (if she also defects). Hence, Player
1 thinks the payoff of her best unilateral change of behavior (which is to defect
forever) is
3 + 0 × δ + 0 × δ2 + 0 × δ3 + . . . = 3.
Player 1 faces a trade-off. On the one hand, if she unilaterally defects, she gets
a short-term benefit: making 3 today instead of 2. On the other hand, she pays
a long-term cost: making 0 in future periods rather than 2. Is this short-term
benefit worth the long-term cost? That depends on how much Player 1 cares
about future payoffs. In particular, there is not a profitable unilateral change of
behavior if
2
1 − δ ≥ 3 ⇒ δ ≥
1
3
.
Since Player 2’s incentives are exactly the same as Player 1’s, if we did this
calculation for Player 2 we’d find the same constraint.
If the players care enough about the future, then it is a Nash equilibrium of
the infinitely repeated prisoner’s dilemma for both players to play the Grim
Trigger. In this equilibrium, the players cooperate with each other, achieving
efficiency despite the social dilemma that exists in the one-shot game.
Here we have an equilibrium that appears roughly like the kind of self-
organized cooperation that Ostrom describes emerging among the farmers
of Murcia and Orihuela. Players use the leverage generated by their ongoing
Externalities 139
relationship to establish a kind of cautious trust, whereby they internalize
their externalities because of the threat of future punishment if they fail to
do so.
This is a very exciting result. Perhaps the social dilemma isn’t so bad after
all. In many important spheres, people interact repeatedly. The analysis and
example above suggest that, as long as people care enough about the long
run, they can self-organize to achieve efficient outcomes even without a policy
intervention. (Good news if you are a person. Bad news, perhaps, if you are
getting a public policy degree.) Before you despair of a career in public policy,
let’s think about how far we want to push this argument for non-governmental
solutions to social dilemmas.
OTHER EQUILIBRIA
Our analysis of the infinitely repeated prisoner’s dilemma shows that if peo-
ple care enough about the future, then the game has an equilibrium in which
players cooperate with one another. That said, it also always has equilibria in
which there is no cooperation.
To see this, consider the strategy profile in which both players always choose
Defect. This strategy profile is also an equilibrium of the repeated prisoner’s
dilemma. In any given period, regardless of what you do, the other player will
always defect in the future. Thus, you face a choice, period after period, of either
defecting (and making 0) or cooperating (and making −1). Clearly, if the other
player will always choose Defect regardless of what you do, your best response
is to always choose Defect. Hence, we have a Nash equilibrium in which players
never cooperate.
Let’s be clear about what thismeans. It is not the case, nomatter how patient
players are, that the only possible outcomeof the repeatedprisoner’s dilemma is
cooperative. It is always an equilibrium for players to defect against each other.
So, while a self-organized solution to the externalities problem is sometimes
feasible, there is no guarantee that it will happen.
This fact points to a potentially important role for leadership. Earlier we ar-
gued that neither communication nor moral suasion were likely to be effective
in situations characterized by externalities. But that need not be the case when
there is a possibility to use repeated interaction to achieve self-organized co-
operation. In such circumstances, good outcomes depend on society reaching
the right equilibrium. It might be that effective leadership and communication
can help push society in that direction by helping to organize self-enforcing
norms of good behavior and sanctions for bad behavior. And, since the good
outcome is in fact an equilibrium, if a leader can get people to settle on
that pattern of behavior, it will be stable. We will return to this theme in
Chapter 5.2.
140 Chapter 4
LARGE SOCIETIES
There is a cooperative equilibrium in the repeated prisoner’s dilemma when
the short-run benefits of defecting are outweighed by the long-run costs in
terms of forgone cooperation. Our analysis thus far indicates that this will be
true when players are sufficiently patient. But there are other factors, besides
patience, that might affect the long-run costs of defection and, thus, the
feasibility of self-organized solutions.
Suppose you live in a large society. Each day you interact with someone by
playing the prisoner’s dilemma. But youmay not interact with the same person
day after day. The relative anonymity offered by a large society significantly
lowers the costs of defecting. In a large society, if I defect against someone
today, odds are I won’t have to interact with that person again for quite some
time. Consequently, it probably won’t be until some point in the far future
that I suffer any punishment for my misdeeds. This suggests that, in large
societies, it may be harder for people to solve social dilemmas without policy
interventions.
To make this a bit clearer, let’s think about a model. There are N people
(with N even for simplicity). In each period, each person is randomly paired
with another person to play the prisoner’s dilemma. Players only observe what
happens in their own personal interactions, not what happens in interactions
in which they are not involved. The probability Player imeets Player j in a given
period is pi,j.
Consider a strategy profile in which everyone plays the following strategy,
which is analogous to the Grim Trigger:
• Play Cooperate with anyone you have never met before.
• If interacting with a player you have met before, Cooperate today if you
have both always played Cooperate against each other in the past.
• If interacting with a player you havemet before, Defect today if either of
you has ever played Defect against the other in the past.
Under what conditions is this modified Grim Trigger strategy profile a Nash
equilibrium in our game with a large society?
Suppose that twoplayers, i and j, are paired in someperiod and that theyhave
always cooperated with one another in the past. Let’s focus on Player i. If Player
i sticks with the Grim Trigger (i.e., cooperates), she will get a payoff of 2 in every
period inwhich she andPlayer j interact.Moreover, this interactionwill haveno
effect on her payoff when interacting with any other player. Call her expected
payoff from an interaction in some period in which she doesn’t interact with
Player j vi,−j. In any given period, she interacts with Player jwith probability pi,j
and with other players with probability 1 − pi,j. So, if Player i cooperates with
Externalities 141
Player j, she will make an expected payoff of
2 + δ (pi,j2 + (1 − pi,j)vi,−j
) + δ2 (pi,j2 + (1 − pi,j)vi,−j
)
+δ3 (pi,j2 + (1 − pi,j)vi,−j
) + . . . .
This can be rewritten as
2 + δ (pi,j2 + (1 − pi,j)vi,−j
) (
1 + δ + δ2 + δ3 + . . .) ,
which can be rewritten
2 + δ
1 − δ
(
pi,j2 + (1 − pi,j)vi,−j
)
.
What if, instead, Player i defects against Player j? She will make a payoff of
3 today, which is a short-term benefit. But in the future, Player j will always
Defect when they meet. Thus, in all future interactions with Player j, Player i
willmake a payoff of 0. Player i’s defection has no effect onher interactionswith
players other than j. So her expected payoff from interacting with a player other
than j in the future remains vi,−j. Hence, Player i’s expected payoff from her best
unilateral change of behavior (which is to defect against j forever) is
3 + δ (pi,j0 + (1 − pi,j)vi,−j
) + δ2 (pi,j0 + (1 − pi,j)vi,−j
)
+δ3 (pi,j0 + (1 − pi,j)vi,−j
) + . . . .
This can be rewritten as
3 + δ(1 − pi,j)vi,−j
(
1 + δ + δ2 + δ3 + . . .) ,
which is equal to
3 + δ
1 − δ (1 − pi,j)vi,−j.
Player i faces a trade-off similar to the trade-off in the two-person repeated
prisoner’s dilemma. On the one hand, if she unilaterally switches to defecting,
she gets a short-term benefit: making 3 today instead of 2. On the other hand,
she pays a long-term cost: making 0 in future interactions with Player j rather
than 2. But the long-term cost is lower than it was in the repeated prisoner’s
dilemma with only two players. This is because Player i does not interact with
Player j every period. We can compare the two expected payoffs in theN-player
game to find that there is not a profitable unilateral change in behavior if
2 + δ
1 − δ
(
pi,j2 + (1 − pi,j)vi,−j
) ≥ 3 + δ
1 − δ (1 − pi,j)vi,−j.
142 Chapter 4
Rearranging, this implies that Players i and j can cooperate if
δ ≥ 1
1 + 2pi,j
. (4.7)
There are a couple of things to note here. First, if pi,j = 1 (so that Players i and
jmeet every period), this condition reduces to δ ≥ 13 , precisely the condition we
got in the two-player repeated prisoner’s dilemma. This is as it should be.
Second, and more importantly, the smaller pi,j is (i.e., the less likely it is that
the two players meet in any given interaction), the higher δ must be for it to be
a best response for Player i to cooperate with Player j. This is intuitive. When
pi,j is very small, the cost of defecting is very low, since Player i will seldom
interact with Player j and, so, will only rarely be punished for defecting. Hence,
temptation is great and cooperation is hard to sustain—a fact that is reflected in
needing ever more patient players.
What might make pi,j small? Several factors come to mind. Two players may
be unlikely to interact if they are in different ethnic groups, live in different
areas, work in different industries, or are simply part of a larger society. In all of
these cases, cooperative behavior is harder to sustain among players who expect
not to see and interact with one another frequently. Self-organized solutions are
most likely to emerge in smaller or more tightly knit groups.
More generally, the model suggests that as the pool of people one interacts
with increases, it becomes harder and harder to sustain cooperation without
a policy intervention. To see this, suppose that all players are equally likely to
be paired. Then, for any pair (i, j), pi,j = 1N−1 . Given this, as society gets larger,
the probability of any two particular people interacting in any given period gets
smaller. Condition 4.7 tells us how patient players must be, as a function of the
size of society, for cooperation to be sustainable in equilibrium:
δ ≥ 1
1 + 2N−1
.
This condition is illustrated in Figure 4.7. As the figure shows, for even mod-
erately sized groups of potential partners, cooperation becomes difficult to
sustain.
This implies two key facts. First, small, tight-knit groups are more likely
than larger groups to successfully self-organize to solve externalities problems
without intervention. In large groups, players are too anonymous, resulting
in low costs to defection. Thus, while small groups are not guaranteed to find
cooperative equilibria (remember, non-cooperative equilibria always also exist),
it is more likely that doing so will be feasible for such groups.
Second, one key problem of using repeat play to achieve cooperation in
large groups is a lack of information. If players could observe how people other
Externalities 143
1.0
0.8
0.6
0.4
0.2
10 20
Cooperative equilibrium
No cooperative equilibrium
30
N
δ
40 50
Figure 4.7. How high δ must be to sustain cooperation in equilibrium, as a function of
the size of the population.
than those they directly interacted with behaved, then they could punish bad
behavior that was directed against others. Hence, institutions or actors that
facilitate information sharing might be a fairly non-intrusive way to facilitate
efficiency by allowing broader-based punishment strategies. As an example,
think of rating services on Amazon, eBay, or Uber, which allow cooperative
behavior to emerge among large groups of peoplewhodonot knowone another
at all. These ratings allow broad-based punishment for bad behavior. If a seller
were to cheat a buyer, the buyerwould report that seller’s bad behavior, allowing
other buyers to stop interacting with that seller. And if a buyer were to cheat a
seller, the seller would report that buyer’s bad behavior, allowing other sellers to
stop interacting with that buyer.
IMPERFECT MONITORING
Another problem that might limit the ability of people to achieve efficiency
without government intervention is imperfect monitoring. The use of pun-
ishment strategies requires that I know whether you defected against me or
not. But suppose there is some chance that I mistakenly believe you acted well
when you acted poorly or vice versa. In such a circumstance, whether or not
you are punished is tied less directly to your behavior, diminishing the costs
of defection and the benefits of cooperation. The effects of this are not unlike
the effects of a large society. If I think I will only be punished some of the time
if I defect (and will only be rewarded some of the time if I cooperate), then I
144 Chapter 4
am more inclined to defect. Hence, in an environment where the behavior of
individuals is difficult to observe or monitor, it is less likely that people can
successfully self-organize to solve externalities problems.
4.7 Takeaways
• A situation inwhichoneperson’s actions affect another person’s payoffs
is called a situation with externalities.
• Because people don’t take the externalities they impose on others into
consideration whenmaking decisions, externalities create socially inef-
ficient outcomes.
• Collective action and public goods provision are both examples of
situations with positive externalities. The commons is an example of a
situation with negative externalities.
• Pigovian subsidies for actions with positive externalities induce people
to internalize their externalities and move society in the direction
of Pareto improvements. Pigovian taxation of actions with negative
externalities does likewise.
• Typically, policy interventions that help people internalize their ex-
ternalities impose their own, new, inefficiencies. Hence, the socially
optimal policy intervention is typically not the one that actually gets
people all the way to the first best. Rather, it trades the benefits of
increased internalization of externalities off against the costs of the
intervention itself. The socially optimal intervention and the associated
actions are referred to as the second best.
• In settings with repeated interaction, it is sometimes feasible for groups
to self-organize a solution to externalities problems. Such self-organized
solutions aremost likely in close-knit and small groups. But even in such
groups, they are not certain to emerge.
4.8 Further Reading
Any intermediate microeconomics textbook will include an extensive discus-
sion of externalities. There are lots of good ones.
Mancur Olson’s The Logic of Collective Action is the classic statement of
the collective action problem, while Hardin (1968) articulates the tragedy of
the commons. Mankiw (2009) is a nice, accessible introduction to Pigovian
taxation.
Coase (1960) provides the intellectual foundations for the Coase theorem. It
is worth noting that Coase clearly believed that transaction costs were typically
high and, thus, that a purely market-based approach was not a feasible way of
addressing externalities problems.
Externalities 145
There is also much worth reading on the topic of decentralized solutions.
Elinor Ostrom’s celebrated Governing the Commons is an essential source on the
success and failure of self-organization.Milgrom, North, andWeingast (1990) is
a classic game theoretic and historical analysis of the role of repeat interactions
in self-organization. Fearon and Laitin (1996) discuss these issues in the context
of interethnic conflict and cooperation.
4.9 Exercises
1. Reanswer Problem 6 from Chapter 1 in light of the lessons of this chapter.
2. Consider an example of the collective actionmodel from Section 4.1 in
which there are one thousand people. Each individual values the outcome
at $100 and finds the cost of participation to be $10.
(a) Is it a best response for a player to participate or not participate?
Suppose, now, that you offer everyone a subsidy if they participate. The
subsidy is funded through inefficient taxation. Raising $1 of revenue costs
the taxpayers $τ . As in the chapter, an individual’s subsidy is funded by
everyone other than her paying an equal share of the necessary tax (so my
taxes go to fund everyone’s subsidy other thanmy own).
(b) What is the lowest subsidy that wouldmake it a best response for a player
to participate?
(c) Suppose the government were to offer that subsidy, so that everyone
were to participate. What would be an individual’s tax burden?
(d) Given this, what would be the social payoff with the subsidy?
(e) Given this, for what values of τ is it better for utilitarian social welfare to
offer this subsidy rather than offer no subsidy?
3. As we saw in Section 4.3, the first-best number of boats in the tragedy of
commons game is 45. But, if taxes are distortionary, then the socially
optimal (i.e., second-best) number of boats is not equal to the first best.
Let’s assume we tax each boat at a rate of t dollars and then redistribute the
revenues—giving the revenues collected from firm 1 to firm 2 and the
revenues collected from firm 2 to firm 1. As in Section 4.4, there is some
inefficiency associated with taxation—for each dollar distributed, the
government must collect τ > 1 dollars. That is, if the two firms run b1 and b2
boats, total taxes collected are t(b1 + b2), but firm 1 gets back only tb2τ and
firm 2 gets back only tb1
τ
. We can explore the second-best number of boats in
this setting.
146 Chapter 4
(a) Given the tax policy, t, what are firm i’s expected payoffs, if it believes
the other firmwill run b−i boats?
(b) Calculate firm i’s best response to the tax rate t and b−i boats by the other
firm (BRi(b−i, t)).
(c) By substituting one firm’s best response into the other’s, what is the
equilibrium number of boats each firmwill run, given a tax rate t ?
(d) Given equilibrium behavior, for any tax rate t, what is each firm’s total
payoff?
(e) Use your answer to the previous question to write down the utilitarian
social welfare as a function of the tax rate t.
(f) Use your answer to the previous question to compute the second-best
tax rate and the implied second best number of boats run by each firm.
(g) Show that the second best number of boats is larger than the first-best
number of boats run by each firm.
4. Consider the model of cleaning an apartment in Appendix A.2.3. Suppose
the government offers a subsidy, σ , for each unit of effort by each person. So
if person i chooses effort si, she receives a subsidy of σ × si.
The subsidy is funded through taxation. Each player pays the tax for the
other person’s subsidy. Moreover, taxation is inefficient. Each dollar of
subsidy paid costs the tax payer τ > 1 dollars. So if person 1 receives a
subsidy of σ × s1, then player 2’s tax burden is σ × s1 × τ .
(a) Write down each player’s utility given a strategy profile (s1, s2) and a
subsidy rate σ .
(b) Solve for each player’s best response as a function of the other player’s
strategy and the subsidy.
(c) Identify the Nash equilibrium level of effort by the players, given a
subsidy σ .
(d) Write down each player’s payoff in equilibrium as a function of the
subsidy.
(e) Use your answer to part (d) to write down the utilitarian social welfare as
a function of σ .
(f) Use your answer to part (e) to solve for the second-best subsidy and
effort.
(g) The first-best effort in this model is 2. Show, given the inefficiency of
taxes, that the second-best subsidy leads to higher payoffs than either no
subsidy or a subsidy that leads players to choose the first-best effort.
5. An influential argument makes the following claim: A well-functioning
democracy requires that voters actually knowwhat policies would be in
Externalities 147
their interests so that they can vote for politicians who implement such
policies. However, the argument continues, in a democratic system there is a
“public goods problem” with respect to information leading to
systematically bad vote decisions and, thus, policy choices in democracies.
(a) Explain what externality this argument is pointing to in claiming there
is a public goods problem.
(b) Consider the followingmodel. There are three voters a, b, and c and two
candidates advocating two different policies 1 and 2. None of the voters
knowwhich policy would be better for her. Moreover, the voters believe
it is equally likely that they each prefer either policy.
Each voter, individually, can either invest in becoming an informed
voter (at cost C) or not (at cost 0). If a voter invests, she learns the policy
she prefers, but she does not have the opportunity to communicate it to
the other voters. Moreover, let’s assume (for simplicity) that, were they
all informed, all the voters would prefer the same policy (i.e., there is a
correct policy). The payoff of having the correct policy chosen is B > C.
The payoff of having the wrong policy chosen is 0.
Assume all voters vote and that if a voter is uninformed she flips a coin to
choose between 1 and 2.
i. Suppose a voter expects the other two voters not to become
informed.What has to be true about the relationship between B and
C for her to become informed?
ii. Suppose a voter expects one of the other voters to become informed
and one of the other voters not to become informed. Under what
conditions on B and Cwill she become informed?
iii. Suppose a voter expects both other voters to become informed.
Under what conditions on B and Cwill she become informed?
iv. Given the answers above, there are two things that can happen in
equilibrium.What happens in equilibrium if C < B/4?What
happens in equilibrium if C > B/4?
(c) Compare this to a model with one voter who simply chooses the policy.
Under what conditions does this single voter become informed?
(d) How does the comparison of the results from parts (b) and (c) illustrate
the public goods problem in democracy?
(e) Suggest a policy one could implement to increase the number of voters
who become informed.
(f) What do you think would happen as we increased the number of voters
in part (b)?Why?
148 Chapter 4
6. Consider a public good created through costly effort by individuals. Since
there are positive externalities, the outcome is Pareto inefficient. As such,
the government decides to implement subsidies. But the tax used to fund
the subsidies also creates inefficiencies.
(a) Which is higher: the first-best or second-best level of public goods?Why?
(b) Is the utilitarian payoff higher if the government chooses the subsidy
that induces the first-best or second-best level of public goods?Why?
7. Describe a substantive policy issue (that I didn’t talk about in the chapter)
where you think that people are imposing (positive or negative)
externalities.
(a) Is the result of the externalities, in your example, toomuch or too little
of a particular kind of behavior relative to the social optimum?
(b) What sort of policy intervention do you thinkmight be effective at
mitigating the problem?
(c) Give at least one reason why the socially optimal policy intervention is
not the intervention that would give rise to the first-best original
behavior, but instead, some lesser amount of policy intervention that
gives rise to second-best behavior.
8. Amedical researcher is trying to cure a disease. For each unit of effort she
puts into her work, she generates a utility benefit of 10 for eachmember of
society. There are 1,000 people in society besides the medical researcher.
Themedical researcher doesn’t care about other people. She is in it for the
glory. For each unit of effort she puts into her work, she gets a utility benefit
of 1000 (which is inclusive of the 10 that she gets for being amember of
society, plus a payoff of 990 in glory). If she exerts effort e, she also suffers
cost e2.
(a) Themedical researcher’s payoff from exerting effort e is 1000e − e2.
What level of effort, e∗, will she exert?
(b) Suppose a policymaker who was a committed utilitarian (including
caring about the medical researcher’s glory, since the medical researcher
cares about it) was to choose the level of effort the medical researcher
exerts. That policymaker would add up the total utility in society
(including themedical researcher’s utility) from any given level of effort
and choose the level of effort that maximizes that aggregate utility.
i. What (social) utility function would the policymaker maximize?
ii. Would the policymaker like the medical researcher to exert more or
less effort than your answer to part (a)?Why? (Use words, not math,
to answer this.)
Externalities 149
iii. What level of effort, eFB, would the policymaker demand of the
medical researcher?
iv. Suppose that the policymaker wanted to implement this first-best
policy (eFB) by paying themedical researcher a subsidy σ for each
unit of effort. What level of subsidy, σ FB, must the policymaker offer
to get the medical research to choose the first-best level of effort?
(c) Suppose, now, that our policymaker can only pay for the subsidy
through inefficient taxation. In particular, assume that if a total subsidy
of eσ must be paid to the researcher, then a total amount of revenues 2eσ
must be collected. The tax burden will be shared equally by everyone
except the medical researcher (who pays no taxes). Assume taxes come
linearly out of the payoffs of eachmember of society. Suppose the
policymaker chooses the subsidy that maximizes the utilitarian payoff,
taking account of these taxes and the level of medical research.
i. What (social) utility function would the policymaker maximize?
ii. Will the subsidy she chooses, σ SB, be higher or lower than the
subsidy, σ FB, that implemented the first-best effort?Why?
iii. Calculate the second-best subsidy that the policymaker will
implement.
9. Two people, A and B, are deciding whether to put effort into producing a
public good or not. Each person, i, can either choose no effort (si = 0) or yes
effort (si = 1). The total public good produced isG = sA + sB. The cost of
doing no effort is 0. The cost of doing yes effort is 1.5. The payoff to a player
is the total public goods provided (G) minus her personal costs.
(a) Given a choice by player B, sB, write down player A’s utility from
choosing no effort.
(b) Given a choice by player B, sB, write down player A’s utility from
choosing yes effort.
(c) Comparing these two utilities, calculate player A’s best response
correspondence and write it down.
(d) Noticing that player B’s problem is identical to player A’s, what is the
unique Nash equilibrium of this game?
(e) What is the utilitarian optimum in this game?
(f) In four sentences or less, explain why the Nash equilibrium represents a
social dilemma and how this relates to the idea of positive externalities.
(g) Suppose that you can offer a subsidy of 1 for choosing yes effort, but that
for each person you pay that subsidy youmust collect tax revenue equal
to τ > 1. Assume that you will split the tax burden equally among the
two players, regardless of who participates. For what values of τ is it
Pareto improving to offer the subsidy-and-tax plan?
5
Coordination Problems
In 1933, the United States Congress passed the Tennessee Valley Authority
Act, putting in motion one of the largest economic development projects in
American history. The act created the Tennessee Valley Authority (TVA), a
federally owned corporationwith amandate to rapidlymodernize the economy
of the Tennessee Valley—a swath of land coveringmuch of Tennessee, Alabama,
Kentucky, and Mississippi—which was among the poorest and least-developed
parts of the United States.
Over the course of the 1940s and 1950s, the TVAbuilt dozens of hydroelectric
dams and hundreds of miles of navigation canals. It also invested in significant
new road networks, schools, and flood control. Kline and Moretti (2014) report
that during these two decades the TVA spent over $14 billion (measured in
2000 dollars). During the height of its spending in the 1950s, subsidies through
the TVA amounted to 10% of average household income per family in the
Tennessee Valley.
What was the effect of the TVA? In 1930, the Tennessee Valley had an
overwhelmingly agricultural economy. By the mid-1940s, it was the largest
supplier of electricity in the country. Moreover, Kline and Moretti find that
during the period of peak investment by the TVA (i.e., the 1940s and 1950s) the
ten-year growth rate in both agricultural and manufacturing employment was
10–12 percentage points higher than it would have been absent the TVA.
But most interesting are the different trajectories of the Tennessee Valley’s
agricultural andmanufacturing sectors. Once federal subsidies began to decline
(starting in the 1960s), not only did growth in the agricultural sector cease, but
the gains that had been made during the 1940s and 1950s disappeared. After
1960, counties in the TVA saw a 13–16 percentage point decrease in the ten-
year agricultural employment growth rate relative to non-TVA counties. This
decline was sufficiently large that, by the end of the twentieth century, Kline
andMoretti estimate the agricultural sector had declined on net.
Manufacturing is an entirely different story. Once federal subsidies stopped,
the extraordinary growth rates in manufacturing declined. But they did not
reverse. Indeed, Kline and Moretti show that manufacturing employment con-
tinued to grow at a rate approximately 3 percentage points higher in TVA
counties relative to non-TVA counties.
Coordination Problems 151
Kline andMoretti argue that the TVA affected agriculture andmanufacturing
so differently because of what are known as economies of agglomeration. There
are spatial returns to scale in certain industries. These returns to scale can come
from many sources. For instance, if many firms are producing similar products
in a particular city or region, then there are likely to be many qualified workers
available locally. This decreases the costs of production. Similarly, when multi-
ple firms in the same regionwork in the same industry, it becomes cost-effective
to invest in industry-specific infrastructure, attracts industry innovators, and
so on.
Such agglomeration economies give firms within an industry incentives to
coordinate on locating in specific regions. As the number of firms in some in-
dustry increases in a region, locating in that region becomes more attractive to
other firmswithin the same industry. It is typically thought thatmanufacturing
has increasing returns to scale as a result of economies of agglomeration (Green-
stone, Hornbeck, and Moretti, 2010), but that agriculture does not (Hornbeck
and Naidu, 2014).
Given this, it is not surprising that the effects of the TVA were long lasting
in manufacturing, but not in agriculture. The early investments from the
TVA spurred manufacturing growth which put in motion a virtuous cycle of
increasing returns. The TVA disappeared, but the agglomeration economy did
not, so a positive effect on manufacturing persisted. No such agglomeration
economy exists for agriculture. Thus, the early investments spurred agricul-
tural employment through straightforward subsidization, but did not create
increasing returns. Hence, once the subsidies disappeared, the positive effects
disappeared as well.
This example highlights many of the most important features of our sec-
ond type of social dilemma, coordination problems. In many situations, good
outcomes require actors to coordinate their behavior in the right way. But two
things can go wrong. First, actors may fail to coordinate entirely. For instance,
different companies within an industry may locate in different regions, never
realizing the benefits of agglomeration.
Second, actors may coordinate on a bad outcome, rather than a good out-
come. Think about the much-discussed problem of poverty traps in economic
development. The fundamental idea behind a poverty trap is a failure of
coordination. A poor country lacks infrastructure and human capital (this is
similar to the problems of a region lacking agglomeration economies). If that
poor country could attract outside investors, it could raise revenues to build
infrastructure and human capital. If an outside investor believes that other
outside investors are going to invest, she believes the poor country will raise
the necessary revenue and, thus, will want to invest herself. But if that outside
investor believes other outside investors are not going to invest, she doesn’t
believe the poor country will raise the necessary revenue and, thus, does not
152 Chapter 5
invest herself. Each investor wants to do what the other investors are going
to do, creating the possibility of a self-confirming poverty trap, whereby poor
countries stay poor because everyone believes they will stay poor.
Collier (2007) explicitly links poverty traps in Africa and parts of Asia to
agglomeration economies.He argues that in the 1980s and1990smanufacturers
moved production from the developed world to relatively stable, low-wage
countries in Asia. This set off the virtuous cycle of agglomeration, as those
economies grew, created infrastructure, and invested in human capital. Other
countries missed this initial wave of offshoring. And now, because they lack
both political stability and agglomeration economies, they are not attractive to
manufacturers. Thus, these countries are trapped in poverty, at least until the
wage differential between these truly poor countries and the middle-income
manufacturing countries of Asia grows large enough that manufacturers are
willing to relocate despite the absence of agglomeration economies.
There aremany situationswith the basic structure of a coordinationproblem.
For instance, the adoption of a new technology often involves coordination.
Whether you should purchase a Blu-ray or HD DVD player depends on which
will become the dominant technology. And that depends on whether more
people buy Blu-ray or HDDVDplayers. Thus, youwant to buy a Blu-ray player if
everyone else is going to buy a Blu-ray player and anHDDVD player if everyone
else is going to buy an HDDVD player, regardless of which is actually the better
technology. If you buy the wrong one, you will end up like all those people
with eight-tracks and Betamaxes in their basements. You can tell a similar story
about the adoption of business software (e.g., Excel vs. Lotus) and many other
technologies.
You might think similarly about whether to buy an electric or hybrid car.
Electric cars might be attractive, if the government and industry make an
investment in the necessary infrastructure (e.g., lots of charging stations or
exchangeable batteries). But the government and industry will only make such
an investment if lots of people buy electric cars. So, again, you want to do what
everyone else is doing.
An example closely related to the poverty traps story arises in thinking about
public schools in urban environments. A common concern is that educated
parents send their children to private schools, draining the public schools of a
valuable resource. If educated parents believe other educated parents will send
their children to the public schools, they might also be inclined to send their
children to the public schools. The key, for any given parent, is to coordinate—
sending their kids to the same kind of school as all the other educated parents.
Coordination games model these type of situations, characterized by what
we call strategic complementarities—the benefit to one person of taking some
action is larger the more that action is being taken by other people. Broadly
speaking, coordination games come in three varieties.
Coordination Problems 153
First, there are pure coordination games, inwhich the only thing players care
about is that they successfully coordinate. They are indifferent as towhat action
they coordinate on. Thismight, for example, describe the decisionofwhich side
of the road to drive on.
Second, there are coordination games with distributional consequences.
Consider national governments trying to harmonize financial standards. All
governments might agree that sharing a set of financial standards is good, as it
encourages trade and foreign investment. However, if different countries have
different economies, natural resources, financial institutions, and so on, then
theymay disagree on the optimal financial standards.
Third, there are coordination games with a Pareto dominated equilibrium.
That is, games where everyone wants to coordinate, but in which we can all
agree that coordinating ononeoutcome is better than coordinating on another.
Think about bank runs. Suppose that if everyone withdraws their money but
you don’t, then you lose all your money because the bank folds. But if nobody
withdraws their money, and you also don’t, you make a reasonable interest
rate. There are incentives to coordinate in such a scenario—if everyone else is
going to withdraw their money, you want to withdraw yours, but if everyone
leaves his or her money on deposit, you want to leave yours too. We can all
agree that not having a bank run is preferable to having one. So, although we
have coordination incentives, we prefer coordinating on one outcome rather
than another. The public versus private school example discussed above might
describe another such situation. Parents might prefer to coordinate on pub-
lic schools, thereby saving tuition expenses. Poverty traps are another such
example.
All three of these types of coordination games share some features. Impor-
tantly, we want to avoid coordination failure in all of them. But the last class of
games—those with a Pareto dominated equilibrium—also suggest another set
of issues. In particular, these games present the possibility of coordinating, but
on the wrong outcome.
In this chapter, we consider both kind of problems. In Section 5.1we focus on
coordination failure due to strategic uncertainty—a dilemma that can arise in
any of these situations. In Section 5.2 we turn our attention to coordination
traps—the problem of coordinating on the wrong outcome in games with a
Pareto dominated equilibrium.
5.1 Coordination Failure
For a company to list its shares on a stock exchange, that company must
comply with national securities regulations. One particularly important such
regulatory hurdle is producing books in compliance with relevant accounting
rules.
154 Chapter 5
Outlet
0, 0
Pump
Government
Hybrid
Electric
Car company
2, 2
2, 20, 0
Figure 5.1. A coordination game.
There are many stock exchanges in the world, including major exchanges
in Frankfurt, London, New York, Hong Kong, and so on. In order to facili-
tate access to global capital markets, companies would often like to list on
multiple exchanges. But historically there has been a problem. Each national
securities regulator imposes a different set of accounting standards. This lack
of harmonization forces companies that wish to list on multiple exchanges to
bear the significant costs of producing multiple sets of books. It also reduces
transparency for investors, since different accounting standards can produce
wildly different pictures of a company’s performance. For instance, Simmons
(2001) relates the story of the German company Daimler Benz deciding in
1993 to list on the New York Stock Exchange in addition to the Frankfurt
Stock Exchange. Under German accounting rules, Daimler reported a profit of
615 million deutsche marks for 1993. Under U.S. Generally Accepted Account-
ing Principles, it reported a loss of 1.8 billion deutschemarks for that same year.
The failure of coordination on a set of internationally recognized accounting
standards imposes unnecessary costs on stock exchanges, investors, and corpo-
rations. Yet it has persisted for decades.
Let’s study coordination failure in the simplest possible environment—a
two-player, two-action, pure coordination game. For instance, consider the
following model of a game between a car company and the government. The
car company must decide whether to invest in hybrid or electric technology.
The government must decide whether to encourage infrastructure investment
in fuel pumps or electrical outlets. The two players are equally happy with
hybrids or electrics becoming the new standard—but they want to coordinate.
The game is represented in Figure 5.1.
I will talk about this particular game, but it should be clear that the game
between the government and car company is just a metaphor for coordination
problems in general. Change the names of the players and actions and you
could think of this as a model of many different kinds of coordination—
companies deciding what type of technology to invest in, governments choos-
ing accounting standards, etc. Moreover, nothing that I am going to tell you
depends on this being a situation of pure coordination. The same issues arise in
all situations in which people have an incentive to coordinate—whether or not
there are, for example, also distributional concerns.
Coordination Problems 155
Outlet
0, 0
Pump
Government
Hybrid
Electric
Car company
2 + θC, 2 + θG
2, 20, 0
Figure 5.2. A coordination game with strategic uncertainty.
Start by noticing that this game has two (pure strategy) Nash equilibria:
(Hybrid, Pump) and (Electric, Outlet). Given this, you might think that we are
in the clear. Our prediction is that there will be no coordination failure.1
But suppose players face some strategic uncertainty. That is, the car company
is uncertain how the government will behave and vice versa. This could be the
case for a variety of reasons. Perhaps the car company thinks there is some
chance that the government will be unduly influenced by special interests or
that voter opinion could change and lead the government to reverse course.
Perhaps the government thinks there is some chance the car company will
make an important technological breakthrough, leading it to prefer one or the
other type of car unexpectedly. There could be lots of reasons for players to feel
uncertain about the strategy the other player will use.
Wewillmodel this strategic uncertainty in a particularly simpleway—players
are uncertain of each other’s payoffs. Let’s assume that there are two random
variables, θC and θG, that represent this uncertainty. We refer to these as the
players’ types. Each player’s type can take a value of 1 or −1. The two values
are equally likely. The random variables are independent—so the value that θC
takes provides no information about the value θG will take and vice versa. We
will assume that the car company’s payoff from the outcome (Hybrid, Pump)
is 2 + θC and, similarly, the government’s payoff from (Hybrid, Pump) is 2 + θG.
This modified game is represented in Figure 5.2.
Each player knows her own type, but not the other player’s. Consequently,
the players are uncertain which outcome the other player prefers. From the car
company’s (respectively, the government’s) perspective, with probability 1/2
the government (respectively, the car company) gets a payoff of 3 from (Hybrid,
Pump) and so prefers it to (Electric, Outlet). And from the car company’s (re-
spectively, the government’s) perspective with probability 1/2 the government
(respectively, the car company) gets a payoff of 1 from (Hybrid, Pump) and so
prefers (Electric, Outlet). What do the Nash equilibria look like in this modified
game with strategic uncertainty?
1As I do throughout, I’m not going to study mixed strategy Nash equilibria. Instead, below,
I model strategic uncertainty explicitly.
156 Chapter 5
A strategy profile specifies how each type of each player will behave. Hence,
we can think of each player having four possible strategies. The car company’s
strategies are as follows:
• Always play Hybrid
• Play Hybrid if θC = 1 and Electric if θC = −1
• Play Hybrid if θC = −1 and Electric if θC = 1
• Always play Electric
The government’s strategies are as follows:
• Always play Pump
• Play Pump if θG = 1 and Outlet if θG = −1
• Play Pump if θG = −1 and Outlet if θG = 1
• Always play Outlet
Call a strategy in which a player takes the same action regardless of her
type non-responsive and a strategy in which a player’s action depends on her
type responsive. Notice, if Player i is using a responsive strategy, then from
the perspective of the other player, Player i is randomizing between her two
possible actions, playing each with probability 1/2.
The two equilibria we have identified in this game prior to introducing
strategic uncertainty persist. If the government always plays Pump, the car com-
pany’s best response is to always play Hybrid and vice versa. If the government
always plays Outlet, then the car company’s best response is to always play
Electric and vice versa. Hence, (Always play Hybrid, Always play Pump) and
(Always play Electric, Always play Outlet) are Nash equilibria of this game.
The presence of strategic uncertainty now also creates the possibility of
another equilibrium, one in which players play responsive strategies. As we’ve
already noted, if the government plays either of its responsive strategies, then
from the perspective of the car company, the government is playing the action
Pump with probability 1/2 and the action Outlet with probability 1/2. What is
the car company’s best response?
If the car company believes the government is using a responsive strategy,
then the car company’s expected payoff from the action Hybrid is
1
2
× (2 + θC) +
1
2
× 0.
Its expected payoff from the action Electric is
1
2
× 0 + 1
2
× 2.
Coordination Problems 157
Comparing these expected payoffs, the car company strictly prefers the action
Hybrid if θC = 1 and strictly prefers the action Electric if θC = −1. Hence, the car
company’s best response to either responsive strategy by the government is to
play Hybrid if θC = 1 and Electric if θC = −1.
If the government believes the car company is playing a responsive strategy,
it’s calculations are very similar. The government’s expected payoff from the
action Pump is
1
2
× (2 + θG) +
1
2
× 0.
Its expected payoff from the action Outlet is
1
2
× 0 + 1
2
× 2.
Comparing these expected payoffs, the government strictly prefers the action
Pump if θG = 1 and strictly prefers the action Outlet if θG = −1. Hence, the
government’s best response to either responsive strategy by the car company
is to play Pump if θG = 1 and Outlet if θG = −1.
This analysis implies that the gamewith strategic uncertainty has three Nash
equilibria—the two equilibria in non-responsive strategies already described,
and an equilibrium in responsive strategies in which the car company plays
Hybrid if θC = 1 and Electric if θC = −1 and the government plays Pump if
θG = 1 and Outlet if θG = −1.
This last Nash equilibrium formalizes the idea that strategic uncertainty can
lead to coordination failure. In both of the Nash equilibria where players use
non-responsive strategies, there is no chance of coordination failure. But in
the Nash equilibrium where players use responsive strategies, each possible
outcome—(Hybrid, Pump), (Hybrid, Outlet), (Electric, Pump), and (Electric,
Outlet)—is equally likely. This means that, because no player can be sure what
the other player will do, the players fail to coordinate half the time.
Coordination failure due to strategic uncertainty is inefficient. Both players
are better off coordinating than not coordinating (since all coordinated out-
comes provide positive payoffs, while all non-coordinated outcomes provide
zero payoffs). Hence, coordination failure is a social dilemma. Players would all
be better off if they could guarantee coordination.
To see this even more clearly, let’s compare expected payoffs across the
equilibria. In the equilibrium in which the car company always plays Hybrid
and the government always plays Pump, each player makes a payoff of 3 with
probability 1/2 and a payoff of 1 with probability 1/2. Hence, each player’s
expected payoff is 2. In the equilibrium in which the car company always plays
Electric and the government always plays Outlet, each player makes a payoff
158 Chapter 5
of 2 for certain. Finally, in the responsive-strategy equilibrium, four things can
happen, each with equal probability:
1. If θC = 1 and θG = 1, the players coordinate on (Hybrid, Pump) and each
makes a payoff of 3.
2. If θC = 1 and θG = −1, the players fail to coordinate—the outcome is
(Hybrid, Outlet)—and eachmakes a payoff of 0.
3. If θC = −1 and θG = 1, the players fail to coordinate—the outcome is
(Electric, Pump)—and eachmakes a payoff of 0.
4. If θC = −1 and θG = −1, the players coordinate on (Electric, Outlet) and
eachmakes a payoff of 2.
A player’s expected payoff in this equilibrium is
1
4
× 3 + 1
4
× 2 = 5
4
< 2.
The equilibria in which coordination is achieved for certain Pareto dominate
the responsive-strategy equilibrium in which strategic uncertainty creates the
possibility of coordination failure.
5.1.1 Interpretation
We opened this chapter with the case of the long-standing failure of coor-
dination on international accounting standards. And, indeed, there are many
such examples of coordination failure in regulation.
Consider the case of automobile safety standards. Within the United States,
the process of regulatory harmonization began in 1926, when the federal
Uniform Vehicle Code (UVC) emerged as a potential replacement for a variety
of state and local regulations on automobile safety. By 1946 only 30 states had
adopted the UVC in full. Regulatory harmonization increased with the con-
struction of the Interstate Highway System in the 1950s.Many lawswere passed
and regulations promulgated throughout the 1960s. Most significant was the
National Traffic and Motor Vehicle Safety Act of 1966, which imposed federal
standards on state highway safety programs and empowered the secretary of
commerce (later the secretary of transportation) to issue federal safety standards
for motor vehicles. During floor debate, the need to solve coordination failure
was specifically raised. For instance, Connecticut Senator Abraham Ribicoff
argued, “The Federal Government must have a role. It is obvious the 50 states
cannot individually set standards for the automobiles that come into those
50 States from amass production industry” (Congressional Record, vol. 112, Part I
(June 24, 1966)).
In Europe, safety regulations developed separately for each country into the
1950s. In 1952, as part of the process of European economic integration, the
United Nations Economic Commission for Europe established a working group
Coordination Problems 159
with the objective of “worldwide harmonization or development of technical
regulations for vehicles.” A 1958 UN agreement that came out of this working
group established harmonized standards inside much of Europe. However,
because doing so would require recognition of regulatory standards established
by non-American authorities, the United States did not join the UN agreement.
Thus, U.S. and European automobile standards remain unharmonized.2
This lack of harmonization in safety regulations comes at real cost for
manufacturers and consumers. Most importantly, like with unharmonized
accounting standards, variation in safety regulations makes it difficult for
automobile manufacturers to sell models across markets. Consider just a few
differences between the United States and Europe. U.S. rules require that cars
demonstrate certain safety protections for passengers not wearing a seat belt,
while Europe has no analogous regulation. U.S. bumper tests focus on damage
to the automobile, while European bumper tests focus on protection of pedes-
trians. Standards for crash tests are different—for example, U.S. and European
regulations mandate barriers with different physical properties, different crash
dummy positioning, and so on. There are further differences concerning light-
ing color, door locks, head restraints, side lights, electronic stability control,
andmany other features.3 All of these regulatory coordination failures increase
costs, with little if any benefits for safety.
There are also many examples of coordination failure outside the sphere
of government regulation. Often competition among competing technologies
leads to coordination failure. Cell phone manufacturers each use a differently
shaped power supply. Computer manufacturers have not coordinated on a
standardized set of ports for connecting peripherals. And so on.
5.2 Coordination Traps
Terrible social conventions—fromhonor killings, to genitalmutilation, to caste
systems—persist for long periods of time throughout the world. In many cases,
all parties might be better off if the social convention were altered. But the risk
of social sanction for non-conformity keeps the undesirable practice in place.
Mackie (1996) tells the story of foot binding, a form of female mutilation
involving tight wrapping to contort a young girl’s feet that persisted in China
for a thousand years. The practice, according toMackie, “was extremely painful
in the first 6 to 10 years” and led to many complications including “ulceration,
paralysis, gangrene, and mortification of the limbs.” Studies suggest that 10%
of girls did not survive having their feet bound.
2The previous two paragraphs draw on Congressional Research Service Report “U.S. and
EU Motor Vehicle Standards: Issues for Transatlantic Trade Negotiations.” https://www.hsdl.
org/?view&did=751039
3http://www.nbcnews.com/id/26444467/ns/business autos/t/perfectly safe car just not us/
https://www.hsdl.org/?view&did=751039
https://www.hsdl.org/?view&did=751039
http://www.nbcnews.com/id/26444467/ns/businessautos/t/perfectlysafecarjustnotus/
160 Chapter 5
Foot binding first emerged during the Sung dynasty (around the turn of the
millennium). Over the course of several centuries, it spread from a practice of
the royalty, to the nobility, to the upper classes, and finally to the middle and
lower classes. Mackie reports that “[f]ootbinding was the normal practice by
the Ming Dynasty (1368–1644). As measured in 1835, it prevailed in the whole
empire among the Chinese, affecting 50 to 80 percent of women.” Although
foot binding was understood to be both economically costly (it prevented
women from participating in the agricultural economy) and physically cruel,
it was enforced through strong social norms. Perhaps most importantly, foot
binding was associated with suitability for marriage. Despite its deleterious
effects, the practice was so strongly entrenched that it even survived being
formally banned by theManchu conquerors in the seventeenth century.
In the late nineteenth and early twentieth century, public opinion began to
shift with the emergence of a “natural foot” movement. According to Mackie,
the natural foot movement “propagandized the disadvantages of footbinding
in Chinese cultural terms, promoted pledge associations, and subtly conveyed
international disapproval of the custom.” Interestingly, consistentwith the idea
that foot binding was a practice sustained only through mutually reinforcing
social pressure, once it started to decline, it disappeared extraordinarily rapidly.
For instance, Mackie cites a study showing that “the population of Tinghsien, a
conservative rural area 125 miles south of Peking, went from 99 percent bound
in 1889 to 94 percent bound in 1899 to zero bound in 1919.”
Foot binding illustrates a different type of coordination problem. Here, we
don’t see a bad outcome occurring because people fail to coordinate. Rather,
we see people successfully coordinating, but on an equilibrium that is itself
Pareto dominated by another equilibrium. We refer to such a situation as a
coordination trap—people are trapped in a self-reinforcing pattern of behavior
that they regret.
Coordination traps are important for understanding a variety of policy rele-
vant outcomes. These include cultural phenomena like foot binding or honor
killings; economic phenomena like bank runs, financial crises, and persistent
underdevelopment; political phenomena like failures of accountability, the
longevity of dictatorial governments, and revolutions; and social phenomena
like educated parents sending their children to private schools.
To make clear what these environments have in common, it will be useful to
study a couple of models.
5.2.1 A Basic Model of Coordination Traps: Investment in Developing
Countries
Let’s start with a simple model with two players and two actions, inspired by
our earlier discussion of poverty traps. Suppose there are two firms, each decid-
ing whether to invest in a developing country. The country lacks infrastructure.
Coordination Problems 161
Don’t invest
–1, 0
Invest
Firm 2
Invest
Don’t invest
Firm 1
4, 4
0, 00, –1
Figure 5.3. Coordination with a Pareto dominated equilibrium.
As a result, neither firm wants to invest on its own—doing so would result in a
loss. However, the firms believe that if they both invest, the economywill grow,
the government will be able to build infrastructure, and the investments will be
profitable. If neither firm invests, theymake no profits, but suffer no costs.
The model is illustrated in Figure 5.3. There is no uncertainty. The game
has two pure strategy Nash equilibria—(Invest, Invest) and (Don’t Invest, Don’t
Invest).
The players agree that one equilibrium is better than the other—both pre-
fer the (Invest, Invest) outcome to the (Don’t Invest, Don’t Invest) outcome.
Nonetheless, if a firm believes that the other firmwill not invest, then it is a best
response not to invest. So (Don’t Invest, Don’t Invest) is also an equilibrium.
The equilibrium in which neither firm invests illustrates a simple coordi-
nation trap. It is stable for the players to coordinate on not investing, even
though it is inefficient. The players are trapped—Firm 1 doesn’t invest because
it believes Firm 2 won’t invest and vice versa.
As we discussed at the outset of this chapter, coordination traps like this lie at
the heart of the way much of the policy community thinks about economic
development and foreign aid. Investing in countries that lack infrastructure,
human capital, and the other features of an agglomeration economy is not
profitable. But to build infrastructure andhuman capital, countriesmust attract
investment. Hence, poor countries can get caught in poverty traps. The idea
behind short-run economic aid is to give the government an infusion ofmoney
(sometimes called a “big push”) so that investors don’t need to coordinate—if
the government can unilaterally build infrastructure, each individual company
will find investment worthwhile even if others don’t invest. Indeed, this was
the idea behind the Tennessee Valley Authority, a point we will come back to
shortly.
You may be tempted to dismiss coordination traps as unrealistic. Surely, you
might think, players could find their way out of such situations by talking. If
these two firms could sit down and agree to invest, they’d both be better off.
But finding a way out of a coordination trap may sometimes be difficult.
Theremay bemany players, making communication difficult or costly. Further,
in some situations, players may find it risky to communicate a desire to shift
equilibria. For instance, this same model might describe how societies get
162 Chapter 5
caught in unpleasant cultural practices like foot binding or honor killings.
People want to coordinate on following social norms. Failing to act as others do
leads to social sanctions. Although almost everyone would presumably prefer
to coordinate on not engaging in honor killings or the like, once a society is in
that equilibrium, expressing a preference for change is often risky or dangerous.
Hence, escaping a coordination trap may be more difficult than it seems at first
blush.
5.2.2 A Model of Bank Runs
To flesh the story out a bit more, and to see another set of applications, let’s
turn to a coordination model with many people. Suppose there are N people,
eachwith $1000 deposited in a bank. Each person decides whether toWithdraw
or Leave his or her money in the bank. The bank has sufficient cash reserves to
payT < N people. So if fewer thanT peoplewithdraw theirmoney, they all get it
back and everyone else gets paid interest of r. If somenumber of people n greater
than T withdraw their money, then the bank becomes insolvent. A person who
tried to withdraw her money has a Tn chance of getting it back. Anyone who
didn’t withdraw loses his money for certain.
People care only about how much money they have. No one has short-term
need for the money (maybe they all have credit), so there is no direct benefit
fromwithdrawing themoney early.
Let’s look for equilibria of this game. If everyone leaves his or her money in
the bank, everyonemakes a payoff of $1000(1 + r). A personwhowithdraws her
money would only make a payoff of $1000. So everyone is happy leaving the
money in the bank and we have an equilibrium in which the bank is solvent.
If some positive number of people, n ≤ T, withdraw their money, they each
make a payoff of $1000. But if one such person instead left her money in
the bank, she would make a payoff of $1000(1 + r). Hence, this is not an
equilibrium.
If some positive number of people, n ∈ (T,N), withdraw their money, the
bank fails. A person who didn’t withdraw her money makes a payoff of 0. If
instead shewithdrewhermoney, she’dmake an expectedpayoff of Tn+1 × $1000.
So she should have withdrawn. Hence, this is also not an equilibrium.
This argument points toward the logic of bank runs. If I believe that more
thanT peoplewillwithdraw theirmoney, I shouldwithdrawmymoney. That is,
like other coordination games, this is a gamewhere players’ actions are strategic
complements—the more other people withdraw their money, the larger the
benefit to me of withdrawingmymoney.
If everyone withdraws their money, each person makes an expected payoff
of TN × $1000. If instead some individual had left her money in the bank,
she would make 0. So this is an equilibrium in which everyone attempts to
withdraw and the bank fails.
Coordination Problems 163
This situation is very similar to the two-person model we discussed above.
Again there are two pure strategy equilibria. In one equilibrium, all deposits are
left in the bank. In the other, everyone attempts to withdraw his or her money.
The equilibrium in which everyone attempts to withdraw is Pareto dominated
by the equilibrium in which everyone leaves his or her money deposited.
Nonetheless, if a person is convinced that everyone else will withdraw their
money, it is indeed a best response for her to withdraw hermoney. So bank runs
can occur in equilibrium as part of a coordination trap.
As described at the beginning of this chapter, a variety of phenomena can
be usefully thought about with models like this one. The key feature of such
models is that players get trapped in an undesirable pattern of behavior because
each individual believes all the other individuals will behave in that way and no
one wants to be the only person to behave differently.
5.2.3 A Model of Revolutions
Thinking about coordination in this way also gives us some insight into
the logic of revolutions. Again consider a group of N people. Each person can
choose to Participate or Not Participate in a protest. The number of people who
participate affects the probability that the revolution succeeds.
Just as in our model of collective action from Chapter 4.1, if n people partic-
ipate, the probability that the regime falls is nN and the benefit to an individual
of regime change is B. But now we will change one crucial assumption. Assume
that the costs of participating are decreasing in the number of other partici-
pants. In particular, if n other people participate, the cost tome of participating
is cn+1 .
The assumption that individual costs are decreasing as participation in-
creases seems pretty natural. For instance, one is more likely to be arrested or
hurt as one of only a few protestors, than as a relatively anonymous participant
in a group of tens-of-thousands. Importantly, when costs are decreasing in
participation, the revolution game becomes a situation of strategic comple-
mentarities. The more other people participate, the smaller are the costs of
participating and, so, the more tempting it is to participate.
Think about best responses. Suppose a player believes that n other playerswill
participate. The payoff to participating is
n + 1
N
× B − c
n + 1.
The payoff to not participating is
n
N
× B.
164 Chapter 5
Comparing these payoffs, if a player believes n other players will participate, it
is a best response for her to participate if
B
N
≥ c
n + 1. (5.1)
Let’s ask whether there is an equilibrium in which everyone participates.
From Equation 5.1, if a player believes everyone else will participate (so n =
N − 1), then it is a best response for her to participate if
B
N
≥ c
N
,
which is true since we assumed B > c in Chapter 4.1. If I believe everyone else
will participate, then the costs of participating are quite low. As such, I want to
participate too. This means there is an equilibriumwith full participation.
Next consider a strategy profile in which no one participates. Again, from
Equation 5.1, if a player believes no one else will participate, then it is a best
response for her not to participate if
B
N
≤ c.
This looks just like our collective action model. If a player believes no one else
will participate, then unless the benefits of regime change are implausibly large,
she too will not participate because the costs of participating are high. Hence,
as long as c ≥ BN there is an equilibrium in which no one participates.
The existence of these two equilibria creates the possibility of a coordination
trap that drives bad governance. Imagine a ruler who will lead in ways that
benefit the people if and only if she believes that, if she follows bad policies, the
people will revolt. If the society that she leads is coordinated on an equilibrium
in which the people revolt when the leader does a bad job, then the leader has
an incentive to pursue good policies that benefit the public. But if the society is
coordinated on an equilibrium in which the people don’t revolt even when the
leader does a bad job, then the leader has no incentives to pursue good policies.
Hence, a country can get trapped into having a non-responsive government if
the citizens coordinate on the bad equilibrium so that the leader knows that no
matter what, she won’t be held to account.
A model like this might also help us understand “spontaneous revolutions”
like those witnessed in the Arab Spring. Sometimes small events might be
capable of changing people’s beliefs about how their fellow citizens think. For
instance, perhaps Egypt was stuck in a bad equilibrium where its leaders knew
the people would never revolt. The revolution in Tunisia may have changed
these beliefs, making Egyptians think of themselves as part of a society whose
people stood up for their rights, mobilizing for revolution when circumstances
Coordination Problems 165
called for it. The model we’ve just studied shows that this change of beliefs,
on its own, could be enough to move people to a new equilibrium in which
everyone turns out to protest the government.
5.2.4 Interpretation
As alreadymentioned, there aremany situations inwhich coordination traps
are possible. As you begin to think about the world in terms of coordination
problems, you will see them all over the place. Reiterating a few canonical
examples might help to highlight the idea. As we’ve discussed, bank runs
and other financial panics, participation in mass protests or revolutions, and
investment in economically developing countries might all be characterized by
coordination problems. Agglomeration creates the possibility of coordination
problems. A related set of issues arises in urban renewal. If a school district
or neighborhood is considered failing, then people will be disinclined to live
there,making it difficult for the school district or neighborhood to turn around.
However, if people came to believe that the school district or neighborhood
was going to turn around, they might be inclined to participate, creating
a self-fulfilling prophecy. Social norms, from silly fashion trends to terrible
social institutions like foot binding, rest on a set of mutually self-reinforcing
beliefs about others. And the adoption of new technologies often rests on
coordination—among competing technologies, the winner will not necessarily
be the better technology, but the one everyone comes to believe everyone else
will adopt.
5.3 Policy Responses
Addressing coordination problems is quite different from addressing exter-
nalities problems. In the case of coordination problems, a successful policy
intervention involves finding a way to shift players from a bad equilibrium
to a good one. This is not the case for externalities problems, where a policy
intervention has to fundamentally shift players’ best responses. Thus, when
thinking about policy interventions aimed at resolving coordination problems,
we focus on fairly different approaches.
5.3.1 Communication
Communication can be a powerful corrective tool for both coordination
failures and coordination traps. People want to coordinate on good outcomes.
They fail to coordinate because they haven’t found a way to get themselves to
the right equilibrium—whether that means avoiding the risk of coordination
failure due to strategic uncertainty or the unnecessary costs associated with
being stuck in a coordination trap. So if you can find a way to “put them in a
room” theymight be able to simply talk their way into a better outcome.
166 Chapter 5
This is a fundamental difference between coordination problems and ex-
ternalities. As we discussed in Chapter 4.4, a deep challenge in addressing
externalities problems is that, even if you are convinced that everyone else
will take a socially optimal action, you still want to free ride. Hence, in an
externalities setting, if people agreed to choose a socially optimal action, they
would have strong reasons not to trust one another, since everyone would be
claiming they would take an action that is not a best response. This is not the
case in coordination games. Put differently, what makes an agreement to take a
socially optimal action credible is that the agreement be self-enforcing—that is,
a Nash equilibrium. In an externalities setting, such a self-enforcing agreement
does not exist. In a coordination setting, one does.
That said, there is one important link between externalities problems and
coordination problems. In Chapter 4.6.3, we discussed the idea that ongoing
relationships might allow groups to self-organize solutions to externalities
problems. But we also saw that, even when such a cooperative equilibrium
exists, it is not the only equilibrium—inefficient equilibria always exist in
situationswith externalities. In this sense, the idea of self-organization through
repeated interaction transforms an externalities problem into a coordination
problem. The issue shifts from whether policy can get people to internalize
their externalities to whether policy can get people to play the equilibrium in
which they compel one another to internalize their externalities. Hence, like
in other situations where there is a risk of coordination failure or coordination
traps, leadership and communication can play a role in creating self-organized
solutions to externalities problems.
It is also important to note that there are situations where simple communi-
cationmight not solve coordination problems.
When there aremany players, communicationmay be extremely difficult (or
dangerous, in the case of revolutions). Once the panic associated with the bank
run equilibrium sets in, it may be difficult to talk people back into the Pareto
improving equilibrium of leaving their money deposited.
Further, when deeply held social norms—like foot binding, honor killings,
or racial bias—are involved, it may be profoundly difficult to change people’s
beliefs about how one another will act or think.
Finally, distributional considerations can also mitigate the efficacy of com-
munication. For instance, consider the problem of regulatory harmonization—
for example, accounting standards or automobile safety. As we’ve discussed,
there are significant benefits from governments coordinating on mutually
accepted standards. But individual governments may also strongly prefer their
particular regulations for a variety of economic and political reasons. Over-
coming these distributional concerns may be difficult. Entrenched interests—
for example, regulators, accountants, engineers, domestic producers—push
for coordination on that country’s preferred outcome. This suggests that,
Coordination Problems 167
sometimes, a more direct type of intervention might be needed to solve coor-
dination problems.
5.3.2 Short-Run Intervention
Direct government intervention is, of course, another possible strategy to
address coordination problems. Importantly, in the case of coordination prob-
lems, often a short-run intervention that pushes players into a better equilib-
rium is all that is required. Once coordination is achieved, if the government
intervention stops, there is no reason for players to fall back into a bad pattern
of behavior, since the good pattern of behavior is self-reinforcing.
This, again, is a difference between coordination failure and externalities.
A regulation, tax, or subsidy meant to address an externalities problem must
be ongoing. If the government ever stops its intervention, the players have
an incentive to revert to inefficient behavior. But if the government stops its
intervention in a coordination game, then assuming players have learned that
they are all now playing the new equilibrium, efficient behavior will persist.
The long-run effects of the Tennessee Valley Authority illustrate the point.
As we discussed at the outset of this chapter, manufacturing benefits from
economies of agglomeration, while agriculture does not. As a result, the TVA
worked quite differently for these two industries. In the case of manufacturing,
TVA subsides helped to overcome a coordination trap by building up the
infrastructure necessary to create the virtuous cycle associated with economies
of agglomeration. Hence, when the TVA subsidies disappeared starting in the
1960s, the growth in manufacturing persisted. As predicted in the case of a
coordination trap, the short-run TVA intervention pushed the Tennessee Valley
into a new equilibrium—one with higher returns to manufacturing—that did
not disappear when the policy disappeared. In the case of agriculture, there was
no coordination trap to solve. In the agricultural sector, the TVA subsidies were
simply a transfer to agriculture, the effects of which disappeared as soon as the
money dried up.
5.3.3 Insurance and the Second Best
Another intervention that is common in settings like that described by the
bank run model is government insurance. For instance, if the government can
guarantee players that they will not face a bad outcome, even if everyone runs
on the bank, then the players have no incentive towithdraw theirmoney. Inter-
estingly, by insuring everyone against the risk of a bad coordination outcome,
the government can sometimes actually eliminate the risk of such an outcome
occurring. Policies like this, that insure people against negative coordination
events, can be very powerful. By promising to spend money if needed, the
government can achieve a Pareto improvement without ever actually having to
spend a dime.
168 Chapter 5
In the United States, as asset values plummeted during the Great Depression,
bank runs were a recurring problem. Banks began to fail and depositors became
increasingly concerned about the security of their assets. This led to a rush of
withdrawals, causing further insolvencies and further bank runs. The Banking
Acts of 1933 and1935 created the FederalDeposit InsuranceCorporation (FDIC)
for precisely the reasons outlined above. The FDIC was charged with providing
deposit insurance, reassuring depositors of the security of their assets, and
thereby stemming the tide of destructive bank runs.
Importantly, the idea that government insurance might alleviate the prob-
lem of coordination traps also points back toward the idea of the second best.
Government insurance against bank failure reduces incentives for depositors to
run on the bank. But it also reduces incentives for depositors to favor banks that
invest prudently. As a result, competition for depositors becomes a less effective
tool for disciplining banks to behave responsibly. So, once deposits are insured,
banks may have an incentive to make investments that are too risky.
This is thewell-knownmoral hazard problem thatwasmuchdiscussed during
the financial crisis of 2007–2008. During that crisis there was considerable
concern that if the government bailed out major financial institutions, then
those institutions would behave even more irresponsibly in the future. The
fact that government insurance prevents runs but creates moral hazard leads
governments to further regulate the behavior of insured banks. For instance, the
United States government requires that banks keep a certain amount of liquid
capital (in proportion to their liabilities) ondeposit at the Federal Reserve. These
capital requirements are intended to reduce the risk that the banks behave in
a way that leads to the government actually having to make good on deposit
insurance. Of course, leaving capital on deposit with the Federal Reserve may
not be the optimal use of that capital. Hence, a new source of inefficiency is
created by the capital requirements that the government imposes to address the
moral hazard problem that is caused by the deposit insurance that is needed to
avoid coordination traps in the form of bank runs. And, so, we see a return of
the theory of the second best. A policy intervention like deposit insurance has
benefits and costs. The optimal (second-best) policy balances these costs and
benefits.
5.4 Takeaways
• Coordination games describe situations in which players all benefit if
they take coordinated actions.
• Strategic uncertainty can lead to inefficient coordination failure.
• Some coordination games have equilibria that are Pareto dominated
by other equilibria. In such situations, it is possible for players to be
caught in a coordination trap—playing a Pareto dominated equilibrium
Data
Highlight
Coordination Problems 169
despite the fact that all would agree that some other equilibrium ismore
desirable.
• Sometimes coordination failure or coordination traps are solvable by
communication. However, in situations where there are many actors
or in which stating a counter-normative opinion might carry risks
of social sanction, communication alone may be insufficient to solve
coordination problems.
• Often short-run interventions that move people to a coordinated or
Pareto improving equilibrium can address coordination problems. Since
coordination problems are solved by moving people to a new pattern of
behavior that is also an equilibrium, it may not be necessary to engage
in long-run interventions.
5.5 Further Reading
The classic treatment of coordination problems is in Schelling’s stunning The
Strategy of Conflict. For a modern, technical take onmodels of coordination, see
Morris and Shin (2003).
For fairly academic treatments of agglomeration economies, you should read
Edward Glaeser’s Agglomeration Economics and Paul Krugman’s Geography and
Trade. For a non-technical introduction in the context of urban economics,
have a look at Glaeser’s Triumph of the City.
Weingast (1997) and Fearon (2011) relate failures of democratic accountabil-
ity to coordination traps. Azariadis (1996) overviews the relationship between
coordination and poverty traps, while Kraay and McKenzie (2014) ask the
empirical question, “Do poverty traps exist?”
Kwame Appiah’s The Honor Code is a thoughtful historical and philosophical
take on how honor codes are sustained and overcome.
Friedman and Schwartz’s great book, A Monetary History of the United States,
1867–1960, discusses the role of bank runs in American economic history in
detail. The classic model of bank runs and deposit insurance is Diamond and
Dybvig (1983). Cooper and Ross (2002) extend the analysis to include moral
hazard and capital requirements.
5.6 Exercises
1. Consider a model of revolutions. Society is made up ofN > 1 people.
Simultaneously, each person chooses whether or not to participate. If n
people participate, the probability the revolution succeeds is nN . If the
revolution succeeds, eachmember of society receives the benefits of a public
good worth B. In addition, each person who participated in the revolution
Data
Highlight
Data
Highlight
Data
Highlight
Data
Highlight
Data
Highlight
170 Chapter 5
receives a benefit R if the revolution succeeds. (This extra benefit, called a
club good, might represent special access to government jobs for people who
helped unseat the government once the new government is formed, or it
might just represent an expressive benefit of having participated in a
victorious revolution.) The cost of participating is c > 0. Assume that R > c
and that B + R < N × c.
(a) Suppose a player believes n other people will participate. What is her
expected utility from participating?
(b) Suppose a player believes n other people will participate. What is her
expected utility from not participating?
(c) Write down a player’s best response correspondence.
(d) Identify all of the pure strategy Nash equilibria of this game.
(e) Calculate the utilitarian payoff associated with each equilibrium.
(f) Does this game have the potential for a coordination trap? Explain why
or why not.
(g) What feature of this gamemakes it a situation that exhibits strategic
complementarities?
2. Consider a society of 2 people trying to achieve a collective goal. Each
individual, i, must choose an effort ei ≥ 0 at cost e2i . We will study two
different scenarios:
Scenario 1 The society produces a public good G = e1 + e2. Each
individual’s payoff is
ui(e1, e2) = G − e2i .
Scenario 2 The society produces a public good
G =
⎧
⎨
⎩
e1 + e2 if e1 + e2 ≥ 2
0 if e1 + e2 < 2.
Each individual’s payoff is again
ui(e1, e2) = G − e2i .
Notice, players bear the costs of their individual efforts even if society
ends up producingG = 0.
(a) The first-best level of effort is the same in both scenarios. What is it?
(b) What is the Nash equilibrium in scenario 1?
(c) Is that same strategy profile a Nash equilibrium in scenario 2?
Coordination Problems 171
(d) Is it a Nash equilibrium in scenario 2 for no one to exert any effort?
(e) Is it a Nash equilibrium in scenario 2 for each player to exert the first-best
effort?
(f) Suppose, in scenario 1, that a policymaker were able to convince player i
that the other player will choose the first-best level of effort. Will player i
choose the first-best level of effort?
(g) Suppose, in scenario 2, that a policymaker were able to convince player i
that the other player will choose the first-best level of effort. Will player i
choose the first-best level of effort?
(h) What do your answers to the previous two questions show about how
different kinds of policy interventions work for different kinds of social
dilemmas?
(i) Suppose the policymaker could subsidize effort in scenario 1, but doing
so required funding through inefficient taxation.Without doing any
calculations, if she implemented the second-best subsidy, howwould the
induced second-best efforts compare to the equilibrium efforts and the
first-best efforts?Why?
3. Suppose there are five firms in an industry. Eachmust individually decide in
which of two cities to locate its manufacturing plant. If firm i locates in city
j, its profits are π × nj, where π > 0 and nj is the number of firms from this
industry that locate in city j (including itself).
(a) Give a substantive explanation for why profits might look like this.
(b) Identify all of the Nash equilibria of this game.
Now suppose that one of the cities (city 1) is better for this industry than the
other (city 2). A firm that locates in city 1makes profits π1 × n1 and a firm
that locates in city 2makes profits π2 × n2. Assume π2 < π1 < 5π2.
(c) Have the Nash equilibria of the game changed?
(d) Explain how your answer suggests that agglomeration economies can
create coordination traps.
(e) Often local governments offer incentives to induce a few large firms in
some industry to relocate to their city. Evaluate the likely efficacy of such
a policy in light of this model.
4. Explain why short-run policy interventions can help to solve Pareto
inefficiencies caused by coordination traps, but are unlikely to solve Pareto
inefficiencies due to externalities.
5. Let’s revisit Exercise 4 from Chapter 1. In O’Hare’s (2015) discussion of why
it is so difficult to convince major museums to consider selling some of their
172 Chapter 5
art to fund other activities (e.g., free admissions, expanded space,
educational staff) he writes:
If you open this discussion with museum people, as I have done, you
find out very quickly that you have walked into a hornet’s nest called
the “deaccessioning debate.” Deaccessioning is fancy art language for
selling, and the first thing the director you have provoked will tell you
about is themuseumdirectors’ code of ethics, which forbids him to ever
sell art except to buy more art. If he did, he could never lend anything
to other museums or borrow any art from them. He probably couldn’t
have coffee with his pals at the next convention either: outer darkness,
and how appropriate for unethical behavior.
For the sake of argument, assumemajor museum directors generally agree
with O’Hare that museums should sell off a small amount of their art to
fund other activities. Explain how the above passage implies they are caught
in a coordination trap and suggest an intervention that might move them to
a better outcome.
6
Commitment Problems
In 2012, the government of Argentina nationalized its largest energy company,
YPF, amajority stake of which had been owned by the Spanish energy company
Repsol. The temptation to nationalize was clear—in 2011, Argentina became
a net oil importer for the first time in decades. Moreover, the nationalization
followed quickly on the heals of the discovery, by Repsol, of vast reserves of
shale oil in Argentina’s Neuquén province. Argentina’s government saw an
opportunity to simultaneously take control of a valuable economic resource
and claim credit for turning around the oil industry.
There was, however, a problem with this plan. Extracting shale oil requires
both expertise and capital—tens, perhaps hundreds, of billions of dollars—
that Argentina lacks. The only way for Argentina to exploit its shale oil re-
serves is through partnership with foreign oil companies. But, fearful that
their assets might ultimately suffer the same fate as Repsol’s, such companies
are understandably reluctant to invest in Argentina. As a consequence of the
government’s limited ability to credibly commit to respecting the property
rights of foreign firms, to date, Argentina hasmade little progress in developing
its shale resources.
This story is an example of a general phenomenon called a commitment
problem. PartyA could take some action—investing in a new technology, setting
a good policy, resolving a conflict through negotiated settlement, etc.—that
would benefit both himself and Party B. However, Party A anticipates that, in
the future, Party B will have the power to exploit him, taking the benefits for
herself and leaving Party A worse off than if he hadn’t taken the initial action.
As a consequence, Party A doesn’t ever take that initial action. But if Party B
could credibly commit not to exploit her future power, Party A would take the
action and they’d both be better off. PartyB’s inability to credibly commit yields
a Pareto inefficient outcome.
The unwillingness of foreign firms to invest in countries where the risk of
government expropriation is high is a classic example of the inefficiency caused
by commitment problems. If the government could commit not to nationalize
valuable resources, foreign firms would invest, making both the firm and the
government better off. But if a government has a reputation for not respecting
property rights, foreign investors fear that the governmentwill seize any profits,
174 Chapter 6
leaving them worse off than if they hadn’t invested. Consequently, investment
is inefficiently low.
In this chapter we will explore two models of commitment problems to see
the variety ofways inwhich this social dilemma creates opportunities for public
policy to yield Pareto improvements. First, we will look at a model of how
commitment problems give rise to costly conflicts—wars, lawsuits, strikes, and
so on. Second, we will consider how the structure of certain markets creates a
commitment problem inside the supply chain that can cause inefficiently low
levels of investment. Finally, we will discuss policy interventions that might
help mitigate commitment problems.
6.1 A Model of Conflict
From the Easter Rising of 1916 through the signing of the Good Friday Agree-
ment in 1998, the armed conflict over independence, known as the Troubles,
defined much of twentieth-century Irish history. The Troubles were a tragedy
for both sides. Thousands of lives and billions of dollars were lost in seemingly
intractable conflict.
Throughout this history, both sides made intermittent attempts to negotiate
a settlement. A reasonable observer might wonder why such negotiations did
not succeed. Since conflict is costly, there should be a deal that avoids conflict
and makes both parties better off. That is, in any setting of costly conflict (war,
lawsuits, labor strikes), there should be a negotiated settlement that is a Pareto
improvement over fighting.
To see the logic of this puzzle, imagine the British and Irish are in a dispute
over a prize of value R. They believe that if they fight, the Irish will win with
probability p and the British will win with probability 1 − p. Conflict imposes
a cost of c on each of them—these costs reflect loss of life, destruction of
infrastructure, and time and resources spent fighting. So the expected utility
to the British of a conflict is
UB(conflict) = (1 − p) × R − c,
while the expected utility to the Irish of a conflict is
UI(conflict) = p × R − c.
Clearly, both sides would be better off with a negotiated settlement that splits
the prize, giving the Irish a p-share and the British a (1 − p)-share. So why don’t
they reach such a settlement?
There are several possibilities. First, the prize might be indivisible and utility
might not be transferable. For instance, amajor problem in finding a negotiated
Commitment Problems 175
settlement between Israelis and Palestinians is that it is difficult to divide
Jerusalem between them while preserving its value to either. Hence, while the
sidesmight be better off reaching a deal that divides the prize, such a dealmight
not be technologically feasible.
Second, the players may disagree about how likely each of them is to win a
dispute. If they are both overly optimistic, then there may be no deal they are
both willing to take. For instance, if they are both certain they would win the
conflict, neither would settle for less than B − c in the agreement.1
Third, theremay be commitment problems.While amutually beneficial deal
exists, the players may have concerns that the deal will not be honored. Such
lack of trust was an important part of the story in the case of the Irish Troubles.
One can see this most clearly in disputes over weapons decommissioning,
which proved a stumbling block in many negotiations between the British and
Irish Republicans. The British demanded that the Irish Republican Army (IRA)
decommission its weapons, first as a precondition to negotiations and later as
a precondition for concessions. The IRA feared the British would renege on
promises were it to disarm before concessions were made. As a spokesman for
the IRA stated in 1996:
There will be no decommissioning either through the front or the back
doors. This is an unrealistic and unrealizable demand which simply won’t
be met. The IRA will under no circumstances leave nationalist areas de-
fenseless this side of a final settlement.2
The story is straightforward. The IRA had the power to extract concessions from
the British because they were armed. The British promised such concessions
in exchange for decommissioning. But the IRA believed that, if it were to
decommission, its power would be diminished and the British would no longer
have an incentive to honor the promised concessions. Hence, the inability of
theBritish to credibly commit to concessions led to a conflict thatwas inneither
side’s interest.
We are going to look at a simple model of this commitment problem logic. It
was originally proposed by Fearon (1998) as an account of the spread of ethnic
civil wars. I will present it in terms of negotiations between the British and IRA.
We will build up the model in steps. There are two groups, the British
and IRA, in dispute over resources of value R. The British make a take-it-or-
leave-it offer of a division of the resources between themselves and the IRA.
1The mutual optimism story is actually quite a subtle one and there is some dispute in the
literature as to whether or not it is a coherent account of conflict. In particular, the question is,
can rational players really persist in being mutually optimistic throughout the run up to conflict?
See Fey and Ramsay (2007) for a discussion of these issues.
2Quoted in English (2003, p. 326).
176 Chapter 6
Co
nfl
ict
No co
nfl
ictB
ri
ti
sh
IRA:
B:
p2R + (1 – p2) × 0 – c
p2 × 0 + (1 – p2)R – c
IRA:
B:
(1 – α)R
αR
α
IR
A
Figure 6.1. Amodel of negotiations and conflict.
In particular, the British propose to keep a share α ∈ [0, 1] for themselves, offer-
ing the balance, 1 − α, to the IRA. The IRA decides whether to accept the offer,
making a payoff of (1 − α)R, or start a conflict. The IRA wins the conflict with
probability p2. The winner gets the full resource, but conflict imposes a cost of
c on each player.
This game is represented in Figure 6.1, where the fact that the British face
a continuous choice (any α between 0 and 1) is represented by the curve and
dashed line coming from the British decision node.
We can solve this game for its subgame perfect Nash equilibria via backward
induction. At the final stage of the game, the IRA strictly prefers to accept an
offer of 1 − α if
p2R − c < (1 − α)R ⇒ α < 1 − p2 +
c
R
.
Similarly, it strictly prefers to reject an offer if α > 1 − p2 + cR . So the IRA has
a unique best response to every possible offer, α, with one exception. If α =
1 − p2 + cR , the IRA is indifferent between starting a conflict and accepting the
British offer.
Suppose the IRA accepts any α ≤ 1 − p2 + cR and rejects any α > 1 − p2 + cR .
What offer will the British make? If the British make an offer that is rejected
(i.e., α > 1 − p2 + cR ), then there is conflict and their payoff is (1 − p2)R − c. If
the British make an offer that is accepted (i.e., α ≤ 1 − p2 + cR ), then there is no
conflict and their payoff is αR. Given this, the British want tomake an offer that
is accepted if they can do so with some α satisfying
αR > (1 − p2)R − c ⇒ α > 1 − p2 −
c
R
.
What have we seen? Any α that is less than or equal to 1 − p2 + cR will be
accepted. Any α that is greater than 1 − p2 − cR is better for the British than
conflict. Since 1 − p2 − cR < 1 − p2 + cR , the British can make an offer that they
prefer to conflict and that the IRA will accept. The largest such offer is α =
1 − p2 + cR . Thus, there is a subgame perfect Nash equilibrium of this game
Commitment Problems 177
Co
nfl
ict
No co
nfl
ictB
ri
ti
sh
IRA:
B:
p2R + (1 – p2) × 0 – c
p2 × 0 + (1 – p2)R – c
IRA:
B:
(1 – α)R
αR
α
IR
A
Pr
ee
m
pt
ive
co
nfl
ict
Ne
go
tia
te
IRA:
B:
p1R + (1 – p1) × 0 – c
p1 × 0 + (1 – p1)R – c
IR
A
Figure 6.2. Amodel of conflict due to commitment problems.
involving the following strategy profile:
• The British offer α = 1 − p2 + cR .
• The IRA accept any α ≤ 1 − p2 + cR and reject any α > 1 − p2 + cR .
No conflict occurs in equilibrium.3
One critical fact to notice about this game is that because the British get
to make a take-it-or-leave-it offer, in equilibrium the IRA ends up indifferent
between conflict and no conflict—in either case the IRA’s payoff is p2R − c. (You
can see this algebraically by plugging α = 1 − p2 + cR into (1 − α)R.) Substan-
tively, this is because the British keep as much of the prize for themselves as
possible, subject to the constraint that the IRA take the deal. The British, thus,
make concessions just sufficient to leave the IRA exactly indifferent between
accepting the offer and fighting.
Now that we’ve understood that interaction, let’s add an earlier stage to the
game. Suppose that the IRA can start a preemptive conflict before the British
make their offer. Moreover, assume that the IRA wins this preemptive conflict
with probability p1 > p2. There might be several reasons this would be the case.
First, if the British demand decommissioning of weapons as precondition for
talks, then the IRA might be stronger prior to the negotiations. Second, the
process of negotiating may undermine some of the operational and personnel
secrecy that give the IRA power as a clandestine organization. Third, the process
of negotiating may allow the British to consolidate control or public support,
weakening the IRA. The game is illustrated in Figure 6.2.
3This equilibrium is unique. If we consider the case where the IRA breaks indifference in favor
of conflict, we find that the British want to offer the largest α that is strictly less than 1 − p2 + cR .
Since there is no largest α that is strictly less than 1 − p2 + cR , there is no such equilibrium. This
issue is discussed inmore depth in Appendix B.6.4.
178 Chapter 6
Our previous analysis tells us what happens in most of this extended game.
The only question left is what the IRA will do at the beginning of the game.
If the IRA negotiates, it will end up accepting an offer that results in a
payoff of p2R − c. If the IRA starts a preemptive conflict, its payoff is p1R − c.
Since p1R − c > p2R − c, the IRA starts a preemptive conflict rather than entering
negotiations.
6.1.1 Inefficient Conflict
The IRA starts a preemptive conflict because it understands that, if it enters
negotiations, it will be in a weaker position and will end up with a negotiated
settlement whose terms are worse than the expected payoff of fighting at
the outset. Although preemptive conflict is rational, the equilibrium outcome
is also clearly inefficient, since conflict is costly. At root, the source of the
inefficiency is the British inability to commit to giving the IRA a sufficient share
of the resources once negotiations get going.
To see the inefficiency, notice that in equilibrium the IRAmakes an expected
payoff of p1R − c and the British make an expected payoff of (1 − p1)R − c. Sup-
pose the British could credibly commit to proposing α = 1 − p1. The IRA would
accept such a proposal rather than fight at the second stage. Moreover, such a
commitment would convince the IRA not to start a preemptive conflict, since
p1R > p1R − c. Finally, such a commitment would also make the British better
off (relative to the equilibriumwith preemptive conflict), since (1 − p1)R > (1 −
p1)R − c. Thus, if the British could make this commitment, inefficient conflict
would be avoided and both sides would be better off—a Pareto improvement.
The problem, aswe’ve already seen, is that once negotiations start, the British
have gained strength relative to the IRA and so have no incentive to honor such
a commitment. Indeed, at the time the Britishmake a proposal, they know that
the IRA will take a much worse offer. As such, the British will choose a higher
α—that is, will keep more resources for themselves. Anticipating this fact, the
IRA distrusts any promise the British make. This distrust leads the IRA to start
a preemptive conflict rather than negotiate. Hence, the commitment problem
leads to inefficiency.
6.1.2 Interpretation
I’ve couched this model in terms of a commitment problem that arises when
a government demands, say, that a rebel group disarm prior to negotiations.
Fearon originally proposed it as a way to understand the spread of ethnic civil
wars after the fall of the Soviet Union. There the mechanism was the same, but
the anticipated power shift that drives the commitment problem derived from
a different source.
During the Cold War, the Soviets served as a third-party guarantor of the
peacewithin the Eastern Bloc. Thereweremany ethnic groups that did not trust
Commitment Problems 179
one another, but the Soviets, through military strength, prevented the abuse
of ethnic minorities. With the fall of the Soviet Union, there was no longer
a third-party guarantor. Ethnic minorities suddenly felt threatened by ethnic
majorities. The ethnicminorities believed that once themajorities consolidated
power, establishing control of the government and the military, they would
use their increased strength to exploit minority groups. There was nothing the
majorities could do to credibly promise not to do so. And so, the argument goes,
the ethnicminorities started preemptivewars, fighting for autonomybefore the
majorities consolidated power.
This logic played out in a fairly interesting way in Croatia in the early 1990s.
In 1991, Serb nationalists began to consolidate control over Yugoslavia. Ethnic
Croats saw themselves as a vulnerable minority. Following the logic of the
model, in June of 1991, Croatia preemptively declared independence, sparking
a war between Croats and Serbs that lasted until 1995.
What happened once the Croatians established independence is even more
interesting. Within Croatia, the Croats were a majority and the Serbs, who had
been part of the majority prior to the separation of Croatia from Yugoslavia,
were aminority. These ethnic Serbs, whowere primarily located in the Croatian
region of Krajina, now viewed themselves as a potentially exploitable minor-
ity within the newly independent Croatia. As a result, they started another
preemptive conflict to separate from Croatia—an attempt that was ultimately
unsuccessful.
Thus, in Croatia, we see the logic of the model play out twice in a series
of cascading civil wars. First a Croatian minority starts a preemptive war
in response to the Serbian majority’s inability to commit not to exploit its
Croatianminority. Then a Serbminoritywithin the newly independentCroatia
starts another preemptivewar in response to theCroatianmajority’s inability to
commit not to exploit its Serb minority.
While Fearon presented this as a model of ethnic conflict, its basic
mechanism—conflict due to commitment problems borne of shifting power—
can be thought ofmuchmore broadly. Aswewill see inChapter 8.3,many types
of government policy may be distorted because of commitment problems. For
instance, a political partymight resist immigration reform if it is concerned that
immigrantswill vote for another party. But there are also exampleswithinmany
other kinds of organizations. Let me give a few possible examples.
Imagine a company or organization controlled by a group of elites (e.g.,
senior executives, tenured faculty). Those elites have to decide whether to allow
or block the adoption of a new technology. This new technology will lead to
increased growth. But it also makes it more likely that the elites will lose power
because younger members of the organization have greater facility with the
new technology. The board and shareholders cannot credibly commit not to
transfer authority to these younger employees as the current elites’ knowledge
180 Chapter 6
becomes obsolete. Hence, the elites block the new technology for as long as
they can. This is inefficiency due to a commitment problem. If the board or
shareholders could commit to not challenge the elites’ authority, then the
elites would allow the technology, making the company more profitable. But
because they can’t commit, the company is kept stagnant. A related argument,
sometimes made in academic circles, is that one of the benefits of tenure is that
it frees faculty to hire new assistant professors whom they believe to be smarter
or better trained than themselves.
Consider a union negotiating with management. Management wants the
unionmembers to take a small pay cut. However, the union believes that if they
take a small pay cut now, then fewer shops will join the union in the future,
weakening the union relative tomanagement. Consequently, the unionworries
that management will exploit the effects of a small pay cut today to demand
even larger pay cuts in the future. As a result, the union strikes rather than
taking a small pay cut, an inefficient outcome. If management could credibly
commit not to demand more concessions in the future, then costly conflict
could be avoided. But such a promise is not credible.
6.2 The Hold-Up Problem
In many industries, local dealerships have the exclusive right to sell certain
products. For instance, in the United States, a variety of state laws protect local
automobile dealerships from both competition and sanction by automobile
manufacturers. All states require that dealerships be licensed, restricting new
dealerships from entering the market. Many states limit the circumstances
under which a manufacturer can terminate a dealership franchise and require
manufacturers to repurchase unsold cars from terminated dealers. The vast
majority of states also directly protect dealerships from local competition with
restrictions on “encroachment.”
For example, Massachusetts General Law Part I, Title XV, Chapter 93B,
Section 6, includes the following provisions:
It shall be a violation . . . for a manufacturer, distributor or franchisor
representative without good cause, in bad faith or in an arbitrary or
unconscionable manner to . . . grant or enter into a franchise agreement
with a person who would be permitted under or required by the franchise
agreement to conduct its dealership operations from a site any boundary
of which is situated within the relevant market area of an existing motor
vehicle dealer representing the same line make.
States are likely willing to provide these protections because they generate
significant tax revenue from dealerships. But such restrictions also create in-
efficiencies. They allow dealerships to demand a larger share of profits from
Commitment Problems 181
manufacturers by restricting the ability of manufacturers to sell to consumers
through other outlets. As a result, the dealership structure and its various
policy protections likely raise prices for consumers and reduce investment and
innovation by manufacturers, who don’t expect to enjoy a large percentage of
the fruits of such investments.4
This is another instance of inefficiency caused by commitment problems.
This particular type of commitment problem is called the hold-up problem. Let’s
look at a model.
Imagine a simple supply chain. There is an upstream producer who produces
e ≥ 0. The cost to the upstream producer of producing e is c × e2, with c > 0.
There is a downstream user who values the product at α × e. The next best
use for the product is for the upstream producer to sell it to some other user
for β × e with β < α. This lower value reflects the fact that the product is
in some way particularly well suited to the downstream user. Perhaps it is
designed specifically for the downstream user, the upstream producer has to
pay a penalty for selling to a different user because of regulatory protections,
or the downstream user is especially good atmarketing the upstream producer’s
product.
The game is played as follows. First, the upstream producer chooses a produc-
tion level. Then the downstream user offers the upstream producer a price p per
unit of the product. The upstream producer can take it or reject it.
The upstream producer’s payoffs are pe − ce2 if he accepts the offer. His
payoffs are βe − ce2 if he rejects the offer. The downstream buyer’s payoffs if
the offer is accepted are αe − pe and if the offer is rejected are 0. This game is
represented in Figure 6.3.
At the final stage of the game, the upstream producer strictly prefers to take
the downstream user’s offer if p > β and strictly prefers to reject it if p < β.
The upstream producer is indifferent if p = β. As in our conflict model, there
is only an equilibrium if the upstream producer accepts an offer of p = β. So the
upstream producer accepts any offer of p ≥ β and rejects any offer of p < β.
Anticipating this, what will the downstream user offer? If the downstream
user offers p < β, she makes a payoff of 0. If she offers p ≥ β she makes (α − p)e.
Clearly, if the downstream user is going to make an offer that will be accepted,
she wants to offer as little as possible. Hence, she offers p = β.
What level of investment will the upstream producer make? The upstream
producer anticipates that he will get a price of p = β from the downstream user.
So he chooses his investment level to solve
max
e
βe − ce2.
4See Lafontaine andMorton (2010) for details.
182 Chapter 6
RejectAccept
Downstream
Upstream
Upstream
U:
D:
pe – ce2
αe – pe
U:
D:
βe – ce2
0
e
p
Figure 6.3. Hold up problem.
Maximizing, the equilibriumproduction level, e∗, is given by the following first-
order condition:
β − 2ce∗ = 0 ⇒ e∗ = β
2c
.
This equilibrium is inefficient. Since the product will end up with the down-
stream user, its final value is αe and its cost is ce2. Hence, the efficient level of
production solves
max
e
αe − ce2.
The first-best investment is
α − 2ceFB = 0 ⇒ eFB = α
2c
.
Comparing the first-best investment to the equilibrium investment, it is clear
that the equilibrium has inefficient underproduction:
eFB = α
2c
>
β
2c
= e∗.
The problem is that while the social value of the product is α, the upstream
producer knows he will not be paid a price of α. He will only be paid a price of
β. If the downstream user could commit to pay α, the upstream producer would
invest efficiently. But the downstream user cannot credibly commit to do so.
Once production decisions are made, the downstream user has an incentive to
Commitment Problems 183
“hold up” the upstream producer—paying only enough tomatch the upstream
producer’s next best option.
6.2.1 Interpretation
The hold-up problem suggests that a lack of credible commitment leads to
inefficiently low levels of investment. This sort of problem might emerge in a
variety of settings.
In many industries, an upstream supplier must bear up-front costs (e.g., new
technology, a specialized workforce) to build products to a downstream user’s
specifications. By making downstream user-specific products, the upstream
supplier diminishes the outside marketability of the upstream product. This
means the upstream supplier is particularly subject to hold-up. Hence, the
upstream supplier will be disinclined to bear the up-front costs, leading to
inefficiency.
Firms invest in research to develop a new product (e.g., medicine, tech-
nology). If the buyers of those products have significant market power, then
the research firm can be held up, leading to underinvestment in research and
development. For instance, a concern about adverse effects on investment in
new treatments is sometimes raised when largemedical insurers or government
agencies use their market power to negotiate lower prices for prescription
medication.
When consumers purchase software, they anticipate that it may require fu-
ture modification or updating that they cannot do on their own—for example,
tax or accounting software. Once a consumer has purchased the software,
the company that has the capacity to modify the software can hold up the
consumer (who doesn’t want to switch platforms) by charging a high price for
future updates. This potential for hold-up will lead to underpurchasing of such
software.
Inside a partnership—for example, a law firm or medical practice—some
partners invest in technical expertise and other partners invest in client rela-
tionships. The partner with client relationships can later threaten to leave with
the clients, holding up the partnerwith technical expertise for a greater share of
profits. Hence, partners might have incentives to overinvest in client relations
and underinvest in technical know-how.
6.3 Policy Responses
In the case of both costly conflict and the hold-up problem, some future action
cannot be credibly committed to even though, from an ex ante perspective,
both actors would be better off if a credible commitment could be made.
Thus, one can think of a lack of enforceable contracts as the fundamental
issue. This lack of enforceability might be because the relevant information
184 Chapter 6
(e.g., how hard someone worked) is unobservable by a court and therefore can’t
be contracted. It might also be because of a lack of institutional capacity for
enforcing contracts, as in the case of the absence of a third-party guarantor
for agreements during civil war. The basic insight of both models is that non-
contractibility leads to inefficiency of various sorts—conflict, underinvestment,
and so on. And so the policy challenge is to find ways—legal, institutional, or
informal—to facilitate credible commitment.
In the context of conflict, one approach is for the international commu-
nity to serve as a third-party guarantor. The most direct approach is sending
peacekeepers to enforce agreements. But international institutions, such as the
International Criminal Court, which have the ability to hold actors to account
for illegal acts, also play such a role.
In the context of the hold-up problem, economists have thought a fair bit
about how firms and other economic actors might try to solve commitment
problems on their own. One provocative idea is that firms themselves are a
response to problems like hold-up. The argument is that a vertically integrated
firm might solve the hold-up problem by unifying upstream and downstream
actors within one overarching economic agent. If both actors can be placed in
a setting in which they only care about firm profits, then the hold-up problem
disappears. While this is a powerful idea, there are at least some reasons to be
skeptical about vertical integration as a solution to the hold-up problem. In
particular, it is often the case that units within a firm view themselves as in
competition. If this is the case, it might well be that the hold-up problem is
re-created within the firm.
In the context of other commitment problems, social scientists argue that
various kinds of institutions might aid with commitment. For instance, a
government that faces a potential rebellion might like to promise all sorts
of policy concessions to avoid revolution. However, such a commitment may
not be credible if the revolutionary threat itself diminishes over time. If the
government democratizes (i.e., changes institution), then it actually places
at least partial control of government decisions in the hands of the people
considering rebelling, perhaps credibly committing to follow compromise poli-
cies and avoiding a costly rebellion (Acemoglu and Robinson, 2001, 2006).
Of course, this idea raises deep questions about why democracy itself
constitutes a credible commitment, but we will leave those questions for
another day.
Actors can also find less dramatic ways to limit future discretion in order to
solve commitment problems.Wediscussed the idea that strikesmight be caused
bymanagement’s inability to commitnot to exploit increasedpower that comes
from union wage concessions in future contract negotiations. In such a setting,
management might willingly give up some of its future negotiating power, for
Commitment Problems 185
instance by subjecting future contract disputes to binding arbitration, in order
to avoid a strike.
6.4 Takeaways
• Commitment problems arise in dynamic settings due to the absence of en-
forceable contracts and shifting power (political, military, social, market,
or legal). These commitment problems give rise to inefficient behavior “up
the tree.” This inefficient behavior can takemany forms: underinvestment,
conflict, and so on.
• One way to solve commitment problems is to create institutions (formal
or informal) that allow players to credibly commit (e.g., democracy as a
commitment device for policy change).
• Another solution to commitment problems is to find ways for players to
write binding and enforceable contracts.
6.5 Further Reading
Fearon (1995) provides the classic discussion of the puzzle of costly conflict.
Fearon (1998) is the clearest articulation of the basic workings of the relation-
ship between commitment problems, shifting power, and inefficient conflict.
Themost general characterization of this relationship is Powell (2004).
For classic work on the relationship between the hold-up problem and the
theory of the firm, see Williamson (1975, 1985), Klein, Crawford, and Alchian
(1978), and Hart (1988).
6.6 Exercises
1. Consider the followingmodel of a budget process. At the beginning of the
game, a Leader chooses a punishment to impose on all players if the
Congress fails to pass a budget. Call this punishment p. The Leader can
choose p = 0 (i.e., no punishment) or p = 1.5. The Congress then either
compromises or it does not compromise. If the Congress compromises, a
reduced budget is passed. If the Congress fails to compromise, then the
status quo budget is passed and the penalty is implemented.
Payoffs are as follows. The payoff to the Leader of the status quo is 0 and
the compromise is 1. The payoff to the Congress of the status quo is 1 and
the compromise is 0. Thus, the game is represented in Figure 6.4 (where the
first payoff is always the Leader’s):
(a) Write down all of the Leader’s strategies. Write down all of the
Congress’s strategies.
186 Chapter 6
Leader
Congress
Co
m
pr
om
ise
No com
prom
ise
Congress
1
0
1
0
0
1
0 – 1.5 = –1.5
1 – 1.5 = –0.5
p = 1.5p = 0
Co
m
pr
om
ise
No com
prom
ise
Figure 6.4. Budget game.
(b) Write down the unique subgame perfect Nash equilibrium of this game.
Describe what happens in this equilibrium.
Now suppose that, should Congress fail to compromise, the Leader gets to
choose whether or not to impose the punishment. That is, the game is now
the one represented in Figure 6.5:
(c) In this revised game, write down all of the Leader’s strategies and write
down all of the Congress’s strategies.
(d) In this revised game, write down any one subgame perfect Nash
equilibrium.What happens in this equilibrium?
(e) Explain how comparing the equilibrium outcomes in these twomodels
illustrates how an inability to commit canmake a player worse off.
Leader
Leader Leader
Congress
Co
m
pr
om
ise
No com
prom
ise
Pu
ni
sh
Don’t punish
Congress
1
0
1
0
0
1
0
1
0 – 1.5 = –1.5
1 – 1.5 = –0.5
0
1
p = 1.5p = 0
Co
m
pr
om
ise
No com
prom
ise
Pu
ni
sh
Don’t punish
Figure 6.5. Budget game without commitment.
Commitment Problems 187
RejectAccept
Downstream
Upstream
Upstream
U:
D:
pe – ce2
4e – pe
U:
D:
e – ce2
0
e
p
Figure 6.6. Hold up game.
2. Consider the model of hold-up in Figure 6.6. At the beginning of the game,
player U chooses a level of effort, e. Then playerD offers a price, p. Finally,
player U chooses to accept or reject the offered price.
If U accepts, it gets pe in revenues. If it rejects, it can use what it produced
at value 1, so gets revenues e. The cost to U of effort is ce2 (where c > 0 is a
parameter that affects U’s marginal cost of effort, which, differentiating,
is 2ce).
D values e at 4e. So if U accepts,D’s payoff is 4e − pe. If U rejects,D’s payoff
is 0.
(a) Solve for the unique subgame perfect Nash equilibrium.
(b) Assuming that the outcome involves the price being accepted, what is
the utilitarian payoff in this game? (Your answer will be a function
of c.)
(c) What is the utilitarian optimum level of investment? (Your answer will
be a function of c.)
(d) Explain why the equilibrium and utilitarian levels of investment are
different.
(e) Now, suppose thatD could actually commit, up-front, to a price. That is,
suppose the payoffs stay the same, but the order of play changes so that
the game is as in Figure 6.7. What is the unique subgame perfect Nash
equilibrium of this game?
(f) Is the equilibrium identified in (e) a Pareto improvement relative to that
identified in (a)?
(g) Does your answer to (f) suggest thatD did or did not suffer from a
commitment problem in the original game?
188 Chapter 6
Figure 6.7. Hold up game with commitment.
RejectAccept
Upstream
Downstream
Upstream
U:
D:
pe – ce2
4e – pe
U:
D:
e – ce2
0
p
e
3. In Stanley Kubrik’s classic satirical film,Doctor Strangelove, a nuclear-armed,
American bomber is on its way to bomb the Soviet Union and cannot be
recalled. Upon learning this, the Russian ambassador is forced to reveal to
the Americans that the Soviets have built a doomsdaymachine—amachine
that will automatically detonate enough nuclear weapons to destroy the
earth if Russia is attacked or if anyone tries to disarm the doomsday device.
Such doomsday devices were indeed discussed by policymakers during the
height of the ColdWar. Explain why such devices might have some appeal
in terms of commitment problems.
4. Figure 6.8 is a model in which the “people” can credibly threaten revolution
if a leader does not democratize.
The best outcome for the people is to get democracy without revolting.
The second-best outcome is to get democracy after threatening a revolution.
The third-best outcome is to get no democracy and not revolt. The worst
outcome is to get no democracy and have to revolt.
The best outcome for the leader is to neither democratize nor have a
revolution. The second-best outcome is to democratize without being
threatened. The third-best outcome is to democratize under threat of
revolution. The worst outcome is to not democratize and then actually face
a revolution.
(a) Write down all of the strategies for each player.
(b) Identify all the SPNE of this game.
Commitment Problems 189
People
Leader
De
m
oc
ra
tiz
e Don’t
dem
ocratize
Leader
P:
L:
4
1
P:
L:
0
0
P:
L:
5
2
P:
L:
1
5
Th
rea
ten
re
vo
lt
Don’t
dem
ocratize
Don’t threaten
De
m
oc
ra
tiz
e
Figure 6.8. First revolution game.
Now consider the alternate game in Figure 6.9, in which the leader moves
first and the people only consider revolting if there is no democratization.
(c) Write down all of the strategies for each player.
(d) Identify all the SPNE of this game.
(e) Suppose we define democratization as “good policy” here. (That is, we
are not focused on Pareto improvements or utilitarianism, we just want
democracy.) Use a comparison of (b) and (d) to explain how a
commitment problem can give rise to a bad policy outcome.
Leader
People
L:
P:
0
0
L:
P:
2
5
L:
P:
5
1
De
m
oc
ra
tiz
e
Don’trevolt
Don’t
dem
ocratize
Re
vo
lt
Figure 6.9. Second revolution game.
5. (This problemwas inspired by a problem from Ben Polak.) A company is
considering building a new factory. The factory will cost c to build. To
operate, the factory requires 100 workers. Once operating, it will generate
profits of π . If the company builds the factory and hires the workers at wage
w, it makes a payoff of
π − 100w − c.
If the company builds the factory but fails to hire workers, it makes a payoff
of −c. If it doesn’t build the factory, it makes 0.
190 Chapter 6
The workers currently have jobs that pay a wage of v. The workers’ payoff
is equal to their wages (either at the new factory or in their current jobs).
(a) Suppose the workers can be hired at their current wage—that is,w = v.
For what values of cwill the firm build the factory?
(b) Suppose that, after the factory is built, the workers’ union canmake a
take-it-or-leave-it wage demand to the firm. The firm’s only choice is to
pay that wage or have the factory not operate (thereby losing its up-front
investment of c). What demand will the unionmake? Anticipating this,
for what values of cwill the firm build the factory?
(c) Explain how the difference between your answers to parts (a) and (b) are
the result of a hold-up problem.
Summing Up Social Dilemmas
In Part II we learned about three kinds of social dilemmas—externalities, coor-
dination problems, and commitment problems. Each of thesemodels describes
a broad array of social phenomena. Moreover, when any one of them occurs,
the right policy intervention could achieve a Pareto improvement. The hope is
that having a conceptual understanding of these dilemmas clarifieswhere there
are opportunities for policy to do good.
Importantly, different dilemmas require different types of policy responses.
Table 6.1 offers a summary, showing the policy technologies best matched to
each social dilemma.
We also discussed the idea that for certain types of social dilemmas, ongoing
relationships may make it possible for people to self-organize a solution. This
is particularly likely in tight-knit and relatively small groups. Importantly, even
when self-organization is possible, it requires coordination. Hence, another role
for policymakers is to use the tools appropriate for addressing coordination
traps to help groups self-organize solutions to externalities and commitment
problems.
TABLE 6.1. Social Dilemmas and Policy Interventions.
Social Dilemma Types of Intervention Length of Intervention
Externality Pigovian tax or subsidy Long Run
Regulation
Coordination Problem Leadership and Communication Short Run
Insurance Long Run
Enforceable contracts
Commitment Problem Limit discretion Long Run
Vertical integration
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PART III
Constraints on Good Governance
The ubiquity of social dilemmas creates many opportunities for good policy
to yield Pareto improvements. Yet much of the policy implemented by govern-
ments does not look like the textbook policy solutions we’ve described. To be
sure, there are examples of Pigovian taxes in response to externalities, publicly
provided insurance that eliminates coordination traps, and so on. But there are
alsomany actions taken by policymakers that are hard tomake sense of in terms
of social dilemmas or Pareto improvements.
Indeed, a widely held view among political economists is that much policy
is motivated not by opportunities to do good, but by rent seeking—that is, using
policy to benefit particular individuals or groups. Stigler (1972, p. 100) provides
some classic examples:
Particular industries and occupations obtain from the state a variety of
economic privilegeswhich are injurious to the vastmajority of the popula-
tion. Farm subsidies, oil import quotas, tariffs, and occupational licensing
are examples.
Let me offer a few specifics.
The price of sugar in the United States is more than twice its price inmuch of
the rest of the world. The reason is a series of U.S. policies—import restrictions,
price guarantees, etc.—designed to protect the domestic sugar industry. These
policies benefit certain agricultural interests, including both sugar producers
and corn growers (demand for corn syrup is driven by high sugar prices). But
they impose costs on many other domestic constituencies. Most directly, they
harmU.S. food producers and consumers. They also impose costs on taxpayers,
who foot the bill for a program in which the government buys surplus sugar
194 Part III
when prices drop. Finally, a study by the U.S. Commerce Department estimates
that, for every job in the sugar industry saved by U.S. sugar subsidies, three
jobs are lost in industries that use sugar as an input.1 Beghin et al. (2003)
estimate that, on net, the U.S. sugar program generates half a billion dollars (in
1999 dollars) in annual deadweight loss. Sugar subsidies are, of course, just one
among many such policies involving price supports and import restrictions in
the United States and around the globe.
Concern about the anti-competitive effects of professional licensing date
to at least Adam Smith, who, in Chapter 10 of the first volume of The Wealth
of Nations, argues that such restrictions harm welfare “by restraining the
competition in some employments to a smaller number than would otherwise
be disposed to enter into them.” As Kleiner (2006, p. 189) summarizes, Smith
worries about “the ability of the crafts to lengthen apprenticeship programs
and limit the number of apprentices per master, thus, ensuring higher earnings
for persons in these occupations.” Kleiner notes that by 2000, over 20% of
U.S. workers required some sort of licensing. To be sure, in some settings,
licensingmay play an important role monitoring quality, enforcing ethics, and
informing consumers. But, as Smith and many observers since have noted,
licensing also has costs. By restricting entry into the market place, licensing
requirements decrease supply, benefiting a small group of incumbents at
the expense of new entrants and consumers. These issues arise in a wide
array of venues. In some areas—like the efforts of physicians’ groups to use
licensing requirements to restrict the type of care that can be provided by nurse
practitioners or the attempts by lawyers’ groups to restrict the services that
can be provided by paralegals—there may be serious questions about how to
weigh the trade-offs between ensuring high quality service, on the one hand,
and fostering competition, on the other. In other areas—like the attempts
by taxi drivers to use licensing requirements to avoid competition from ride-
sharing companies like Uber or the mandate that bartenders, barbers, and
cosmetologists be licensed in many states—it is hard to imagine a compelling
public interest argument for the practice of professional licensing.
The reason we observe such inefficient policies, of course, is because public
policy is not made by a Pareto improving machine. Public policy is made
by governments, which is to say by politicians and bureaucrats. Political de-
cision making is a (perhaps the) critical determinant of what kinds of poli-
cies get made and enforced. Policymakers are people, with their own beliefs
and incentives, working within strategically complicated environments to
achieve their goals. Indeed, all of the dilemmas we studied in Part II as a
1U.S. Department of Commerce International Trade Administration. 2006. “Employment
Changes in U.S. Food Manufacturing: The Impact of Sugar Prices.” http://trade.gov/media/
Publications/pdf/sugar06.pdf
http://trade.gov/media/Publications/pdf/sugar06.pdf
http://trade.gov/media/Publications/pdf/sugar06.pdf
Constraints on Good Governance 195
motivation for policymaking—externalities, coordination problems, commit-
ment problems—and many others, also exist within the governmental orga-
nizations in which policy gets made. Moreover, the people and organizations
that are governed by policy are also strategic actors who work hard to influence
the policy process to suit their own interests. Hence, if you want to understand
policy, you must understand the politics of the policymaking process. And if
you want to be a leader of policy debates, youmust be able to work within these
political constraints.
In what follows, we will examine some reasons why governments might fail
to achieve Pareto improvements in the face of social dilemmas. Broadly speak-
ing, we will consider two classes of explanations—technological and incentive
constraints.
By a technological constraint Imean some factor in theworld that limits even
a well-intentioned policymaker’s ability to achieve good outcomes. The tech-
nological constraints wewill consider include people’s ability to adjust their be-
havior to avoid a policy’s intended effects, policymakers’ limited commitment
power, and lack of information needed tomake optimal policy decisions.
By an incentive constraint Imean features of the politics of the policymaking
process that affect policymakers’ interests. We will consider various ways in
which the governed attempt to influence policymakers, including through
interest group politics and lobbying, political donations, and electoral politics.
We will also look at how the institutional rules that govern how a leader
maintains power shape policymakers’ incentives.
It is worth reiterating a point made in the introduction to this book. I do
not provide a fine-grained analysis of the legislative, judicial, or bureaucratic
politics of the policymaking process. Understanding those politics is also essen-
tial for understanding policy. But the details of those subjects are, in my view,
best covered in more specialized courses and books. My goal, here, is to offer
general principles that lend insight into government decision making across
many institutions. Just as with the treatment of social dilemmas, in so doing,
I hope to provide models that clarify how one thinks about the challenges of
moving from a good policy idea to successful policy reform. Along the way,
I will also present some evidence that these kinds of governance challenges and
constraints really domatter for policy and welfare.
Finally, let me highlight one other important point. In what follows, I
will provide a variety of examples and models in which governments fail to
implement optimal policy solutions. This should not be taken as an argument
against or critique of government or public policy. That is emphatically not
the point I am trying to make. Rather, I want you to see something more
nuanced. Traditional policy analysis stops at the point of identifying policy
solutions that would be effective if faithfully implemented. Such an analysis
196 Part III
has a hidden, and unrealistic, assumption about how governments act. A more
thoroughgoing policy analysis takes these political constraints seriously as first-
order concerns for policy design and implementation. The various analyses that
follow are meant to move us in the direction of this more satisfying notion of
what constitutes good policy, all things considered.
7
Strategic Adjustment
Corporate Average Fuel Economy (CAFE) standards, which regulate the fuel
efficiency of fleets of cars produced by a given manufacturer, were first imple-
mented in the 1970s. The goal was to improve the fuel economy and reduce the
environmental impact of automobiles. And, indeed, fuel economy improved
dramatically in the United States starting in the 1980s.
But CAFE standards also had another effect. Because light trucks are used in
agriculture, they were not treated as cars for the purpose of CAFE standards.
They were subject to laxer fuel economy regulation. In effect, CAFE standards
reduced automobile manufacturers’ costs of selling light trucks relative to cars.
In response, the auto industry all but eliminated the station wagon (which
was classified as a car), substituting minivans and SUVs (both of which were
classified as light trucks) into their personal vehicle fleets. They could sell these
large vehicles cheaply (relative to cars) because of the regulatory advantage. A
combination of well-intentioned regulation, government failure to anticipate
strategic adjustments by automobile manufacturers, and good old-fashioned
American love of big stuff are, at least in part, to thank for the rise of the SUV as
a passenger vehicle.
The Clinton-era “welfare to work” reform seems to have had a similar un-
intended consequence.1 Welfare to work was meant to move people toward
self-sufficiency by making public assistance conditional on finding work. And
a first glance at the data suggests it was a major success. The number of welfare
recipients dropped from about 5 million families in 1995 to about 2 million
families in 2010. But it is worth digging a little deeper.
Since much of the financial burden of public assistance fell to state govern-
ments, welfare to work gave states strong incentives to move people into the
work force. Of course, one way to do so was to actually help people find jobs.
But state governments also found other ways to do so—for instance, by turning
unemployed workers into disabled workers. People who qualify as disabled are
not counted as unemployed. Moreover, since they qualify for federal disability
payments, disabled workers don’t cost the states anything. So, following the
adoption of welfare to work, the states started working hard to help people
1See Chana Joffe Walt. Unfit for Work: The startling rise of disability in America. National Public
Radio. http://apps.npr.org/unfit for work/
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198 Chapter 7
who might otherwise end up on public assistance instead apply for disability.
Many states hired private companies to search lists of welfare recipients for
people who couldmake disability claims and to assist those people through the
application process. And, indeed, just as the welfare rolls started their dramatic
decline, the federal disability rolls started a significant increase, from about
4million former workers in 1995 to about 8million in 2010.
One last example comes from my own industry, higher education. A variety
of federal government policies in the United States seek to make higher educa-
tionmore affordable.Most notably, the government offers education tax credits
and subsidized student loans. Itmight seemobvious that suchpolicies lower the
price of college for students, but let’s think about it a little more.
Offering a college tax credit or subsidized loan is equivalent to lowering
the price of college for students. If tuition stays fixed, this will in fact help
with affordability. The problem is that colleges are free to increase tuition to
whatever level the market will bear. Even at current prices, admission to a
research university is very competitive. If the price of tuition drops as a result of
new federal subsidies, demandwill increase. Two things can happen in amarket
when there is excess demand. Supply can increase or prices can go up.
The thing about education at a research university, unlike many other busi-
nesses (e.g., gas stations, grocery stores), is that it is very hard for supply to
increase in the short- to medium-run. Research universities depend on enor-
mous, very expensive infrastructures (physics labs, libraries, dorms, faculties,
and so on). They also depend on reputation. So an entrepreneur cannot easily
increase supply by creating a new research university where there wasn’t one
before. Another way that supply might increase is for research universities to
admitmore students.Universities arewilling to do so to some extent in response
to excess demand. But that extent is limited because universities care about
selectivity, student to faculty ratios, and the like.
If the supply of research universities can’t expand tomeet the excess demand
created by a new federal subsidy, only one other thing can happen. Prices go up.
That is, universities increase tuition or decrease internal financial aid to suck up
those new federal benefits. In this scenario, the federal subsidy doesn’t make
college more affordable. The real cost to students stays the same. The policy is
simply a transfer from taxpayers to research universities.
Recent evidence demonstrates that research universities do in fact strate-
gically adapt to policy changes in this way. The best study concerns the Pell
Grant Program, which in 2011 provided over nine million low-income college
students with subsidies of $35 billion (Turner, 2014). Research universities
appear to reduce institutional financial aid by about 66 cents for every dollar
a student receives in federal grants. So the federal subsidies help students a bit,
but most of the money flows to the colleges. Interestingly, the same is not true
at community colleges and technical schools, where it is easier for supply to
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expand to meet excess demand. As a result, such schools are not able to adapt
in a way that captures all of the benefits of government subsidies. And, indeed,
subsidies do appear to increase affordability for students at these schools.
Each of these examples illustrates a key insight that comes from thinking
game theoretically. Actions taken “up the tree” affect behavior “down the tree.”
This idea is particularly important when thinking about public policy. Often
in policy debates, people estimate the expected effects of some policy change
assuming that behavior won’t change in a meaningful way when the policy
shifts. As we’ve just seen, this is amistake that can lead to bad policy choices. In
the remainder of this chapterwe consider twomodels that illustrate particularly
important forms of strategic adaptation and how they create challenges for
policymakers.
7.1 Strategic Adversaries
Inmany policy settings—policing, counterterrorism, regulatory oversight—the
government has limited resources which it must use to prevent bad behavior
by non-governmental actors. For instance, police must deploy a finite number
of patrols across neighborhoods, counterterrorists only have the resources to
harden a limited number of potential targets, and nuclear regulators must
decide which plants to monitor. In deciding how to deploy its resources, it is
critical that the government think about how other actors’ behavior will shift
in response. Let’s consider a simple model in the context of counterterrorism.
There are two potential terrorist targets: A and B. A government allocates
counterterrorism resources between the targets. Let α ∈ [0, 1] be the resources
devoted to protecting A and 1 − α be the resources devoted to defending B. The
terrorists then choose to attack one or the other target.
The probability that an attack against a given target succeeds depends on
the counterterrorism resources devoted to protecting that target. For simplicity,
assume that if the counterterrorism resources devoted to protecting a particular
target are x, then the probability of an attack on that target succeeding is 1 − x.
For now, let’s assume the terrorists value the two targets equally.
We can solve this game via backward induction. What will the terrorists do,
given the government’s counterterrorism strategy, α? There are three cases to
consider:
1. If the government chose α > 12 , an attack against target A succeeds
with lower probability than an attack against target B. So the terrorists’
unique best response is to attack target B.
2. If the government chose α < 12 , an attack against target A succeeds with higher probability than an attack against target B. So the terrorists’ unique best response is to attack target A. Data Highlight 200 Chapter 7 3. If the government chose α = 12 , the terrorists are indifferent between attacking A or B. (It turns out that, to sustain an equilibrium, the terrorists randomize between the two targets, but don’t worry about that for now.) What does this imply about how the government should allocate its coun- terterrorism resources? If the government expends more resources protecting one target than another, those resources are wasted because the terrorists will adapt, attacking the other target. All the government can do is to spread its resources thin, defending both targets equally. Several points are interesting here. First, the optimal counterterrorism policy is not responsive to howmuch the government cares about the two targets. Even if the government caresmassively more about defending target A than target B, it still isn’t the right decision to devote more resources to target A. The reason is the strategic adaptation of the terrorists. If the government devotes lots of resources to the target it cares most about, the terrorists will simply attack the other target, and so the government would have been better off devotingmore resources to protecting that target. Second, the optimal counterterrorism policy is responsive to how much the terrorists care about the two targets. Suppose the value to the terrorists of an attack against A is vA and against B is vB. The terrorists strictly prefer to attack A if (1 − α)vA > αvB,
which can be rewritten
α < vA vA + vB . Thus, the terrorists’ best response correspondence is now BR(α) = ⎧ ⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎩ Attack A if α < vA vA + vB Attack either if α = vA vA + vB Attack B if α >
vA
vA + vB
.
So the government again spreads its resources thin in the optimal counterterror-
ism scheme, but weighted by howmuch the terrorists care about each target, so
as to equalize the terrorists’ expected value of attacking any given target.
Third, this logic holds even more starkly if there are lots of potential tar-
gets, rather than just two. In particular, the optimal counterterrorism policy
looks like this. Start by spending on the target considered most valuable by
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Strategic Adjustment 201
the terrorists. Keep spending until the terrorists’ expected value from attacking
it is equal to their expected value from attacking the second most valuable
target. Then spend on both of those until the expected value of attacking either
of them is equal to the expected value of attacking the third most valuable
target. Then spend on all three of those until the expected value of attacking
any of them is equal to the expected value of attacking the fourthmost valuable
target. Continue this process until you are out of money. Thus, if there are lots
of targets, the government must spread its resources very thin because of the
terrorists’ capacity to strategically adapt.2
7.1.1 Do Terrorists Really Strategically Adjust?
You might think that we are leaning a little too heavily on the rationality
of terrorists in this story. The only reason the government’s optimal policy
calls on it to spread its resources so thin is because our hyperrational terrorists
strategically adapt whenever the government fails to do so. Let me offer you a
little bit of evidence to suggest this isn’t so crazy.
Starting in the mid-1960s, hijacking became a serious problem in American
civil aviation. Over 80 airplanes were taken by hijackers in 1969 alone. The
hijackers included Americans, Croatians, Cubans, Japanese, North Koreans,
Palestinians, and many others. Their motivations ranged from simple ransom
to nationalist, leftist, and other global political causes.
In the early 1970s, in response to this growing assault on air safety, theUnited
States and European countries increased airport security. Most importantly,
metal detectors were installed in every major American airport by early 1973.
We’d taken our first step on the road toward only using toiletries that come in
three-ounce packages andnot being able towear sockswith holes to the airport.
Did this heightened security work to increase public safety? In one sense,
the answer is clearly yes. The upper cell of Figure 7.1 (which is a simplified
replication of the analysis from Enders and Sandler (1993)) shows hijackings
decreased fairly dramatically right after metal detectors were installed in 1973.
But that is not the whole story. After metal detectors were installed, other kinds
of terrorist hostage takings becamemore frequent, as shown in the lower cell of
Figure 7.1. Indeed, Enders and Sandler show that during the course of the 1970s
there is almost a one-for-one relationship between the decline in hijackings and
the increase in other types of hostage-taking terrorist attacks.
There are a couple of points to see here. First, there is a general point
for thinking about counterterrorism, policing, and so on. Trying to protect
individual sites—airports, nuclear reactors, tourist destinations, skyscrapers,
government buildings, and so on—requires us to spread our resources thin.
Thus, such a policy is unlikely to be terribly effective in the presence of a large
2See Bueno deMesquita (2007) and Powell (2007) for discussions of these and related issues.
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1968 1970
40
30
20
10
0
25
20
15
10
5
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1972 1974 1976 1978
Worldwide Skyjackings per Quarter, 1968–1977
Horizontal line is average incidents per quarter before and after 1973:Q1.
Year and quarter
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1968 1970 1972 1974 1976 1978
Worldwide Hostage Takings per Quarter, 1968 1977
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Year and quarter
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Figure 7.1. Change in hijackings and non hijacking hostage takings following installa
tion of metal detectors. The data are from Mickolus (1982). The analysis is a simplified
version of that in Enders and Sandler (1993).
number of potential targets.Much better are policies that are broad-based in the
sense of protecting everything at once. Such policies might include restricting
terrorist financing or access toweapons, intelligence gathering to detect attacks,
border security, and the like.
Second, these adjustments suggest that a major portion of the U.S. govern-
ment’s response to the 9/11 attacks may have been suboptimal. In policing
and counterterrorism, there is often a tendency to fight yesterday’s war. If
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Strategic Adjustment 203
the terrorists attack airplanes, we protect airports. If there is a rash of crime
in a particular neighborhood, we send police to that neighborhood. But such
policies may fail due to strategic adaptation.
7.1.2 The War on Drugs
The problem of disrupting the drug trade is not unlike the problem of
preventing terrorist attacks. If the government tightens airport security, ter-
rorists take hostages in some other location. If the government makes it more
difficult to move drugs into the United States through some entry point, the
drug smugglers find a different one, often with toxic effects along the new
route.
The Mexican drug war resulted from precisely this kind of adaptation. In
the 1970s and early 1980s, very few drugs reached the United States through
Mexico. The transshipment route of choice was from Colombia through the
Caribbean and into Florida. In 1980, the Drug Enforcement Administration
launched Operation Swordfish—amajor offensive against the Colombian drug
cartels. The government deployed thousands of agents and considerable naval
and air power to shut down the Caribbean transshipment route.
Not unlike the case of metal detectors, there is a sense in which Operation
Swordfish and other U.S. government efforts in the Caribbean and southern
Florida were a stunning success. By the mid-1980s, the Colombian drug cartels
were actively pulling out of the Caribbean and the flow of drugs into Florida
diminished considerably. In 1985, 75% of all cocaine seized by authorities
was captured in the Caribbean. By the early 1990s that number had fallen to
around 10%.3
But to call these outcomes a victory is to ignore the fact that drug smugglers
adapt. The reduction in drugs flowing through the Caribbean and into Florida
in the 1980s does not reflect a reduction in drugs flowing to the United States
during that period. Indeed, drugs continued to enter the United States at
increasing rates, as evidenced by the fourfold decrease in cocaine prices during
the course of the 1980s—from a wholesale price of around $200 per pure gram
in 1980 to under $50 in 1989—despite soaring demand.4
So what did happen? The Colombian cartels abandoned the Caribbean in
favor of Mexico. In 1989, one-third of all cocaine in the United States entered
through Mexico. Just three years later, that number had increased to one-half.
Today, 90% of cocaine sold in the United States is smuggled up fromMexico.
3See United Nations Office on Drugs and Crime. 2010. “The Globalization of Crime: A Transna
tional Organized Crime Threat Assessment.” Chapter 4. http://www.unodc.org/documents/data
and analysis/tocta/TOCTA Report 2010 low res.pdf
4See Office of National Drug Control Policy. October 2001. “The Price of Illicit Drugs:
1981 through the Second Quarter of 2000.” https://www.whitehouse.gov/sites/default/
files/ondcp/policy and research/bullet 5.pdf
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204 Chapter 7
This adaptation by the drug traffickers has had devastating effects on Mex-
ico. Throughout the 1990s, the Mexican drug trafficking organizations be-
came larger and more powerful. They shifted from being middlemen for the
Colombians to having their own suppliers and distribution networks. In the
course of this expansion, Mexican drug trafficking organizations became more
violent. In 2010, theMexican drug war claimed over 1,000 lives permonth. The
Mexican government struggled to exert basic control over parts of the country.
Suppose the Mexican government were to succeed in preventing drugs from
flowing across theMexican border into the United States.What would happen?
We can’t know for sure. But both our model of adaptation and past history sug-
gest that, since American demand for drugs doesn’t seem to be going anywhere,
the drug trafficking organizations would find a new transshipment route. The
most depressing scenario I can think of is that they would go right back to
the Caribbean, where American interdiction efforts are no longer focused. If
this were to happen, the expenditure of several decades of government efforts,
billions of dollars, and an untold number of lives would have been undone by
the basic logic of strategic adaptation.We’d be right backwherewewere in 1975.
On the up side, maybe they’d bring back Don Johnson andMiami Vice.
Well, that was quite depressing. Let me leave this subject on a somewhat
more optimistic note. As we’ve seen, the fact that people strategically adapt
makes a lot of trouble for drug policy. But, if you are really clever, sometimes
you can also make adaptation work for you. Kleiman (2011) offers the cleverest
such suggestion that I’ve seen. Here’s what he has inmind.
Kleiman’s proposal starts with theMexican government crafting andmaking
public a measure of how violent each drug trafficking organization is. Armed
with this information, the United States andMexican governments could then
focus their drug enforcement resources on the most violent organization. The
Mexican police would attack the organization directly in Mexico. The United
States governmentwould direct its investigative and enforcement efforts against
drug distribution networks that imported drugs sourced from the most violent
Mexican drug trafficking organization.
What would be the result of such a policy? In Mexico, the most violent
drug trafficking organization would find itself at a significant disadvantage
relative to the other drug traffickers. Presumably the remaining organizations
would pick up the slack, so total drugs exported to the United States would
be unlikely to change. But life and business would be bad for the most violent
organization.
In the United States, drug distributors that sourced from the most violent
drug trafficking organization would also find themselves at a disadvantage.
They would face greater risk, more police infiltration, and so on. Again, other
drug distributors might pick up the slack domestically, but life and business
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would be bad for those American distributors who sourced their drugs from the
most violent Mexican organization.
If other organizations pick up the slack, so that drug exports anddrug dealing
aren’t actually disrupted by targeting themost violent organization, what good
is this policy? Here is where you have to think about strategic adaptation. The
most violent Mexican drug trafficking organization faces two bad situations.
First, the Mexican government is going to focus its anti-drug resources on this
organization. Second, because of U.S. policy, its customers in the United States
are going to look to source their drugs from one of the other Mexican drug
suppliers.
There is a straightforward way for the most violent Mexican drug organi-
zation to avoid this fate—adapt, by reducing its use of violence so that some
other organization becomes themost violent one. Once that happens, the next
most violent organization becomes the focus of the two governments’ attention
and faces the same incentives to adapt. Once it does so, the third most violent
organization becomes the focus andhas incentives to reduce violence.When all
is said and done, then, this policy induces a race to the bottom. Each organization
wants to avoid being themost violent. The only way to avoid being leapfrogged
into the position of most violent is to keep becoming less violent until there is
basically no violence in theMexican drug business.
I must confess I love this idea. Its brilliance is that it exploits strategic
adaptation by drug traffickers—the historic bane of drug enforcement policy—
to induce a race to the bottom in violence. On the down side, it does nothing
to reduce the amount of drugs entering the United States. But we are already
failing to stop drugs from entering. At least under this policy tens of thousands
of people’s lives won’t have to be sacrificed in the service of getting those drugs
to market.
7.2 Incentivizing Multiple Tasks
My sister is a public school teacher. She is pretty intrinsically motivated. She
didn’t get into teaching for the money. She got into it to help kids learn. Like
any public school teacher in the United States in the twenty-first century, she
spends a lot of her time worrying about standardized tests. Her fate, the fate
of her students, and the fate of her school depend on test scores. And so she
describes what is a very familiar story to anyone who follows contemporary
education debates. Given the pressure to help her students perform well on
tests, she focuses a fair bit of effort on teaching test-relevant skills, sometimes
at the expense of other skills that may be more important for the student in
question but are less useful for the test.
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Her story illustrates a classic problem—how do we create incentives for
achieving an outcome that requires multiple inputs, when some of the inputs
are better measured than others? The output we care about in primary educa-
tion is how well the children are educated in some encompassing sense. But
this is very hard to observe. Some of the inputs might include teacher effort
devoted to math, teacher effort devoted to literacy, and teacher effort devoted
to socio-emotional skills. Each of these is also difficult for an outsider to observe
directly. Insteadwe observe coarse performancemeasures, like test scores. These
scores are probably informative about both the outcome we care about (overall
education) and each of the inputs. But they are certainly not equivalent to
any of them. Moreover, a performance measure like test scores is likely more
informative about some of the inputs (like math skills) than others (like socio-
emotional skills). So,whenyougive teachers incentives basedon test scores, you
push them to emphasize the skills that translate into test scores at the expense
of the skills that don’t.
Similar incentives are at work in medicine. The outcome we care about is
something like the amount of patient health provided per dollar spent. Patient
health depends on many inputs from the doctor. But the final outcome may
not be observable. Instead, programs like Medicare compensate physicians for
particular procedures. Thus, physicians are incentivized to provide observable
and well-compensated procedures, at the expense of other inputs that may be
more effective, if those alternative inputs are not as easily observed or as well
compensated.
Settings like this—and, of course, there aremany besides education or health
care—are another key arena in which strategic adaptation limits the power of
policy to improve outcomes. The key problem is that we have two goals:
1. We want to give some agent (e.g., a teacher) incentives to work hard.
2. We want the agent to allocate his effort appropriately across various
tasks.
As we will see, sometimes there is a trade-off between these two goals. Themore
we give the agent incentives towork hard, themore effort hewill devote to tasks
that are influential for observable performance, whether or not such tasks are
the most important input to the actual outcome. Surprisingly, this implies that
sometimes, as our ability tomeasure one task relative to another improves (e.g.,
we start testing kids in a way that is more informative about math skills than
socio-emotional skills), we should actually reduce the extent to which we use
such information to provide incentives. Let’s see this in a model.
There is some output, π , that is produced through two inputs, a1 and a2. The
production function is simple:
π = αa1 + (1 − α)a2,
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Strategic Adjustment 207
with 0 < α < 1. The parameter α measures how important task 1 is relative to
task 2 in producing the output. We can think of π as representing the overall
quality of a child’s education, while a1 and a2 are the teacher’s investment in
teaching test preparation and socio-emotional skills, respectively. The bigger α
is themore important the test preparation skills are, relative to socio-emotional
skills, for overall education.
Neither the inputs nor the output are observable. We can only observe some
performancemeasure that is also increasing in the inputs, but is not identical to
the output. The performancemeasure is
p = βa1 + (1 − β)a2,
with β �= α. We can think of p as test scores. Then β represents how responsive
test scores are to task 1 relative to task 2. Put differently, β represents how well
measured task 1 is relative to task 2. I will focus on the case where
β ≥ 1/2,
so that task 1 is assumed to be the better measured input. Notice, inside this
model, we can use β to think about policy changes. If we introduce a new
standardized test, β increases, because a teacher’s investment in teaching skills
relevant to the test (a1) becomes better measured relative to that teacher’s
investment in socio-emotional skills.
There is a single agent, let’s call him the teacher, whomust choose howmuch
effort to devote to the two tasks. The teacher is paid both a salary, s, and a pay-
for-performance wage, w ∈ (0, 1). If measured performance is p, the teacher’s
total compensation is s + wp.
The teacher is also intrinsically motivated to work on each task (i.e., he
gets a direct benefit). We measure his intrinsic motivation by I > 1. That is, in
addition to his pay, the teacher gets an additional benefit I × (a1 + a2) because
he finds his work inherently meaningful.
Finally, the teacher has costs for effort, given by
c(a1, a2) =
a21 + a22 + a1a2
2
.
These costs are like others we’ve already seen, in that they are quadratic in effort
devoted to each task. The additional term a1a2 means that if effort is higher on
task 1, then the marginal cost of effort on task 2 is higher (and vice versa). This
captures the idea that increasing effort on one taskmay crowd out effort on the
other task.
208 Chapter 7
Let’s start by solving for howmuch effort the teacher will devote to each task.
He solves the following problem:
max
a1,a2
s + wp + I(a1 + a2) −
a21 + a22 + a1a2
2
.
Substituting for p, this is the same as
max
a1,a2
s + w (βa1 + (1 − β)a2) + I (a1 + a2) −
a21 + a22 + a1a2
2
.
We maximize this function by taking the two first-order conditions (with
respect to a1 and a2), which yield
wβ + I = a∗1 +
a∗2
2
and
w(1 − β) + I = a∗2 +
a∗1
2
.
Solving these two equations in two unknowns, we have
a∗1 =
2
3
(I + w (3β − 1)) and a∗2 =
2
3
(I + w (2 − 3β)) .
There are several things to see here.
First, consider the total effort that the teacher exerts as a function of the
amount of performance pay he receives:
Total Effort(w) = a∗1 + a∗2 =
2
3
(2I + w).
Total effort is increasing in w—increasing pay-for-performance leads to an
increase in teacher effort.
Now consider how an increase in pay-for-performance affects the teacher’s
effort on each task separately:
da∗1
dw
= 2(3β − 1)
3
and
da∗2
dw
= 2(2 − 3β)
3
.
Since β > 1/2, a∗1 is clearly increasing in w (i.e.,
da∗1
dw > 0)—increasing pay-for-
performance increases effort on task one. However, a∗2 may be increasing or
decreasing in w. If β < 2/3, then a∗2 is increasing in w. If β > 2/3, then a
∗
2 is
decreasing in w. This implies that if one of the tasks is reflected much more
strongly than the other task in measured performance (p), then an increase
Strategic Adjustment 209
in pay-for-performance leads to an increase in total effort, but a decrease in
effort allocated to the less well-measured task. The intuition is that as pay-
for-performance increases, the teacher has an incentive to adjust her behavior
toward the task that has the larger impact on measured performance. Doing so
tends to crowd out effort toward the other task.
In light of this, we might wonder when pay-for-performance is good policy.
On the one hand, it increases total teacher effort. On the other hand, it can
distort the allocation of that effort. To assess the policy, consider the effect of
pay-for-performance on the output we actually care about, π = αa∗1 + (1 − α)a∗2.
Plugging in the teacher’s equilibrium effort choices as a function ofw, we have
π(w) = α
(
2
3
(I + w (3β − 1))
)
+ (1 − α)
(
2
3
(I + w (2 − 3β))
)
.
How does a change in pay-for-performance affect this overall outcome?
dπ
dw
= 2
3
(
α (3β − 1) + (1 − α) (2 − 3β)
)
The overall outcome is improved by an increase in pay-for-performance if this
derivative is positive, which is true if
α
1 − α >
3β − 2
3β − 1.
It is clearly possible for this condition not to hold—increased pay-for-
performance can be counterproductive. In particular, the outcome we care
about (π) is decreasing in pay-for-performance (w) if β is relatively large and α
is relative small. This fact is illustrated in Figure 7.2. In each of the two upper
cells, the horizontal axis represents the amount of pay-for-performance and
the line traces out the actual outcome we care about, π , as a function of w.
I fix α low (1/8), so the first task is relatively unimportant for the outcome
we care about. In the left-hand cell β is large (3/4), so the first task is very
important for the performance measure. As a result, the quality of the outcome
is decreasing in pay-for-performance. In the right-hand cell β is smaller (1/2),
reducing mismatch between the outcome and the performance measure. As a
consequence, the quality of the outcome is increasing in pay-for-performance.
In the lower cell, α is on the horizontal access and β is on the vertical access.
The shaded region identifies situations in which the mismatch is sufficiently
large that pay-for-performance is counterproductive.
Why is the outcome sometimes decreasing in w when total effort is increas-
ing? The answer has to do with the allocation of efforts across the tasks. As
we’ve seen, if β > 2/3, then when pay-for-performance goes up, a∗1 increases
and a∗2 decreases because task 1 is reflected better in the performance measure
210 Chapter 7
1.33
1.32
1.31
1.30
0.2 0.4 0.6
w
π(
w
)
π(
w
)
w
α
β
0.8 1.0 0.2 0.4 0.6 0.8 1.0
0.2 0.4 0.6 0.8 1.0
1.65
1.55
1.45
1.35
1.0
0.9
0.8
0.7
0.6
α = 1–
8
β = 3–
4
I = 2 α = 1–
8
β = 1–
2
I = 2
Figure 7.2. Depending on the extent of mismatch between the outcome of interest
and the performance metric, increasing pay for performance can make outcomes bet
ter or worse. In the upper left hand cell there is considerable mismatch and the
quality of the outcome is decreasing as pay for performance increases. In the upper
right hand cell there is less mismatch and the quality of the outcome is increas
ing in pay for performance. The shaded area of the lower cell indicates the set of
parameter values where mismatch is sufficiently severe that pay for performance is
counterproductive.
than is task 2. The problem is, when α is relatively small, task 2 is more
important for the actual outcome we care about than is task 1. As a result, in
this case, an increase inw increases themismatch between the allocation of the
teacher’s effort (which is primarily devoted to task 1) and the allocation of effort
that is optimal for generating the outcome we care about (which puts greater
emphasis on task 2). If this mismatch is sufficiently large (which is true when
β and α are far apart), this increased misallocation can have a large enough
negative effect to more than offset the benefits of greater total effort. Hence, as
a result of strategic adaptation toward themore measurable task by the teacher,
Strategic Adjustment 211
sometimes giving stronger incentives actually leads to worse outcomes. This is
particularly likely to be the case when there is a mismatch between the import
andmeasurability of various inputs.
It is important to recall that I’ve emphasized an interpretation of the model
in an educational setting. But the basic problem of multitask incentives is quite
general.
7.2.1 High-Stakes Testing
In recent years, and especially with the adoption of the NoChild Left Behind
Act, high-stakes testing has become an increasingly important part of American
education policy. Under high-stakes testing, students only advance grades or
graduate if their scores on various standardized tests meet some minimum
threshold. Our model suggests that teachers will strategically adapt, focusing
on those activities most relevant for getting students over the test thresholds
and on those studentsmost likely tomove from one side of the threshold to the
other.
Let’s start by seeing evidence that teachers are in fact responsive to incentives
to meet these standardized test thresholds. Jacob (2005) studies the effect
of the first move to high-stakes testing in mathematics and reading by the
Chicago Public Schools. In 1996, Chicago began tying student promotion to
performance on the Iowa Test of Basic Skills (ITBS)—a standardized test that
students had already been taking. Following the move from low- to high-stakes
testing, there was a clear increase in test performance in Chicago relative to
other large midwestern cities.
But Jacob also finds several pieces of evidence that this improvement in test
scores was, at least in part, the result of strategic adaptation by teachers.
First, test scores inmath and reading improved at two to four times the rate of
test scores in science and social studies—subjects whose exams were not subject
to high-stakes testing. This suggests that teachers and schools may have shifted
resources away from social studies and science and towards math and reading.
We do not know whether or not this reallocation of resources was optimal for
student education.
Second, because the test scores of special education students are not counted
towards the overall performance of a school, the move to high-stakes testing
gave teachers and schools an incentive to shift low-performing students into
special education. And, indeed, Jacob finds that the advent of high-stakes test-
ing is associated with a roughly 8% (one percentage point) increase in the num-
ber of students classified as special education. Moreover, this reclassification
happened overwhelmingly in schools in the bottom quartile of performance,
precisely the schools that were at risk of sanction for poor test performance. For
similar reasons, high-stakes testing led to roughly a 64% (two percentage point)
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212 Chapter 7
increase in the number of students held back a grade, especially among low-
performing schools.
Another, and perhaps more disturbing, form of strategic adaptation high-
stakes testingmight cause involves distorting how teachers allocate their efforts
across students.Only a small segment of students actually benefit from teaching
to the test. The strongest students will pass standardized tests no matter what.
The weakest students are likely to fail the standardized tests no matter what. If
high-stakes testing motivates teachers to get as many of their students to pass
the exam as possible, then not only will they teach to the test, they will devote
a disproportionate amount of their efforts and attention to those students just
on the cusp of passing.
Neal and Schanzenbach (2010) provide evidence that high-stakes testing can
have precisely this effect of pushing teachers to focus on the students near
the margin. Neal and Schanzenbach begin their study with a quotation from
amiddle school teacher, taken from theWashington Post. The teacher, speaking
of high-stakes testing, lays out exactly the kind of adaptationwe’ve been talking
about:
We were told to cross off the kids who would never pass. We were told to
cross off the kids who, if we handed them the test tomorrow, they would
pass. And then the kids who were left over, those were the kids we were
supposed to focus on.
To show that these distortionary incentives are real, Neal and Schanzenbach
study the second implementation of high-stakes testing in the Chicago public
schools. For years, the state of Illinois has administered the Illinois State Apti-
tude Test (ISAT) to third, fifth, and eighth graders. For most of this time, the
test was relatively low stakes—not tied to promotion to the next grade, school
resources, and so on. The stakes changed in 2002, when the ISAT became the
test that the Chicago Public Schools used to comply with the federal No Child
Left Behind Act.
Neal and Schanzenbach compare students who were fifth graders in 2001
to students who were fifth graders in 2002. The ISAT was low stakes when
both of these cohorts took it in third grade. For the 2001 cohort, it was still
low stakes when they took it as fifth graders. But, for the 2002 cohort, the
ISAT had become high stakes when they took it as fifth graders. Focus, for a
moment, on students who were in fifth grade in 2001. One can calculate how
much improvement different types of students showed from third grade to
fifth grade. For instance, you can group the students into 10 groups based on
their scores in third grade. Then you can calculate how much students who
were in the bottom decile in third grade improved by fifth grade, how much
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Strategic Adjustment 213
students who were in the 2nd decile in third grade improved by fifth grade,
and so on for each decile. Doing so tells you, under low-stakes testing, how
much each type of student is expected to improve from third grade to fifth
grade.
Now, do this same thing for the students who were in fifth grade in 2002
when testing became high stakes. If teachers don’t change their behavior in
response to high-stakes testing, then you should expect to see the same pattern
for these kids as you do for the 2001 kids. But if, once the test becomes
high stakes, teachers focus their efforts on students who are on the cusp of
passing the test, then you’d expect to see a different pattern between the
2001 and 2002 groups. In particular, you’d expect less improvement by 2002
kids who were at the very bottom and very top of their third grade classes,
since starting in 2002 the teachers are incentivized to focus on them less.
You’d also expect more improvement by 2002 kids who were in the middle of
their third grade class, since in 2002 teachers have more incentive to focus on
these kids.
This is precisely what Neal and Schanzenbach find, as reflected in Figure 7.3.
Fifth graders in 2002 who were in the middle of their third grade class show a
bigger improvement in their test scores than did 2001 fifth graders who were
in the middle of their third grade class. But the same is not true of 2002 fifth
graders who were at the bottom or top of their third grade class.
7.3 Takeaways
• People adapt in response to policy changes.
• In order to anticipate the effect of a policy change, one must take into
account how behavior will change.
• In order to minimize strategic adjustment, implement policies that
target the broadest category of behavior your policy is aimed at. For
instance, if your goal is to reduce greenhouse gas emissions, a tax on
carbon is more effective than an increase in CAFE standards because it
is more difficult to adjust behavior to dodge the use of carbon. If your
goal is to improve security from terrorism, increased intelligence ismore
effective than increased airport security because intelligence degrades
terrorist capacity for all types of attacks, whereas airport security only
degrades terrorist capacity to attack airplanes, which allows for strategic
adaptation.
• Tominimize the negative effects of strategic adaptation towards observ-
able tasks, sometimes, as youmeasure certain inputs better, it is optimal
to provide weaker, rather than stronger, performance-based incentives.
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214 Chapter 7
2.0
1.5
1.0
0.5
0.0
–0.5
–1.0
2.5
2.0
1.5
1.0
0.5
0.0
–0.5
–1.0
1 2 3 4 5
Decile in distribution of third grade achievement
Change in Fifth Grade Reading Scores, 2002 versus 2001
Change in Fifth Grade Math Scores, 2002 versus 2001
C
h
an
g
e
in
I
SA
T
s
ca
le
s
co
re
C
h
an
g
e
in
I
SA
T
s
ca
le
s
co
re
Decile in distribution of third grade achievement
6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
Figure 7.3. Students close to the passing threshold improve more than other students
only after tests becomehigh stakes. The figure replicatesNeal and Schanzenbach’s (2010)
Figure 1 using estimates reported in their Table 1.
7.4 Further Reading
Holmström and Milgrom (1991) is the original statement of the multitask
problem, though the formulation I use in Section 7.2 is closer in spirit to
the models of Feltham and Xie (1994), Baker (2002), and Gibbons (2010).
It isn’t reading, but you should also watch the video of John Roberts explaining
the weak incentives idea at the London School of Economics available at
https://www.youtube.com/watch?v=K-2vJVppBgk.
Strategic Adjustment 215
7.5 Exercises
1. A city experiences a spate of crime and decides to try to arrest more
criminals. To do so, it increases the size of the police force. After pursuing
the policy for four months, the city receives the following data on arrest
rates in the four months prior to and following the policy intervention.
Month −4 −3 −2 −1 1 2 3 4
Number of Arrests 150 220 175 190 80 85 82 91
The press reports that the policy is a failure, as the increase in police
presence did not result in “more criminals being taken off the streets.”
Explain why the fall in the number of arrests might constitute good news for
the efficacy of this policy. (A really great answer to this question would
propose, informally, a simple model that would yield these results in
equilibrium.)
2. Suppose there are two states—A and B—that border one another. State A has
1 poor person living in it. State B has 10 poor people living in it. Any poor
person canmove states at any time for a cost of $100.
The government of State Awould like to give somemoney to the poor.
Suppose that State A’s government’s payoff from giving an amount of
money, t, to the poor is equal to 1000t − t2. This implies that the
government of State Awould be willing to give up to $1000 to the poor and
wouldmost like to give $500. However, it also implies that the government
of State Awould prefer to give nothing to the poor than give more than
$1000. The government of State B is uninterested in helping the poor.
(a) The government of State A notices it has only 1 poor person and sets up a
programwhereby any poor person living in State A is entitled to $500.
Has the government of State A implemented a policy that is consistent
with its goal (as defined by its utility function) of supporting the poor
while giving away nomore than $500? If so, why? If not, what is the
problem?
(b) Suppose the government of State A is not allowed to discriminate among
its poor residents. It can only choose policies of the form “we giveX
dollars to each poor person living in State A.” Given its goals (as defined
by its utility function), what is the best such policy that the government
of State A can implement?
(c) What happens to this policy if the number of poor people living in
State B increases?Why?
216 Chapter 7
3. The Transportation Security Administration runs a program in which
Behavior Detection Officers attempt to use behavioral cues to identify
terrorists at the airport. Critics of this program point out that, in its
decade-long history, this program has never successfully identified and
arrested a terrorist. (Themost common arrest associated with the program is
undocumented immigrants.)
(a) If you were a defender of the TSA, howmight you use the arguments
from our models of strategic adjustment to defend the program against
such critics?
(b) If you were a critic of the TSA, howmight you use the arguments from
our models of strategic adjustment to critique the program?
4. Two potential patients come to a doctor, who has time to see only one of
them. One patient is sicker than the other, which the doctor can observe. In
particular, untreated, patient one will have an overall health outcome of θ1
while patient two will have an overall health outcome of θ2 > θ1, so patient
one is sicker than patient two.
The doctor first chooses which patient to treat. She then chooses to expend
effort e on treating the patient. Her effort makes more of a difference for the
sicker patient. In particular, if she exerts effort e treating patient 1, the
patient’s health outcome is h1(e) = θ1 + 2e. If she exerts effort e treating
patient 2, the patient’s health outcome is h2(e) = θ2 + e. The doctor bears
costs e2 for effort.
The doctor has twomotivations. First, she is intrinsically motivated. In
particular, she cares directly about each patient’s health (regardless of which
patient she takes). Second, she is paid a fee for good health outcomes for
whichever patient she takes. The policymaker who pays for the good health
outcomes cannot observe how sick the patients were coming in, nor can he
observe the effort the doctor expended. He just observes a measure of the
patient’s overall health outcome. So if the health outcome for the doctor’s
patient is h, the policymaker pays the doctor a fee h × w.
Putting this all together, if the doctor takes patient 1 and exerts effort e, her
payoff is
(θ1 + 2e)(1 + w) + θ2 − e2.
If the doctor takes patient 2 and exerts effort e, her payoff is
θ1 + (θ2 + e)(1 + w) − e2.
Data
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Data
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it’s because we have the program that the terrorists do not come anymore.
Data
Insert text
Terrorists still come in but they adapt to other methods.
Strategic Adjustment 217
(a) Howmuch effort does the doctor exert if she takes patient 1?What is her
total payoff?
(b) Howmuch effort does the doctor exert if she takes patient 2?What is her
total payoff?
(c) If the policymaker cares about the sum of health outcomes, which
patient would he prefer the doctor take?
(d) Ifw = 0, which patient does the doctor take?
Now, to keep things simple, suppose θ1 = 1 and θ2 = 10 (so person 1 is much
sicker than person 2).
(e) Ifw = 1, which patient does the doctor take?
(f) Ifw = 0, given the patient choice and equilibrium effort, what is the
sum of health outcomes?
(g) Ifw = 1, given the patient choice and equilibrium effort, what is the
sum of health outcomes?
(h) Comparing these two answers, explain what it has to say, substantively,
about how high-powered incentives can create perverse outcomes in
multitask environments.
(i) Substantively, in this case, what is the strategic adaptation that is giving
rise to the perverse outcome?
8
Dynamic Inconsistency
The launch of the HealthCare.gov website in October 2013 constituted a signif-
icant policy setback for the federal government. The website was intended to
provide online marketplaces to facilitate the purchasing of mandatory health
insurance under the 2010 Patient Protection and Affordable Care Act. However,
it did not work as intended—users had trouble accessing the site, experienced
long delays, and were unable to enroll in health insurance.
Many factors contributed to the problems at HealthCare.gov. The United
States Government Accountability Office (GAO) reports that one important
factor was a failure of oversight inside the Centers for Medicare & Medicaid
Services (CMS).1 According to the GAO report, in early 2013, CMS identified
significant problems in the work done by one of its major contractors, CGI
Federal. Although CMS had the authority to hold CGI Federal accountable, the
GAO reports that CMS “delayed key governance reviews” and “chose to forgo
actions, such as withholding the payment of fee, in order to focus on meeting
the website launch date.”2 Indeed, in August of 2013, CMS sent a letter stating
it “would take aggressive action, such as withholding fee . . . if CGI Federal did
not improve or if additional concerns arose,” but quickly withdrew the letter in
order to “better collaborate with CGI Federal in completing the work in order to
meet the October 1, 2013, launch.”3 It was only after the actual website launch
failure that CMS took any significant actions to hold CGI Federal to account,
transitioning responsibility from CGI Federal to Accenture Federal Services in
January 2014.4
This episode illustrates a general problem in governance—dynamic inconsis-
tency. To try to create incentives for good performance, CMS asserted that the
contractorwould be held accountable for actions taken throughout the process.
But once a given task was completed, CMS was primarily concerned with
achieving good outcomes going forward. As such, it was willing to renegotiate
1See GAO 14 694, “HEALTHCARE.GOV: Ineffective Planning and Oversight Practices Un
derscore the Need for Improved Contract Management,” July 2014. http://www.gao.gov/assets/
670/665179.pdf
2GAO 14 694, page 1.
3GAO 14 694, page 34.
4GAO 14 694, page 37.
http://www.gao.gov/assets/670/665179.pdf
http://www.gao.gov/assets/670/665179.pdf
http://HealthCare.gov
http://HealthCare.gov
http://HEALTHCARE.GOV
Dynamic Inconsistency 219
along the way in order to optimize incentives going forward. This commitment
problemmeant the standards announced early in the process were not credible.
Governments face a variety of such problems of dynamic inconsistency. In
this chapter we consider three—commitment problems that undermine the
credibility of policy promises of the sort just described, the desire to pass costs
for current projects onto future generations, and incentives to take inefficient
actions that preserve the current power structure.
8.1 Time Inconsistency
Sometimes even benevolent governments face commitment problems that
lead to inefficiency. The time inconsistency problem is a classic example. A
benevolent government announces a policy that it plans to implement in
the future. That policy is Pareto improving. However, anticipating the policy,
people make decisions today that influence the optimal policy tomorrow. As
a result, when tomorrow comes, the still-benevolent government wants to
implement a different policy than previously announced. Hence, the people
were wrong to believe the initial promise, although at the time the government
meant it. The people, of course, can anticipate this, so the government is in fact
unable tomake promises that will be believed. Before we look at amodel, let me
give you a couple of heuristic examples that stick a bit closer to the model than
the real-world example fromHealthCare.gov already discussed.
Suppose at somemythical university, a professor cares only about howmuch
her students learn. Moreover, she believes each student learns more if all of the
students study hard. That is, there are positive externalities from studying. So,
even though students are also motivated to learn, they study too little relative
to the social optimum.
At the beginning of the quarter, the professor announces that the course will
have a final exam. She does so not because she cares to evaluate the students,
but to incentivize the students to study harder and therefore help others learn.
Students want to make good grades, so anticipating the exam, the students
study harder, getting closer to the social optimum.
On the day of the exam, students have already chosen whether or not to
study. The professor, who cares only about learning, should now cancel the
exam and instead lecture, since the exam can no longer affect the amount of
learning. But this means the students were wrong to study harder in anticipa-
tion of the exam in the first place. The professor’s announced exam policy was
time inconsistent. Hence, in equilibrium, the professor cannot use the threat of
an exam to achieve a Pareto improvement.
The classic time inconsistency problem comes from thinking about
monetary policy. An important empirical pattern—known as the Phillips
http://HealthCare.gov
220 Chapter 8
curve—suggests that in the short run central banks face a trade-off between
high inflation and low unemployment. The standard economic analysis says
that this relationship depends on expectations about inflation. A central bank
can use inflation to lower unemployment only if inflation exceeds expected
inflation. (This explains why this is only a short-run relationship. In the long
run, expectations are correct.) Hence, the central bank would like the market
to expect low inflation, so that it can lower unemployment without increasing
inflation toomuch.
Imagine that a benevolent central bank announced a policy of low infla-
tion. If the market believed the central bank and expected low inflation—
setting wages, household budgets, prices, and so on, accordingly—these low
inflation expectations would leave the central bank with a favorable inflation-
unemployment trade-off. By increasing inflation a bit, the central bank could
reduce unemployment. The benevolent central bank would be tempted to do
so, making themarket’s expectations incorrect. That is, a low inflation policy is
not time consistent for a central bank that also cares about unemployment. It is
precisely this sort of time inconsistency analysis that is sometimes used to argue
that central banks should have limited discretion, so that, for instance, pledges
of low inflation policies are made credible.
Now that we have a sense of what the time inconsistency problem is, let’s
look at a model to be a little more precise.
Our game has two kinds of players. There is a government and there are
consumers. Each consumer has one unit of money.Wewill assume that there is
a very large number of consumers. In particular, there are so many consumers
that each consumer’s wealth is negligible relative to the size of the economy.5
This assumption simplifies the analysis because, as we will see, when a con-
sumer makes a savings decision, she will not worry about how that decision
affects the total amount of taxes collected by the government, since she is so
small relative to the tax base.
The game is played as follows:
1. The government announces a planned future tax rate on capital (i.e.,
savings), t0. This tax rate is not binding.
2. Each consumer divides her money between consumption (c) and
savings (1 − c). Savings earn a return r > 1.
3. The government sets a capital tax rate, t.
4. The government spends the revenues it collects on providing a public
good. The total public good provided, given revenues R, isG = γR.
5Formally, there is a continuum of consumers of mass 1.
Dynamic Inconsistency 221
Assume that the monetary return to private savings is larger than the
monetary return to public goods investment, but not toomuch larger.
In particular, r − 1 < γ < r.
A consumer’s utility is given by
c + (1 − t)r(1 − c) + 2
√
G.
The first term is consumption in the first period. The second term is after-tax
consumption in the second period. The third term is the payoff from public
goods, whichwe assumehas diminishingmarginal utility (thus the square root,
which is a simple increasing function with diminishingmarginal returns).
8.1.1 The First Best
Money invested instead of consumed generates positive returns. Hence, the
first best involves c = 0, since saving everything maximizes the total resources
available. Given this, the first-best tax rate solves
max
t
0 + (1 − t) × r × 1 + 2
√
G.
SinceG = γ tr(1 − c), this can be rewritten
max
t
0 + (1 − t)r + 2
√
γ tr.
To find the first-order condition, wewill use the fact that d2
√
γ tr
dt = γ r√γ tr . Now, the
first-best tax rate, tFB, satisfies the following first-order condition:
−r + γ r√
γ tFBr
= 0 ⇒ tFB = γ
r
.
8.1.2 What Will the Government Do?
Now let’s see what happens in equilibrium.We solve by backward induction.
Suppose that the government hasmade somepromise, t0, and the consumers
have all made some choice c. What tax policy will the government actually
implement?
Being benevolent, the government will choose a tax rate that maximizes
social welfare (given the choice of c). Notice, this means that the government
will ignore its promised policy (t0). The government identifies the socially
optimal tax rate by balancing the costs of taxation, in terms of forgone con-
sumption, against the benefits of taxation, in terms of increased public goods.
For any c, the government chooses a tax rate to solve
max
t
c + (1 − t)r(1 − c) + 2
√
γ tr(1 − c).
222 Chapter 8
Using the fact that
d2
√
γ tr(1−c)
dt = γ r(1−c)√γ tr(1−c) , the first-order condition for this
problem is
−r(1 − c) + γ r(1 − c)√
γ t∗r(1 − c)
= 0 ⇒ t∗ = γ
r(1 − c) .
Since t∗ is part of a strategy, it tells us what tax rate will be chosen for any c. So
we should really write the tax rate the government chooses for any given c as a
function, t∗(c). Importantly, since t∗(c) is a tax rate, it must be less than or equal
to 1. This means that the first-order condition only gives the government’s
choice if γr(1−c) ≤ 1, which is equivalent to c ≤ 1 − γr . If c ∈ (1 − γr , 1), the best
response is a corner solution, t∗(c) = 1.6 If c = 1 anything is a best response
because there is no revenue to be collected. Thus, given an investment level c,
the government’s choice of a tax rate is
t∗(c) =
⎧
⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎩
γ
r(1 − c) if c ≤ 1 −
γ
r
1 if c ∈
(
1 − γ
r
, 1
)
.
anything if c = 1.
(8.1)
Notice, the government really is benevolent. If the consumers choose to save
all of their resources (i.e., c = 0), then the government chooses the first-best
tax rate:
t∗(0) = γ
r
= tFB.
8.1.3 How Much Will a Consumer Consume?
Recall, each consumer in this model is infinitesimally small relative to the
size of the whole economy. As such, each consumer’s individual consumption
choice has essentially zero impact on overall consumption. Suppose a consumer
believes that overall consumption by the other consumer will be C. Then, she
believes that, regardless of her own choice, the tax rate will be t∗(C) and the
total level of public goods will be G = γ t∗(C)r(1 − C). Given this, a consumer
solves the following problem:
max
c
c + (1 − t∗(C))r(1 − c) + 2
√
γ t∗(C)r(1 − C).
Rearranging, we can rewrite this as
max
c
(
1 − (1 − t∗ (C)) r) c + (1 − t∗(C))r + 2
√
γ t∗(C)r(1 − C).
It is straightforward that a consumer’s payoff is strictly increasing in her per-
sonal consumption if 1 − (1 − t∗(C))r > 0. This is equivalent to t∗(C) > 1 − 1r .
6A corner solution means the government would like to choose t > 1 but isn’t allowed to
because t can’t be bigger than 1. So it is stuck at the “corner,” 1.
Dynamic Inconsistency 223
Similarly, a consumer’s payoff is strictly decreasing in her personal consump-
tion if 1 − (1 − t∗(C))r < 0, which is equivalent to t∗(C) < 1 − 1r . This implies
that, if the consumer believes the tax rate will be t∗(C), her best response is
BR(t∗(C)) =
⎧
⎪⎪⎨
⎪⎪⎩
c = 0 if t∗(C) < 1 − 1r
anything if t∗(C) = 1 − 1r
c = 1 if t∗(C) > 1 − 1r .
(8.2)
8.1.4 Is the Government Time Consistent?
Now let’s ask whether the government’s promise of a tax rate, t0, is credible.
Doing so will also let us find the equilibrium of this game.
First, suppose the government promises a tax rate of t0 < 1 − 1r . If the con-
sumers believe that promise, then Equation 8.2 shows that each consumer’s
best response is to consume nothing in the first period (i.e., c = 0). If the
consumers behave in this way, what tax rate will the government actually
choose? Clearly, 0 < 1 − γr . So, fromEquation 8.1, if all consumers choose c = 0,
the government’s best response is to choose a tax rate of
t∗(0) = γ
r
.
But notice that γr > 1 − 1r . (We know this because we assumed at the beginning
of the model that r − 1 < γ .) So the government is not keeping its promise to
choose a tax rate t0 < 1 − 1r . The government’s promisewas not time consistent.
What is the cause of this time inconsistency? The consumers save because of
the low promised tax rate. But the high savings rate then makes taxation par-
ticularly appealing to the benevolent government because, with high savings,
the government can collect a lot of revenue and provide a lot of public goods.
Hence, there is an inconsistency between the high savings that a promise of low
taxes induces and actually implementing these low taxes, even for a benevolent
government.
Next, suppose the government promises a tax rate of t0 > 1 − 1r . If the con-
sumers believe the promise, then each consumer will best respond by consum-
ing everything and save nothing—that is, c = 1. Of course, if the consumers
actually save nothing, any tax rate is a best response by the government, since
there is no actual revenue to be collected. So a promise of high taxes which
results in low savings is time consistent.
In equilibrium, then, there are low savings and high taxation. This is sur-
prising. The government is benevolent and the social optimum calls for high
savings and intermediate taxes. But if savings are actually high, the govern-
ment will implement high taxes so as to provide lots of public goods. At that
point, doing so is socially optimal. But, anticipating this, consumers don’t save.
224 Chapter 8
Hence, a commitment problem on the part of the benevolent government
prevents society from achieving the socially optimal savings rate.
8.1.5 Time Inconsistency and Externalities
What is really going on here is that consumer saving imposes positive
externalities on other consumers because the tax revenues from individual
savings go to providing public goods for everyone. The benevolent government,
in choosing the tax rate, takes those externalities into consideration. But the
individual consumers, when making their individual consumption decisions,
do not. Hence, when there is a lot of saving, the benevolent government wants
to tax a lot (to provide lots of public goods). However, if there is going to be high
taxation, individual consumers don’t save, because they want to free ride on
the savings of other consumers. In this sense, this time inconsistency problem
hinges on there being a wedge between the preferences of the benevolent gov-
ernment and the individual investors. This wedge means that the consumers
(who do not internalize their externalities) strategically adjust their behavior,
up the tree, in anticipation of the government’s socially optimal behavior down
the tree.7
8.1.6 Rules vs. Discretion
We’ve just seen a model in which a benevolent government that has full
discretion to choose any tax policy fails to achieve a Pareto efficient outcome.
Part of the problem is that the government has too much discretion. Saving is
efficient. But the consumers anticipate that, if they save, their money will be
taxed. As a result, they attempt to free ride on one another by saving too little
(from the utilitarian point of view).
This raises an intriguing possibility. Perhaps the government, despite be-
ing benevolent, could achieve better outcomes by reducing its discretion. In
particular, suppose the government could commit to a tax rule up-front. The
downside of such a commitment is that it eliminates the government’s ability
to implement the socially optimal tax, given the consumers’ savings decisions.
The upside of such a commitment is that it allows the government to commit
to a lower tax, thereby encouraging savings.
Let’s see, in our model, whether eliminating government discretion, by
committing to such a rule, in fact improves welfare. Recall that, when the
government can’t commit (i.e., when the government has discretion), the equi-
librium involves no savings and no public goods provision. Hence, equilibrium
social welfare is 1.
7One way to convince yourself that this is indeed what is going on is to ask what would happen
in this model with exactly one consumer, so there are no externalities. A good challenge is to
re solve themodel under this assumption and see that the outcome is efficient.
Dynamic Inconsistency 225
Now suppose the government’s announcement, t0, is in fact a binding com-
mitment. For any choice of t0, the consumers will each save according to the
best responses in Equation 8.2. So, for instance, if the government chooses
t0 = 1 − 1r , it is a best response for the consumers to save everything. And since
1 − 1r ≤ tFB, this is the best outcome that can be achieved. In this scenario,
social welfare is 1 +
√
γ (r − 1) > 1. Taking away the government’s discretion
allows the government to commit to a tax rate that makes everyone better off
by increasing savings and public goods.
8.1.7 Applications
The global financial crisis sparked by the 2007 banking crisis in the United
States exposed an important time inconsistency problem at the core of the
governance structure of the European monetary union.8 The member coun-
tries of the eurozone share a common currency. However, each country is
nonetheless empowered to issue its own sovereign debt. This arrangement
creates externalities problems—if one country borrows irresponsibly, it may
devalue the currency for all the other eurozonemembers.
The Stability andGrowth Pact—one of the treaties governing the eurozone—
includes provisions meant to mitigate the risk. First, it sets a limit on
borrowing—a country’s annual budget deficit and its total debt are not to ex-
ceed 3% and 60% of its GDP, respectively. Second, it articulates a “no bailouts”
principle—countries are responsible for meeting their individual debt obliga-
tions, they cannot expect aid from other eurozone countries. However, given
the externalities problem, this latter position is of questionable credibility.
Should either a lender or leader believe that other eurozone countrieswill refuse
to aid a country at risk of defaulting on its debt, if such a default would have
devastating spillovers on the regional economy?
As it turns out, the no bailouts commitment was not credible. Starting with
the collapse of the U.S. investment bank Lehman Brothers in September of
2008, the banking crisis became a global financial crisis. The effect on global
lending and construction had a massive negative impact on many eurozone
economies, most notably in Greece, Ireland, and Portugal. As a result, by late
2009, it became clear that several eurozone member states were no longer in
compliance with the debt-to-GDP rules.
Greece was the most dramatic case. Following an October 2009 election,
a new Greek government released a revised budget projecting a deficit of
almost 13% of GDP, more than four times the allowed limit and more than
twice previous forecasts. As a consequence, the market lost faith in the Greek
government’s ability to meet its debt obligations. Greek bond yields (i.e.,
the price of debt) skyrocketed. By May of 2010, Greece was shut out of the
8This discussion is based on the overview provided by Lane (2012).
226 Chapter 8
bond market. A looming Greek debt default threatened the integrity of the
eurozone. Perhaps more importantly, because so much of Greece’s debt was
held by French and German banks, a Greek default posed a significant risk
for the French and German economies. And so, contrary to stated policy, the
European Union (EU) and International Monetary Fund (IMF) stepped in to
bail out the Greek government, covering its debt obligations in exchange for
commitments of fiscal austerity and structural reform. Over the course of the
next two years, the EU and IMF were forced to provide bailouts for Ireland and
Portugal, as well as a second bailout for Greece. The non-credible commitment
not to bailout eurozone countries had neither prevented the governments of
those countries from excessive borrowing, nor bound the eurozone govern-
ments not to intercede when they found it in their interests to do so, the classic
time inconsistency problem.
The French and German governments did learn certain lessons from the
Greek crisis.Greek debtwas restructuredduring the course of the secondbailout
in 2012. As a consequence, Greece’s debt was now owed to official creditors
(i.e., the French andGerman governments), rather than private banks. This had
two important effects. First, it reduced the risk of massive negative economic
spillovers from a Greek default, since the French and German governments
stand on firmer financial footing than even the most solvent private banks.
Second, it changed the political equation, making French and German voters
less sympathetic to Greece. The combination of these two effects made it easier
for the French andGermangovernments to take aharder line on future bailouts.
And, indeed, in 2015 they forced Greece tomiss debt payments in order to push
Greece to accept very unfavorable terms for a third bailout.
Another, and very different, example of time inconsistency involves the
policy of not negotiating with terrorists held by many governments (Lapan
and Sandler, 1988). In the United States this policy was first articulated by
President Nixon in response to an attack in which the group Black September
took American (and many other) diplomats hostage in Sudan. The idea of
the policy is straightforward. If you refuse to negotiate with terrorists, you
reduce incentives for such hostage takings. But the commitment problem is
also straightforward.When the United States refused to negotiate, the terrorists
killed the American diplomats. A government that anticipates this outcome
may have a hard time sticking to its guns, undermining the very incentives the
policy was meant to create.
And, indeed, the United States has negotiated with terrorists many times.
During the Iran hostage crisis, the Reagan administration facilitated the sale
of arms to Iran, despite an arms embargo, to attempt to secure release of
the American hostages. In 2002, the Bush administration arranged to pay a
ransom to the terrorist group Abu Sayyaf in an attempt to win the release
of American missionaries who were held hostage in the Philippines. In 2010
Dynamic Inconsistency 227
the Obama administration exchanged the terrorist leader Qais al-Khazali for a
British hostage held in Iraq. In 2014, the Obama administration released five
prisoners held in Guantanamo Bay to gain the release of an American soldier.9
And in 2015, the Obama administration changed policies, permitting kidnap
victims’ families to negotiate for their release.When the stakes are high enough,
the commitment not to negotiate is not credible.
8.2 Fiscal Manipulation
State and local governments across the United States face serious financial
problems due to underfunding of pension funds for public sector workers.
No state looks worse than Illinois, where I live. According to a report of the
Illinois Commission on Government Forecasting and Accountability, in fiscal
year 2014, the state had unfunded pension liabilities of approximately $105
billion. The cumulative funded ratio of the state’s retirement plans was only
about 43%.10
My hometown of Chicago can give the state a run for its money. As of 2015,
Chicago’s pension plans had over $20 billion in unfunded liabilities. In 2013,
the city paid under $500 million of the over $1.7 billion it was was supposed
to contribute to its pension plans. The unpaid $1.2 billion is equivalent to over
40% of the city’s annual budget.11
Letme tell you one other story about fiscalmanagement inChicago. In 2008,
the mayor of Chicago reached a deal to privatize the city’s parking meters.
While the deal is complicated, the rough outline is this—the city received a
one-time payment of $1.15 billion in exchange for a lease that gives a private
company the rights to the parking meter revenues for 75 years. A report by the
Office of the Inspector General of the City of Chicago found that the city sold
the parkingmeter concession for less thanhalf of its value.12 And, perhapsmore
importantly, although the lease is for 75 years of revenue, roughly 90% of the
$1.15 billion payment was spent in just five years.13
9Most of these examples are reported by Joshua Keating. May 7, 2015. “We Do Negotiate with
Terrorists.” Slate. http://www.slate.com/articles/news and politics/politics/2015/05/negotiating
with terrorists s stop pretending we don t and craft better.html
10Commission on Government Forecasting and Accountability. February 2015. “Illinois State
Retirement Systems: Financial Condition as of June 30, 2014.” http://cgfa.ilga.gov/Upload/ FinCon
ditionILStateRetirementSysFeb2015.pdf
11Nuveen Asset Management. April 2015. “Chicago Fiscal Stress: New Term, Same Problems.”
http://www.nuveen.com/Home/Documents/Default.aspx?fileId=65715
12Office of the Inspector General, City of Chicago. June 2, 2009. “An Analysis of the Lease of the
City’s Parking Meters.” http://chicagoinspectorgeneral.org/wp content/uploads/2011/03/Parking
Meter Report.pdf
13The Civic Federation. November 10, 2010. “Expiring Parking Meter and Skyway Funds.”
http://www.civicfed.org/civic federation/blog/expiring parking meter and skyway funds
http://www.slate.com/articles/newsandpolitics/politics/2015/05/negotiatingwithterroristssstoppretendingwedontandcraftbetter.html
http://cgfa.ilga.gov/Upload/FinConditionILStateRetirementSysFeb2015.pdf
http://cgfa.ilga.gov/Upload/FinConditionILStateRetirementSysFeb2015.pdf
http://www.nuveen.com/Home/Documents/Default.aspx?fileId=65715
http://chicagoinspectorgeneral.org/wpcontent/uploads/2011/03/ParkingMeterReport.pdf
http://chicagoinspectorgeneral.org/wpcontent/uploads/2011/03/ParkingMeterReport.pdf
http://www.civicfed.org/civicfederation/blog/expiringparkingmeterandskywayfunds
http://www.slate.com/articles/newsandpolitics/politics/2015/05/negotiatingwithterroristssstoppretendingwedontandcraftbetter.html
228 Chapter 8
When policy analysts think about how to address the looming fiscal crises
in state and local governments, they tend to focus on technical concerns—
accounting rules, pension-smoothing schedules, revenue generation. But each
of these examples points to an incentive issue that will persist, no matter the
technical response. Elected officials have a strong interest in spending money
they don’t have. This may be true both because doing so pleases voters and
because the politicians have policy agendas they care about. Since they are
uncertain whether future politicians will agree with them, they’d rather set
priorities now, while they have the power.
A straightforward way to determine the policy priorities on which future
resources are spent is to borrow money from the future and spend it today.
The federal government does so by running a deficit. But almost every state
government is compelled by law to balance its budget each year. So state and
local leaders have to be more creative—spending their grandchildren’s money
by delaying pension payments, selling the rights to parkingmeters or toll roads,
promising raises to public sector employees that don’t take effect for five or ten
years, and a host of other forms of fiscal manipulation. (I hope it hasn’t escaped
your notice that the fact that state and local leaders find ways to avoid the
constraints placed on thembybalanced budget policies is itself a lovely example
of the kind of strategic adaptation discussed in Chapter 7.)
Let’s consider a simple model of the timing of public policy expenditures to
see how thismight work. In thismodel, we will capture the idea that politicians
prefer to spendmoney today by assuming politicians have policy priorities that
may not be the same as those of future voters or politicians.
There are three players: a voter, a left-wing politician, and a right-wing
politician. There are two periods, 1 and 2. Prior to each period, the voter elects
one of the two politicians. During each period, there is a budget of size 1 to be
spent on public policy. In addition, in period 1, the politician in office has the
option to borrow an amount b ∈ (0, 1). If the politician borrows in period 1, the
moneymust be paid back in period 2. Thus, if the politician borrows, the period
1 budget is 1 + b and the period 2 budget is 1 − b.
There are two possible ways to spend the budget in each period. It can be
spent in away consistentwith the right-wing agenda (R) or the left-wing agenda
(L). In each period, one of these two agendas is in fact more effective than the
other. The value to a citizen of money spent on themore effective agenda is λ ∈
(
1
2 , 1
)
, while the value to a citizen of money spent on the less effective agenda is
1 − λ. The idea is that circumstance affects the efficacy of different approaches
to public policy. For instance, perhaps voters prefer different fiscal policies
during times of economic recession versus times of economic expansion.
In addition, in each period, the stakes of public policy can change. In
particular, in period t, the stakes are αt . I assume that, in each period, αt
is equally likely to be any real number between 0 and 1. This implies that
Dynamic Inconsistency 229
the expected value of each αt is one-half. The stakes of public policy are
independent across the two periods.14 This difference in the stakes of public
policy will imply that sometimes it is optimal to borrow money in period 1
because the stakes of public policy are particularly high. Substantively,wemight
think that α is particularly high during times of war, recession, natural disaster,
or other crises.
Unlike regular citizens, politicians are biased towards one of the two agendas.
The right-wing politician values money spent on the right-wing agenda at λ
regardless of which agenda is more effective. Similarly, the left-wing politician
values money spent on the left-wing agenda at λ regardless of which agenda is
more effective.
Politicians and voters both observe which agenda is more effective before
choosing which politician to have in office. Thus, in each period, the voter will
elect the politician whose partisan bias is consistent with the more effective
agenda. The value of αt is observed after the election, but before policy is set.
8.2.1 The First Best
Let’s start the analysis by thinking about the first-best borrowing decision—
that is, the borrowing policy that maximizes the voter’s welfare.
Suppose, in period 1, the stakes of policy are α1. The politician in office will
spend whatever resources she has on her agenda, which is of value λ to the
voter. If the politician in office in period 1 borrows, the voter’s payoff in the
first period is α1λ(1 + b). The voter will then choose whatever party is aligned
with her interests for the second period and her payoff in the second periodwill
be α2λ(1 − b). Of course, at the time of the borrowing decision, α2 is unknown.
Its expected value is one-half. Hence, the voter’s expected second period payoff,
if the first period politician borrows, is 12λ(1 − b). This gives us the voter’s overall
expected welfare if the politician borrows in the first period:
UV(borrow|α1) =
Voter’s 1st Period Welfare
︷ ︸︸ ︷
α1λ(1 + b) +
Voter’s Expected 2nd Period Welfare
︷ ︸︸ ︷
1
2
λ(1 − b).
Following a similar logic, if the politician in office in period 1 does not borrow,
the voter’s expected payoff is
UV(don’t borrow|α1) = α1λ +
1
2
λ.
14A little more precisely, each αt is an independent, uniform random variable on [0, 1].
230 Chapter 8
Comparing these, the first-best policy involves borrowing if
α1 >
1
2
.
Thismakes sense. In this simplemodel, there are no direct costs to borrowing
(e.g., there is no interest). Borrowing simply moves resources from the second
period to the first period. As such, it is optimal to borrow if the stakes of policy
in the first period are higher than average. This is the canonical argument for
the value of government borrowing—in some circumstances, it is efficient to be
able to spend resources now that you won’t actually have until later. We want
our government to be able to borrow during times of crisis.
8.2.2 Electoral Risk
Now that we know the efficient policy, let’s think about what will happen in
equilibrium. Suppose, again, that the stakes of policy in the first period are α1.
Further, suppose that the politician in office in the first period believes that the
probability that the voter will again find her agenda more effective in period 2
is p ∈ (0, 1). When will the first period politician borrow?
If the first period politician borrows, her payoff in the first period is
α1λ(1 + b). Her payoff in the second period will depend both on the stakes of
policy in the second period and on which party is in power. With prob-
ability p her party will remain in power and her payoff will be α2λ(1 − b).
With probability (1 − p) the other party will come to power and her payoff
will be α2(1 − λ)(1 − b). Since the expected value of α2 is one-half, the overall
expected payoff of the politician in power in period 1, if she borrows, is
U1(borrow|α1) = α1λ(1 + b) +
1
2
(
pλ(1 − b) + (1 − p)(1 − λ)(1 − b)
)
.
Following a similar logic, if the politician in office in period 1 does not borrow,
her expected payoff is
U1(don’t borrow|α1) = α1λ +
1
2
(
pλ + (1 − p)(1 − λ)
)
.
Comparing these, the first period incumbent borrows if
α1 >
pλ + (1 − p)(1 − λ)
2λ
.
It is straightforward to see that the right-hand side of this inequality is less than
one-half, the first best. Thus, in equilibrium, the politician borrows more often
than is welfare maximizing for the voter.
Dynamic Inconsistency 231
Why is this? The incumbent politician is concerned that she may be out of
power tomorrow. When she is out of power, public funds are spent on her less
preferred policy agenda. By borrowing, she increases the share of public funds
spent on her preferred agenda. This is because borrowing shifts funds from the
future, when she might not be in power, to the present. Thus, she is sometimes
willing to borrow funds even when the stakes of policy are relatively low.
Herewe see a source of inefficiency clearly related to the exampleswithwhich
we started. A politician, with her own policy priorities, who faces the prospect
of not being in power in the future, has incentives to borrow money from the
future, even if doing so is inefficient.
8.2.3 Discounting the Future
Intergenerational considerations suggest yet another possible source of inef-
ficiency. Suppose we think of the two periods as two separate generations and
assume that politicians care about payoffs for their own generation more than
they care about future generations. To model this, let the period 1 politician
discount period 2 payoffs by δ ∈ (0, 1). Now, even if the politician has no
concern that her party will lose power, she will borrow toomuch because doing
so allows her to spend her children’s money on herself.
To see this, suppose the politician is certain her agenda will still be the
preferred one in the next period. (This is equivalent to p = 1.) If she borrows,
her expected payoff is
U1(borrow|α1) = α1λ(1 + b) + δ
1
2
λ(1 − b).
If she doesn’t borrow, her expected payoff is
U1(don’t borrow|α1) = α1λ + δ
1
2
λ.
Comparing, she will borrow if
α1 >
δ
2
.
Again, the politician borrows more often than is efficient. Here she does so
not because of political concerns, but because she values payoffs to future
generations less than payoffs to her own generation.
This story is a political version of our earlier discussion, in Chapter 1, about
the philosophical problems with discounting the future for policy evaluation.
A politician who discounts the future is too willing to sacrifice future gen-
erations’ interests in service of her own generation’s interests. This suggests
that we might expect it to be difficult to incentivize politicians to take costly
actions on issues, such as global climate change, that require up-front costs for
232 Chapter 8
long-term benefits. Not taking costly actions today to mitigate a future threat
is just like borrowing money today that will have to be repaid in the future.
For a politician who discounts future interests, doing so is tempting. And so,
dynamic political considerations help to explain why even politicians who
might be ideologically inclined to take action on issues such as climate change
find it politically difficult to do so. Moreover, as we discussed in Chapter 1,
governmental rules that require discounting the future in cost-benefit analyses
exacerbate such incentives.
8.3 When Policy Affects Future Power
Acemoglu and Robinson (2001) observe that in many policy domains, govern-
ments seem to pursue a particular goal with inefficient, rather than efficient,
policy tools.
Consider the case of agricultural subsidies. Suppose the world economy has
changed in a way that makes farming in, say, the United States, a less viable
activity today than it was thirty years ago. It is very difficult for a fifty-year-old
farmer to retrain and change industries. Hence, the government might well
want to use policy to help that farmer. As Acemoglu and Robinson point out,
if the United States government wants to support current farmers, it would
be efficient to provide direct transfers, rather than pursuing the current policy
of propping up prices, restricting imports, and subsidizing agricultural inputs.
Such policies distort prices and lead to an inefficiently high level of investment
in agriculture rather than other,more productive, industries. Agricultural subsi-
dies are, thus, an inefficient way to compensate farmers for changing economic
conditions.
One can, of course, make related arguments about a variety of policies. For
instance, price supports and other forms of protectionism for manufacturing
jobs are a distortionary response to outsourcing. Similarly, Acemoglu and
Robinson argue, labor market regulations—for example, restrictions on firing,
closed shops, minimum wages—are an inefficient way to redistribute wealth
to workers. Such rules distort economic decision making, reduce the sorting
of workers into the jobs for which they are well-suited, increase unemploy-
ment, and so on. If the government is concerned with improving the welfare
of workers it would, again, be more efficient to directly transfer resources to
those workers, rather than regulate employers. And, as we’ve already discussed,
professional licensing requirements are away of insulating a group of producers
fromcompetition fromnewentrants to themarket in away that drives up prices
and reduces innovation.
It is unsurprising that organized interests seek rents. But the inefficient form
that such rents often take is a puzzle in its own right. Even if policymakers want
to give particularistic benefits to certain groups, why do they do so in ways that
Dynamic Inconsistency 233
shrink the overall size of the utility pie? Acemoglu and Robinson’s answer has
to do with the dynamics of political power.
Policy changes can affect society in ways that alter future political
power. For instance, a policy that subsidizes some activity with positive
externalities—say food production, building weapons for national defense, or
pharmaceutical research—may also strengthen certain industries relative to
others in ways that allow those industries to exercise power over future policy.
Hence, it is not always right to think of the political system as a fixed constraint
on policymaking. Sometimes policy is made because of the changes it will
induce in the political system itself. This kind of dynamic feedback has two
important implications for the relationship between political power and policy.
First, policymakers may sometimes pursue inefficient policies precisely because
those policies will preserve the current power structure. Second, sometimes
policies that appear to be socially beneficial (say eliminating an externality)
may actually be socially harmful when one considers not just the direct eco-
nomic consequences of the policy, but also the political consequences.
The first of these points suggests a way in which the dynamics of power
may distort government incentives away from pursuing efficient policies. The
second point is a cautionary tale for anyone trying to identify good policies.
Whilemuch of the time good policy involves addressing social dilemmas of the
sort we studied in Part II, onemust always think about the possible unintended
consequences (political and otherwise) of any policy change. As wewill discuss,
this latter point can be seen as a political application of the theory of the second
best.
In Acemoglu and Robinson’s model, young workers are disinclined to enter
a declining industry. The declining industry is currently large and powerful
enough to extract some rents from the government. If the government simply
transfers money to people currently working in that declining industry, the
policy will have no effect on the decision of future generations about whether
to enter that industry. As the number of peopleworking in the industry shrinks,
the industry loses political power. Consequently, the currentmembers of the in-
dustry fear that it will bemore difficult to extract rents in the future. So, instead,
the industry wants the government to make policy concessions that not only
generate rents, but preserve the industry’s power by giving the new generation
incentives to enter the industry. Inefficient policies, like price supports and
input subsidies, achieve this political goal in a way that efficient policies, like
direct transfers, do not. Hence, a powerful group’s desire to preserve its power
leads to inefficient policymaking. Let’s see how this works in a simple model
inspired by Acemoglu and Robinson (2001).
Consider a society withN members, divided into two generations. The share
of the population in the new generation is δ ∈ (0, 1) and the share of the
population in the old generation is 1 − δ.
234 Chapter 8
Each member of the old generation works in one of two industries: farming
ormanufacturing. A share, λ, of the old generation are farmers and a share 1 − λ
are manufacturers. Themembers of the new generation have not yet chosen an
industry. We assume that, while the old generation’s farmers are a majority of
the old generation (λ > 1/2), they are not a majority of the whole population
((1 − δ)λ < 1/2).
The industries differ in two ways. First, farming is less productive than man-
ufacturing. Each farmer produces F, while each manufacturer produces M > F.
Second, for simplicity, we will assume that it is possible to tax the income from
manufacturing, but not from farming, perhaps because farmers can directly
consume their products. (This latter assumption is not substantively important,
but it simplifies the model.)
The game is played as follows.
1. At the beginning of the game, the old generation chooses one of three
policies bymajority vote:
a. Taxmanufacturers at rate t and redistribute to the existing farmers
through a lump sum transfer. (This benefits only existing farmers.)
b. Taxmanufacturers at rate t to fund price supports for agriculture.
(This benefits existing farmers and anyone who becomes a farmer
from the new generation.)
c. Don’t tax manufacturers.
2. The new generation observes the policy and then chooses which
industry to enter. First-period production then occurs.
3. A new tax policy is set by a majority vote of both generations.
4. Second-period production occurs and the game ends.
Each player has utility equal to the sum of her individual production and her
individual transfers.
Before we solve for the equilibrium of this game, note that, in this model,
taxes are not inherently distortionary. Hence, the utilitarian payoff (and, so,
Pareto efficiency) is determined entirely by the total amount produced. Since
manufacturing is more productive than farming, any utilitarian optimum in-
volves the new generation becoming manufacturers. Any policy choice that
leads the new generation to instead become farmers is inefficient.
Now let’s turn to analyzing the subgame perfect Nash equilibrium of this
game to see how concern over future political power can lead to inefficient
policy choices. We will focus on an equilibrium in which all of the members
of the new generation join the same industry.
Consider the end of the game. If themembers of the new generation become
farmers, then there are ((1 − δ)λ + δ)N farmers and (1 − δ)(1 − λ)N manufac-
turers. The farmers, who hold the majority, will impose a tax of t on the
Dynamic Inconsistency 235
manufacturers, redistributing the proceeds to farmers either through a lump
sum transfer or through price supports. (In the second period, the two forms
of redistribution are equivalent.) Each farmer’s transfer is
TF =
t(1 − δ)(1 − λ)M
(1 − δ)λ + δ .
Hence, if the new generation become farmers, in the final period, each farmer
makes a payoff of
F + TF
and eachmanufacturer makes a payoff of
(1 − t)M.
If, instead, the members of the new generation become manufacturers,
then there are ((1 − δ)(1 − λ) + δ)N manufacturers and (1 − δ)λN farmers. The
manufacturers, who hold the majority, will impose no taxes. Hence, if the new
generation become manufacturers, each farmer makes a payoff of F and each
manufacturer makes a payoff ofM.
What careerwill thenewgeneration choose? Suppose that, in thefirst period,
the government chose to tax and redistribute through lump sum transfers to
existing farmers. If the new generation become farmers, they don’t get the
transfer in the first period. Hence, if the new generation become farmers, the
lifetime payoff of an individual from the new generation is
2F + TF.
If the new generation become manufacturers there will be no taxes in the
secondperiod, so the lifetimepayoff of an individual from thenewgeneration is
M(1 − t) + M = M(2 − t).
Suppose, instead, that in the first period, the government chose to use taxes
to fund price subsidies. Now a member of the new generation who becomes
a farmer receives a transfer even in the first period, since she benefits from
the price subsidies. That transfer will again be of value TF. Hence, if the new
generation become farmers, the lifetime payoff of an individual from the new
generation is
2 (F + TF) .
236 Chapter 8
If the new generation becomemanufacturers, the lifetime payoff of an individ-
ual from the new generation is still
M(2 − t).
If, in the first period, the government chose to impose no taxes, then, if the
new generation become farmers, the lifetime payoff of an individual from the
new generation is
2F + TF.
If the new generation becomemanufacturers, the lifetime payoff of an individ-
ual from the new generation is
2M.
Comparing, if the initial tax policy involves redistribution only to existing
farmers, then the new generation become farmers if
2F + TF ≥ M(2 − t).
If the initial tax policy involves redistribution through price supports, then the
new generation become farmers if
2(F + TF) ≥ M(2 − t).
If the initial tax policy involves no redistribution, then the new generation
become farmers if
2F + TF ≥ 2M.
Importantly, the new generation are most willing to become farmers if the
initial policy is redistribution through price supports.
Given all of this, what policy will the old generation of farmers choose?
First, it is straightforward that the old farmers will implement some form of
redistribution in the first period. Now let’s focus on the interesting case where
2F + TF < M(2 − t) < 2(F + TF).
Here, the old generation of farmers faces a trade-off. On the one hand, if they
choose a policy of redistribution through lump sum transfers, they get a larger
initial transfer because they don’t have to share it with the new generation.
On the other hand, if they choose redistribution through price supports, they
Dynamic Inconsistency 237
incentivize the new generation to become farmers, allowing their industry to
retain power over government redistributive policy in the second period.
We can analyze their decision formally. If the old generation farmers choose
redistribution through lump sum transfers, then the new generation become
manufacturers. As a result, in the first period, each old farmer receives a
transfer of
t ((1 − δ)(1 − λ) + δ)M
(1 − δ)λ .
However, in the second period they are no longer in themajority and so receive
no redistribution. Hence, the lifetime payoff to an old generation farmer, if they
choose lump sum redistribution, is
2F + t ((1 − δ)(1 − λ) + δ)M
(1 − δ)λ .
If, instead, the old generation farmers choose redistribution through price
supports, then the new generation become farmers. As a result, the farmers
retain theirmajority, receiving redistribution of value TF in each period. Hence,
the lifetime payoff to an old generation farmer, if they choose price supports, is
2(F + TF).
Substituting for TF and comparing, the old generation farmers will choose
price supports if
δ
(1 − δ)2 ≤ λ(1 − λ).
Recall that λ > 1/2. Hence, this condition says that two factors make the old
generation farmers more likely to choose price supports rather than lump sum
transfers. Price supports are more attractive when the new generation is small
(δ small) andwhen the farmers hold a fairly smallmajority in the old generation
(λ close to 1/2). The intuition for the first of these conditions is straightforward.
If the new generation is small, it costs relatively little to share the redistribution
with the new generation, making price supports more palatable. The intuition
for the second condition is similar. When the old generation has a large share
ofmanufacturers,maintaining a politicalmajority that allows for redistribution
in the secondperiod is very valuable,making the old generation farmerswilling
to adopt a policy that costs them in the first period in order to incentivize the
new generation to become farmers.
The model illustrates a situation in which concerns about maintaining po-
litical power lead to inefficient policy, even when efficient policy instruments
are available. The dominant industry in the old generation wants to maintain
238 Chapter 8
power, so they must convince the new generation to join their industry. To do
so, they use policy instruments that reward people for joining their industry,
even though that industry is less productive than other choices.
At heart, the inefficiency in this model is due to a commitment problem. If
the new generation could commit to continuing redistribution to farmers in
the future, even if farmers are a dwindling share of the population, then the old
generation farmers would permit a non-distortionary policy that doesn’t drive
the new generation into a low-productivity field. But such a commitment is not
credible. Once the new generation entersmanufacturing, political power shifts,
and there is no longer a coalition to support transfers to farmers. Anticipating
this, farmers push for policies that maintain their political coalition.
This kind of story is, I think, broadly applicable to many areas of policymak-
ing. Below are some examples of inefficient policies pursued by governments
that can be understood as helping to maintain the power base of some political
coalition.
Protectionist restrictions on imports are often justified by pointing to the
declining fortunes of some domestic industry. It would be more efficient to
make transfers to the current members of these declining industries than to
restrict trade. But trade restrictions retain the size and power of the industry,
while transfers will eventually lead the industry to decline and lose power. A
savvy industry understands that once its political power declines, the transfers
will disappear. Hence, it pushes for inefficient trade restrictions that prop up the
industry for the long term.
Imagine a government controlled by a group of aristocrats, oligarchs, mil-
itary officers, or other elites. Those elites have to decide whether to allow or
block a new technology (e.g., industrialization, free trade, improved commu-
nication). This new technology will lead to increased economic growth. But it
also makes it more likely that the elites will lose power because with growth
comes the rise of the entrepreneurial, middle class. Themembers of the middle
class cannot credibly commit not to use their economic power to seize political
power in the future. Hence, the elites block the new technology for as long as
they can. If the middle class could commit to not challenge the elites, then the
elites would allow the technology, making the middle class richer. But because
they can’t so commit, the economy is kept stagnant.
Finally, consider immigration policy. Suppose the party in power believes
that allowing immigration will improve economic growth or relieve a demo-
graphic problem in state-run pensions. If the incumbent politicians also believe
that immigrants will eventually become citizens and support the other party,
they might restrict immigration. If immigrants could commit to vote for the
incumbent party, they would be allowed in and everyone would be better off.
But they cannot credibly commit to do so, leading to inefficiently restrictive
immigration policy.
Dynamic Inconsistency 239
8.3.1 The (Political) Second Best
The realization that policy changes can affect the distribution of political
power renders the question of what constitutes good policy even more fraught
than we’ve previously realized. Indeed, Acemoglu and Robinson (2013) argue
that many textbook examples of policy advice derived from analyses like those
in Part II don’t stand up to a comprehensive analysis that takes seriously both
the economic and political consequences of policy changes.
A simple version of this argument concerns the implications of effective pol-
icy reformon the longevity of leaders. Suppose an autocratic leader implements
policies that, say, promote economic growth. If those policies improve the tax
base and, so, provide the leader with more resources, they might contribute
to that autocratic leader surviving in office longer than would otherwise be
the case. Autocratic leaders do many things that are bad for their citizens.
Hence, while efficient economic reform policies might seem obviously good,
considered in isolation, when one factors in their impact on the distribution of
political power, one’s viewmight switch.
The same concern is expressed in contemporary debates over the merits
of giving aid to bad leaders who invest in demonstrably good programs. For
instance, the development economist Angus Deaton argues that15
by providing health care for Rwandan mothers and children, [Rwandan
President Paul Kagame] has become one of the darlings of the [aid] indus-
try and a favorite recipient of aid. Essentially, he is “farming” Rwandan
children, allowing more of them to live in exchange for support for his
undemocratic and oppressive rule. Large aid flows to Africa sometimes
help the intended beneficiaries, but they also help create dictators and
provide them with the means to insulate themselves from the needs and
wishes of their people.
We will return to the politics and political consequences of foreign aid in
Chapter 11.3.
Our model tells a similar (though less tragic) story. In the model, efficient
policy involves allowing the farming sector to decline in favor of the more
efficient manufacturing sector. Suppose, however, that the society also faces
an issue of pollution due to a failure to internalize externalities. Farmers
might play an important role in a coalition against manufacturers pushing for
welfare-enhancing environmental regulation. An unintended political conse-
quence of allowing the agricultural sector to decline might be a diminution
in the political power of the environmental coalition. If the welfare loss as-
sociated with decreased environmental regulation is larger than the welfare
15See http://bostonreview.net/forum/logic effective altruism/angus deaton response effective
altruism.
http://bostonreview.net/forum/logiceffectivealtruism/angusdeatonresponseeffectivealtruism
http://bostonreview.net/forum/logiceffectivealtruism/angusdeatonresponseeffectivealtruism
240 Chapter 8
gain associated with more efficient sorting into productive industries, then
what looked like the optimal policy—letting agriculture decline—was actually
suboptimal.
Acemoglu and Robinson’s (2013) leading example is de-unionization. A
textbook economic analysis suggests that unions (like monopolies) are in-
efficient because they exercise market power—giving union members rents
through above-market wages, while creating distortions in the labor market
that damage the overall economy. Hence, a standard piece of economic pol-
icy advice might be that Pareto efficiency requires reducing the power of
unions.
However, Acemoglu and Robinson argue, unions do many things besides
fight for higher wages for unionized workers. For instance, unions were cen-
tral actors in democratization movements from the late nineteenth century
in western Europe through the twentieth century in Latin America, Africa,
and eastern Europe. The concern is that policies that reduce unions’ market
power also reduce their ability to attract members and, therefore, their political
power. This diminution in political power may have serious consequences—for
democratization, the distribution of income, and many other outcomes whose
negative consequences more than offset any efficiency gains associated with
eliminating wage distortions. Hence, Acemoglu and Robinson suggest, once
one considers the (potentially unintended) political consequences of a policy
that seems obviously beneficial from textbook policy analysis, its net benefits
are less clear.
While this political caveat to standard policy advice is important, we should
also note that it is, in a certain sense, nothing new to us. Acemoglu and
Robinson’s point is that sometimes taking actions that fix some problem—
internalizing externalities, eliminating market distortions—create new prob-
lems as a result of political consequences. Hence, when evaluating policies, one
must consider not only a policy’s effect on the issue at hand, but its spillover
effects on the political equilibrium. This is a specific, and particularly impor-
tant, instance of the theory of the second best. As we discussed in Chapter 4,
when choosing a tax or subsidy policy to make people internalize externalities,
one doesn’t aim for the first best because the taxes or subsidies create other
sorts of problems thatmust be balanced against the benefits of internalizing the
externality. Similarly, aswewill discuss inChapter 9, whendesigning incentives
to extract information needed to set policy, one doesn’t aim to extract all the
information because doing so requires the inefficient expenditure of a huge
amount of resources andopens up the risk of capture.Wemust also addpolitical
consequences to the list of the possible unintended consequences of policy
changes that we have to think about when we do an analysis to identify the
second best. This is a very important point—the second best isn’t only about
economic distortions due to taxation and the like, it is about any spillover from
Dynamic Inconsistency 241
a policy change that affects welfare, including political spillovers—but it is also
important to see that it is closely related to concepts we already understand.
8.4 Takeaways
• Dynamic considerations create a variety of constraints that prevent gov-
ernments from implementing optimal policy solutions. These include
commitment problems in the form of time inconsistency, incentives to
sacrifice future interests for current interests, and the feedback between
current policy and future political power.
• A time inconsistency problem occurs when the government announces
a future policy and if the people believe the policy will be implemented
as announced andmake choices accordingly, then the government ends
up wanting to implement a policy other than the announced policy.
• Fiscal manipulation—whereby current spending is funded by excessive
borrowing from the future—can occur because of electoral threat, lack
of concern for future generations, or because of rules that mandate
discounting future payoffs. Balanced budget rules are often intended to
prevent such manipulation, but in many circumstances governments
can strategically adapt by finding newways to borrow from the future.
• Changes to policy have the potential to change the distribution of
political power. Such concerns can create incentives for leaders to adopt
inefficient policies that preserve the power of some currently powerful
group.
• Policy changes that alter the distribution of political power can have
unintended consequences on other policy domains. Hence, the effect
of policy changes on the distribution of political power creates another
type of second-best constraint that must be taken into account when
evaluating policies.
• Because of these various dynamic considerations, social welfare is some-
times higher when the government is constrained to follow preset rules,
rather than given discretion over policy. This can be true evenwhen the
government is benevolent.
8.5 Further Readings
Kydland and Prescott (1977) is the initial articulation of the time inconsistency
problem, though themodel here is closer in spirit to Stokey (1989).
The model of deficits is in the spirit of Persson and Svensson (1989) and
Alesina and Tabellini (1990).
Themodel of declining interests as a source of policy inefficiency is based on
Acemoglu and Robinson (2001).
242 Chapter 8
8.6 Exercises
1. Solve themodel in Section 8.1 with a single consumer (i.e., so the
consumer’s savings decision has a one-for-one effect on the resources
available to be taxed for public goods) and show that, in that case, there is
no time inconsistency problem. That is, the government in fact achieves the
first best.
2. Consider a government that controls the inflation rate throughmonetary
policy. In particular, the government gets to choose a policy that determines
the amount of inflation ι ∈ [0, 1]. Wages are determined by bargaining
inside an industry. In particular, the industry will choose an amount of
wage increase ω ∈ [0, 1]. The change in real wages (i.e., in the value of wages)
is ω − ι.
Economic productivity is increasing in inflation and decreasing in wages. In
particular, it is y = ι − ω. The government’s payoff is increasing in
productivity, but decreasing in inflation. In particular, it is
uG(ω, ι) = y − ι2 = ι − ω − ι2.
Since wages are determined as part of a bargain between labor and
management, the goal of industry is to keep real wages constant. To capture
this idea, suppose that industry’s payoff is
uI(ω, ι) = −(ω − ι)2,
so it is maximized when ω = ι.
(a) Suppose that industry first sets the wage increase and then the
government sets inflation.
i. What is equilibrium economic productivity?
ii. What is the government’s equilibrium payoff?
iii. What is equilibriumwage growth?
(b) Suppose, instead, that the government first sets inflation and then
industry sets the wage increase.
i. What is equilibrium economic productivity?
ii. What is the government’s equilibrium payoff?
iii. What is equilibriumwage growth?
(c) Explain how comparing these two scenarios suggests that in the first one
the government faces a commitment problem that leads to worse policy
outcomes.
Dynamic Inconsistency 243
(d) This kind of argument is often used to suggest that the government
might be better off giving up its discretion over monetary policy and
instead committing to a rule. Thinking a bit outside the model, what
might be a downside to such amove?
3. In negotiations between rebels and a government, the government typically
wants the rebel group to disarm as a condition of any peace agreement.
Following such negotiations, there is typically a residual group of extremists
who continue the rebellion. The government often depends on the former
rebels’ insider knowledge to fight this residual extremist group. Give an
intuitive explanation, in terms of government commitment problems, for
why, in light of this, the fact that there will be a residual extremist group
might make it easier for the government and themain rebel group to reach a
peace agreement.
4. It has been argued that one cause of the financial crisis of 2007 was banks
taking excessive risk. Following the crisis, reform advocates argued for
breaking up banks that were deemed “too big to fail.” Provide an argument
for the merits of this policy based on the analysis in this chapter.
9
The Need for Information
Providing social insurance is an essential governmental role. Government pro-
grams insure citizens against risk related to ill health, unemployment, disability,
and so on. Social insurance programs can have significant utilitarian benefits.
But they also have pitfalls. For instance, there is the problem of perverse
incentives.
Suppose the government provides unemployment insurance, as many
governments do. On the one hand, such a program provides support for peo-
ple who cannot find work. On the other hand, such a program creates the
possibility that an employable person could claim to be unable to find a job
because that person prefers to collect unemployment insurance rather than
work. It is difficult for the government to differentiate between such people.
Moreover, were the government to simply ask, the employable types would
have an incentive to lie. And so, if the government wants to minimize abuse,
it must design the unemployment insurance program in a way that makes it
attractive to people who genuinely can’t find work, but unattractive to people
who can.
A standard approach to this information and incentives problem is
known as workfare. Under a workfare program, recipients must meet certain
requirements—such as job training or unpaid labor—to qualify for benefits.
The Earned Income Tax Credit in the United States is a version of workfare.
So too are the welfare-to-work programs instituted in the 1996 welfare reform,
which placed both a time limit and aminimumwork requirement on recipients
of public assistance. The Indian government’s National Rural Employment
Guarantee Act (NREGA) is the world’s largest public employment program and
is based on workfare principles. To qualify for benefits, the roughly 47 million
annual NREGA beneficiaries work on local public works projects.
You can see how workfare has the potential to solve the government’s in-
formation problem and mitigate the perverse incentives associated with social
insurance. If a citizen must work in order to receive public assistance, then
only citizens for whom such work is the best option will seek out the program.
A citizen with the option to work in another sector will likely prefer to do so.
The workfare example highlights a general challenge for governments. Many
of the policy recommendations that we have seen—subsidizing activities with
The Need for Information 245
positive externalities, taxing or regulating activities with negative externalities,
pushing people toward efficient equilibria in coordination games—depend on
the policymaker having a lot of information. For instance, in order to figure out
the right tax, subsidy, or regulatory limit to impose in an externalities setting,
the policymaker must be able to figure out the second best. This depends on
knowing things about the participants’ costs, benefits, and so on. Often such
information is dispersed among the interested parties. This presents a problem
because these interested parties might not be willing to release the relevant
information. Indeed, as we will see, these sorts of informational asymmetries
place a fundamental limit on howmuch good policymaking can do, even in the
presence of social dilemmas that, in principle, present opportunities for Pareto
improvements.
For instance, suppose the government is trying to diminish pollution. The
optimal policy involves requiring firms to adopt some new, green technology if
and only if the cost of doing so is below one million dollars. The policymaker
doesn’t know the true costs of adoption, while the firms do. If the policymaker
asks the firms the cost of adopting the new technology, the firms have an
incentive to say the cost is over a million dollars because doing so avoids new
regulation.
The policymaker needs to design an incentive scheme to induce the firms to
reveal their true information. The challenge is that the incentive scheme needs
to do three things at once:
1. Induce truthful revelation of the relevant information.
2. Implement an efficient policy.
3. Be budget balanced.
The first point says the government needs to find a way to actually get the
information.
The second point says that, once the government has the information,
it must be free to implement the efficient policy. This is important because
one way a policymaker might get the firms to reveal their information is
to make a credible promise that the policy won’t change, regardless of the
information supplied. If the policymaker makes such a commitment, the firms
have no reason to lie. So a commitment like this achieves point 1—firms will
truthfully reveal their private information. But this is a Pyrrhic victory, since
that information now can’t actually be used to achieve a socially optimal
outcome.
The third point says that there is no free lunch. You can’t offer to pay the
firms vast amounts of money, in excess of the benefits to be had from the
information, in order to induce truth telling. We are trying to achieve Pareto
improvements. At worst, we want society to break even on the deal.
246 Chapter 9
The field dedicated to the study of this sort of incentive problem is called
mechanism design. Since solving these sorts of problems is a basic challenge for
governments, we will spend some time thinking about mechanism design. Do-
ing so will give us a sense of the extent to which lack of information constrains
government’s ability to identify and implement Pareto improving policies. We
will study three different, but related, problems. First, we will consider how a
government might efficiently allocate an asset when it is uncertain about how
various parties value the asset. Second, we will consider a government deciding
whether to provide a public good and how to finance its provision, again while
facing uncertainty about how various parties value the good. Finally, we will
consider a government regulating an industry when it is doesn’t know key facts
about the production process.
Before commencing, I should say that the discussion in Sections 9.1–9.2 are
heavily based on the wonderful lecture notes from Jeff Ely’s microeconomics
class at Northwestern.1
9.1 Auctions
Suppose the government has a valuable asset—say the right to transmit signals
over some particular bands of the electromagnetic spectrum (for radio or cell
phones), drill in a given oil field, take off and land on a particular airport
runway, or occupy a location in geostationary orbit. There are lots of peoplewho
would like to have control of this asset. A player, i, places a monetary value of vi
on the asset. Players have quasi-linear utility. A player’s valuation of the asset is
her private information.
There is only one asset. So if Player i gets the asset, what is the utilitarian pay-
off? Each playerwhodid not get the assetmakes a payoff of zero. Player imakes a
payoff of vi. Thus, the utilitarian payoff is vi. Given this, it is straightforward that
the utilitarian optimal policy is to give the asset to the player with the highest
valuation.
Even in this simple problem, we see a challenge for the government. In order
to implement the utilitarian optimum, the government needs to figure out who
has the highest valuation. One thing a government might do is simply ask the
players their valuations and then give it to the player who says the highest
number. But that won’t work. All players have an incentive to say an arbitrarily
large number, so the government will not be able to figure out who has the
highest valuation.
Another thing the governmentmight do is auction off the asset. Let’s look at
an auction that will work in this simple setting.
1http://cheaptalk.org/jeffs intermediate micro course/
http://cheaptalk.org/jeffsintermediatemicrocourse/
The Need for Information 247
9.1.1 Second Price Auction
Suppose the government runs a second price auction. Each player submits a
sealed bid. The government opens the bids and awards the asset to the highest
bidder. The winner pays the amount bid by the second highest bidder.
I will show you that the government can implement the efficient policy by
using a second price auction. That is, it is a Nash equilibrium for all players to
bid their true valuation in a second price auction. Hence, the player with the
highest valuation wins the asset. Indeed, I will show you something stronger. It
is a weakly dominant strategy for each player to bid his or her true valuation in a
second price auction. A strategy is weakly dominant if it is a best response to any
profile of strategies by other players. Clearly, if each player is playing a weakly
dominant strategy, then together they are playing a Nash equilibrium. (The
opposite is not true: not all Nash equilibria are made up of weakly dominant
strategies.) Throughout this chapter we will focus on looking for mechanisms
that achieve the government’s goals by making truthful play a weakly domi-
nant strategy for each player.
I proceed in two steps. First, I show that, regardless of what the other players
bid, Player i is always at least as well off if she bids her true valuation rather than
something lower. Second, I show that, regardless of what the other players bid,
Player i is always at least as well off if she bids her true valuation rather than
something higher.
Consider a bid b′i < vi by Player i. Suppose that the highest bid among the
other players is B. Since she doesn’t know B, from Player i’s perspective, there
are three possibilities:
1. b′i < vi < B: In this event, Player i loses whether she bids b
′
i or vi. Under
either bid her payoff is 0. As such, in this case, she is indifferent
between the two bids.
2. b′i < B < vi: In this event, if Player i bids vi she wins andmakes a payoff
of vi − B > 0. If she bids b′i she loses andmakes a payoff of 0. So she
prefers to bid her true valuation, vi, in this case.
3. B < b′i < vi: In this event, Player iwins whether she bids b
′
i or vi. Under
either bid her payoff is vi − B > 0. As such, in this case, she is
indifferent between the two bids.
This analysis implies that bidding any b′i < vi is weakly dominated by bidding vi itself. The logic is straightforward. Changing her bid does not change how much she pays. It only changes the set of circumstances in which she wins. She wants to win whenever the price of the asset is less than her valuation of it, so she should bid her true valuation. The logic for not bidding higher than her true valuation is the same. Con- sider a bid b′′i > vi. Again, suppose the highest bid among the other players
248 Chapter 9
is B. Since she doesn’t know B, from Player i’s perspective, there are three
possibilities:
1. vi < b′′i < B: In this event, Player i loses whether she bids b
′′
i or vi. Under
either bid her payoff is 0. As such, in this case, she is indifferent
between the two bids.
2. vi < B < b′′i : In this event, if Player i bids vi she loses andmakes a payoff
of 0. If she bids b′′i > vi she wins andmakes a payoff of vi − B < 0. So she
prefers to bid her true valuation, vi, in this case.
3. B < vi < b′′i : In this event, Player iwins whether she bids b
′′
i or vi. Under
either bid her payoff is vi − B > 0. As such, in this case, she is
indifferent between the two bids.
Again, bidding any b′′i > vi is weakly dominated by bidding vi itself. The logic is
the same as above. Bidding more than vi simply leaves her in a situation where
she might win an asset for which she must pay more than her valuation of that
asset.
The second price auction, thus, fulfills the government’s goals. It gets each
player to reveal her true valuation and awards the asset to the highest-valuation
player.
Of course, auctions can get much more complicated. For instance, Milgrom
(2004) describes spectrum auctions in whichmultiple assets are for sale and the
value of asset 1 to Player i depends on who ends up owning asset 2 or 3. Clearly,
this creates a variety of additional strategic complications.
Another example involves situations in which the value of the asset is un-
known by the bidders. During the financial crisis of 2007–2008, the Troubled
Asset Relief Program included provisions for auctioning so-called toxic assets—
assets whose valuewas so uncertain that investment banks could findno buyers
on their own.Oftenwhen the government auctions, say, offshore drilling rights
for oil, bidders face uncertainty about the amount of extractable oil. In situa-
tionswhere there is uncertainty about valuations, but parties have some private
information, it is particularly difficult to elicit truth telling. This is because of
concerns over the “winner’s curse” (see Thaler, 1988, for a discussion). A bidder
only wins the auction if she bids higher than everyone else. This presumably
only happens when her guess about the asset’s value was higher than everyone
else’s guess, suggesting she probably paid toomuch.
9.2 Providing a Public Good
Now let’s turn to a case inwhich the government is not allocating an excludable
asset, but instead is considering providing a public good. The government’s
problem is that it doesn’t know how much the interested parties value the
The Need for Information 249
100,000
100,000 v1
v2
Effıcient to not
provide the
public good
Effıcient to
provide the
public good
v
1 + v
2 = 100,000
Figure 9.1. The efficient policy.
good. The parties know their individual valuations, but might have incentives
to lie to the government. The government must devise incentives to extract the
information, so it can figure out whether to provide the public good and who
should pay for it.
To keep things as simple as we can, consider a societymade up of two people.
The society has to decide whether to provide a public good. We can think of
this as a model of two neighborhoods deciding whether to build a shared park,
two cities deciding whether to construct a bridge that connects them, or what
have you. The public good costs $100,000. People have quasi-linear preferences.
Each player, i, values the public good at vi ≥ 0. Players’ valuations are their own
private information.
What is the efficient policy here? If the public good is provided, then the
social payoff is v1 + v2 − 100,000. If the public good is not provided, the social
payoff is 0. Hence, the efficient policy (i.e., the utilitarian optimum) is to
provide the public good if v1 + v2 ≥ 100,000; that is, if the total value of the
public good to the two players is at least as large as the cost of providing it.
Figure 9.1 illustrates the efficient policy.
If the government knew the two players’ valuations, it could simply imple-
ment the efficient policy. But it doesn’t know those valuations, so it must try
to get the players to reveal their private information. The willingness of players
to tell their true valuations will depend on who has to pay for the public good,
should it be provided.
Let’s consider some possible approaches the governmentmight take to try to
learn what it wants to know.
250 Chapter 9
100,000
50,000
100,00050,000 50,000v1
v2
100,000
50,000
100,000 v1
v2
Player 1 wants
public good under
cost splitting
s1 = 100,000
Player 2 wants public good
under cost splitting
s2 = 100,000
Player 1
doesn’t want
public good
under cost
splitting
s1 = 0 Player 2 doesn’t want public
good under cost splitting
s2 = 0
Figure 9.2. Best responses under split the costs.
9.2.1 Split-the-Costs
An intuitively appealing approach is to think that people should share the
costs of the public good. Suppose that the government adopted a mechanism
of the following sort:
• Each player states howmuch she values the public good. People can say
any valuation greater than or equal to zero. Call player i’s statement si.
• If the two statements sum to 100,000 or more, the public good will be
provided and the costs will be split evenly—that is, each player will pay
50,000.
Under this set of rules, if the public good is provided, Player iwill get a payoff
of vi − 50,000, since she pays half the cost. So Player i wants the public good to
be provided whenever her personal valuation is greater than 50,000 and to not
be provided whenever her personal valuation is less than 50,000.
If Player i’s valuation is greater than 50,000, she can guarantee the public
good will be provided by stating that her personal valuation is 100,000. Then,
no matter what the other player says, the government will provide the public
good. If player i’s valuation is less than 50,000 she wants to minimize the
chance that the public good will be provided. So she should say that her
valuation is 0. These incentives are illustrated for each player in the two panels
of Figure 9.2. The government has failed to elicit truthful revelation of peo-
ple’s valuations. People with valuations between 50,000 and 100,000 overstate
their valuations and people with valuations less than 50,000 understate their
valuations.
As a result, the government sometimes fails to implement the efficient policy.
The public good ends up being providedwhenever at least one party’s valuation
is greater than 50,000, even if the two valuations sum to less than 100,000.
The Need for Information 251
100,000
50,000
100,00050,000 v1
v2
Don’t
provide
Shouldn’t
provide but
do
Shouldn’t
provide but
do
Provide
Figure 9.3. Inefficiency under split the costs with each player declaring valuation.
Intuitively, the split-the-costs rule creates externalities. If I bid 100,000, I get
the full benefit of the public good, but I only bear half the cost, imposing the
other half as a negative externality on you. Hence, there is too much public
good provision relative to efficiency, as illustrated in Figure 9.3.
9.2.2 Veto and Split
Simply asking people their valuations and splitting the costs won’t work
because of negative externalities. What if, instead, we go the other way—split-
the-costs, but rather than asking people their valuations (which allows them to
impose the negative externalities), just let them say whether or not they want
the public good, providing it if and only if both people say they want it. Now
what happens? You shouldn’t be surprised to learn that this too will not get us
efficiency. Just as before, as illustrated in Figure 9.4, a player wants the public
good provided if and only if her valuation is greater than 50,000. So a player
with a valuation greater than 50,000 will support provision of the public good
and a player with a valuation less than 50,000 will veto provision of the public
good. Consequently, in any circumstance in which the sum of the valuations is
greater than 100,000, but one of the individual valuations is less than 50,000,
the public goodwill not be provided, even though it should be fromautilitarian
perspective. This inefficiency is illustrated in Figure 9.5.
9.2.3 General Mechanisms
Since splitting the costs won’t work, let’s see if the government can do better
with somemore subtle mechanism.
252 Chapter 9
100,000
50,000
100,00050,000 50,000v1
v2
100,000
50,000
100,000 v1
v2
Player 1 wants
public good under
cost splitting:
don’t veto
Player 2 wants public good
under cost splitting:
don’t veto
Player 1
doesn’t want
public good
under cost
splitting:
veto Player 2 doesn’t want public
good under cost splitting:
veto
Figure 9.4. Best responses under split the costs with vetoes.
100,000
50,000
100,00050,000 v1
v2
Provide
Should
provide
but don’t
Should
provide
but don’t
D
on’t provide
Figure 9.5. Inefficiency under split the costs with each player having a veto.
You could imagine all sorts of very complicated mechanisms in which the
government asks lots of questions,makes people do all sorts of things, and then
uses the output of this procedure to decide whether or not to provide the public
good and howmuch to charge each player should the public good be provided.
However, an important result, whose logic we will not explore here, says that
this is unnecessary. The result is called the revelation principle. Roughly speaking,
the revelation principle says this: if there is any complicated procedure that
gets people to reveal their true valuation and then implements the utilitarian
optimum, then there is also a very simple mechanism—called a direct revelation
The Need for Information 253
mechanism—that achieves the same thing. A direct revelation mechanism is a
procedure in which the government does the following:
• Asks people to state their valuations.
• Before they make their statements, lays out whether or not the public
good will be provided and who will pay what for each possible pair of
stated valuations.
Our first split-the-costsmechanism is an example of a direct revelationmech-
anism. The government asks people their valuation. For any pair of statements
that sums to at least 100,000, the government provides the public good and
charges each player 50,000. For any pair of statements that sums to less than
100,000, the government doesn’t provide the public good.
Another direct revelation mechanism would be to say that the public good
is provided if and only if the statements sum to at least 100,000 and, if the
public good is provided, charges each player according to his or her share of
the sum. That is, if v1 + v2 ≥ 100,000, then the public good is provided, player 1
is charged
(
v1
v1+v2
)
× 100,000, and player 2 is charged
(
v2
v1+v2
)
× 100,000.
To recap, the revelation principle says that if it is possible for the government
to design some mechanism that gets people to tell the truth and then imple-
ments the utilitarian optimum, then the government can do so with a direct
revelation mechanism. It doesn’t say any direct revelation mechanism will do
the job (we’ve already seen that split-the-costs won’t). Nor does it say that there
definitely exists a direct revelation mechanism that does the job. It says that
if achieving efficiency is feasible at all, then it can be done with some direct
revelationmechanism.
The revelation principle implies that if we can’t find a direct revelationmech-
anism that achieves truthful revelationof information and efficient policy, then
we also won’t be able to find a more complicated procedure that achieves these
goals. This is important because it means we don’t have to look at all those
complicated procedures.We can just look at direct revelationmechanisms. This
makes our lives much easier.
So let’s think about direct revelationmechanisms. The government asks each
player to make a statement. Call player i’s statement si. The government wants
to come up with rules of the game (when to provide the public good and how
much to charge each player) that induce players to choose si = vi; that is, to tell
the truth. If it can do so, then it will provide the public good when s1 + s2 ≥
100,000 and it will not provide the public good when s1 + s2 < 100,000.
The government’s key lever is how much it charges each player as a func-
tion of the statements the players make. Can the government come up with
amounts it will charge (as a function of the statements made) that make it
weakly dominant for bothplayers to tell the truth? That is, is there amechanism
254 Chapter 9
under which, for any v1, it is a best response for player 1 to tell the truth
regardless of what player 2 says (and similarly for player 2)?
To answer this question, we will focus on player 1. (Player 2 is symmetric.)
It turns out there is one and only one way to make truth telling a weakly
dominant strategy. Whenever s1 + s2 ≥ 100,000, so that the public good is
provided, player 1 must be charged an amount p∗(s2) = 100,000 − s2. Notice,
this says that the price player 1 is charged, should the public good be provided,
is a function of the statement player 2makes, not the statement person 1makes.
This is just as in the second price auction.
I will demonstrate that this is true in three steps. First, I will show you that if
player 1 is charged 100,000 − s2 when the public good is provided, then truth
telling is weakly dominant for any v1. Second, I will show you that if player
1 will instead be charged some amount p > 100,000 − s2, then truth telling
is not weakly dominant for any v1. Third, I will show that if player 1 will be
charged some amount p < 100,000 − s2, then, again, truth telling is not weakly
dominant for any v1.
First, suppose player 1 knows she will be charged p∗(s2) = 100,000 − s2 when
the public good is provided. Of course, she doesn’t know s2. But let’s see that,
for any v1, it is a best response for player 1 to state her true valuation, regardless
of what s2 turns out to be.
The government provides the public good if and only if s1 + s2 ≥ 100,000.
Rearranging, the government provides the public good if and only if s1 ≥
100,000 − s2. Now think about player 1’s incentives. Player 1’s payoff from the
public good being provided is
v1 − p∗(s2) = v1 − (100,000 − s2).
Her payoff from the public good not being provided is 0. Hence, she wants the
public good to be provided if and only if
v1 ≥ 100,000 − s2.
Since the government provides the public good if s1 ≥ 100,000 − s2, if player
1 chooses s1 = v1 (i.e., states her true valuation), the government provides the
public good precisely when player 1 wants the government to do so (since this
implies v1 ≥ 100,000 − s2). Hence, choosing s1 = v1 is a best response by player
1 to any possible statement by player 2.
These incentives are illustrated in Figure 9.6. The upper panel shows that if
the amount charged will be p∗(s2) = 100,000 − s2, then player 1 will state her
true valuation when v1 > p∗(s2). The lower panel shows that the same is true
when v1 < p∗(s2).
The Need for Information 255
100,000
s2
p*(s2) v1v1
v2
s2 + v1 < 100,000, so if player 1
states true valuation (s1 = v1),
public good is not provided, which
player 1 wants because v1 < p*(s2)
100,000
100,000
100,000
s2
p*(s2) v1v1
v2
s2 + v1 > 100,000, so if player 1
states true valuation (s1 = v1),
public good is provided, which
player 1 wants because v1 > p*(s2)
Figure 9.6. It is a weakly dominant strategy for player 1 to choose s1 = v1 when the cost
of the public good to player 1 is p∗(s2) = 100,000 − s2.
Second, let’s see that if player 1 will be charged some p > 100,000 − s2 when
the public good is provided, then for any v1 there is some s2 such that choosing
s1 = v1 is not a best response. Player 1’s payoff from the public good being
provided is v1 − p. Her payoff from the public good not being provided is 0.
Hence, she wants the public good to be provided if and only if
v1 ≥ p.
Remember that p > 100,000 − s2. Suppose player 2’s statement, s2, is such that
player 1’s valuation, v1, is between 100,000 − s2 and p. Player 1 does not want
the public good to be provided because her true valuation is less than her
price. But if player 1 tells the truth, the public good will be provided because
256 Chapter 9
100,000
s2
p*(s2) v1v1 p
v2
s2 + v1 > 100,000, so if player 1
states true valuation (s1 = v1),
public good is provided, which
player 1 doesn’t want because v1 < p
100,000
Figure 9.7. It is not a weakly dominant strategy to choose s1 = v1 when p > p∗(s2).
v1 + s2 > 100,000. Hence, player 1’s best response is to lie—understating her
valuation. This incentive is illustrated in Figure 9.7.
Finally, let’s see that if player 1 will be charged p′ < 100,000 − s2 when the public good is provided, then for any v1 there is an s2 such that choosing s1 = v1 is not a best response. Player 1’s payoff from the public good being provided is v1 − p′. Her payoff from the public good not being provided is 0. Hence, she wants the public good to be provided if and only if v1 ≥ p′. Remember that p′ < 100,000 − s2. Suppose player 2’s statement, s2, is such that player 1’s valuation, v1, is between p′ and 100,000 − s2. Player 1wants the public good to be provided because her true valuation is greater than the price. But if player 1 tells the truth, the public good won’t be provided because v1 + s2 < 100,000. Hence, player 1’s best response is to lie—overstating her valuation. This incentive is illustrated in Figure 9.8. Player 2’s incentives are symmetric to player 1’s. It is always a best response for player 2 to tell the truth, regardless ofwhat statement player 1makes, if andonly if player 2 will be charged 100,000 − s1 whenever the public good is provided. We have learned that any mechanism that makes revealing true valuations weakly dominant and uses that information to implement the efficient policy is equivalent to the following direct revelationmechanism: • The public good is provided if and only if s1 + s2 ≥ 100,000. • Player 1 is charged 100,000 − s2 if the public good is provided. • Player 2 is charged 100,000 − s1 if the public good is provided. The Need for Information 257 100,000 s2 p*(s2) v1v1p′ v2 s2 + v1 < 100,000, so if player 1 states true valuation (s1 = v1), public good is not provided, which player 1 doesn’t want because v1 > p′
100,000
Figure 9.8. It is not a weakly dominant strategy to choose s1 = v1 when p′ < p∗(s2).
This seems like good news.We have found a way for the government to learn
the information it needs to pursue efficient policy. But there is a catch.
Suppose we are in a situation where the right policy is to provide the public
good—that is, v1 + v2 > 100,000. Under our mechanism, s1 = v1 and s2 = v2,
so the public good will be provided, at a cost of 100,000. How much revenue
will be raised? Player 1 will be charged 100,000 − s2. Player 2 will be charged
100,000 − s1. So the total revenue generated is
100,000 − s2 + 100,000 − s1 = 200,000 − (s1 + s2)
= 200,000 − (v1 + v2).
But remember v1 + v2 > 100,000. So total revenue is less than the cost of provid-
ing the public good. Our mechanism doesn’t have a balanced budget!
What does this mean? The presence of private information presents a real
constraint on the ability of the government to pursue efficient public policy.
There is no budget balanced mechanism under which both players always tell the
truth.And since the government cannot create resources out of thin air, wemust
accept the fact that, at least some of the time, policymakers will be unable to
elicit the information they need to implement optimal policies.
9.2.4 The Second Best
The fact that no mechanism exists that induces truth telling all the time
does not mean the government must make policy with no information. There
are mechanisms that induce truth telling some of the time. Such mechanisms
258 Chapter 9
100,000
100,00070,000100,00070,000 v1
v2
100,000
30,000 30,000
v1
v2
Player 2 wants public good
under 70–30 split
Player 1 wants
public good
under 70–30 split
100,000
100,00070,000 v1
v2
30,000
Provide
D
on’t provide
Should provide
but don’t
Should
provide
but don’t
Figure 9.9. Incentives and inefficiency under a 70 30 split the costs arrangement with
vetoes.
don’t allow the government to always pursue Pareto efficient policies, but they
certainly are better thanmaking policy with no information.
We’ve actually already seen some examples ofmechanisms like this in Figures
9.3 and 9.5. Each of these shows an example of a budget balanced mechanism
that induces truth telling and allows the government to implement the Pareto
efficient policy some of the time. You could imagine other such mechanisms.
For instance, consider a mechanism that gives each player a veto and splits the
costs 70-30 between player 1 and player 2. This mechanism is similar to the
one described in Figure 9.5, but it shifts around when exactly policy fails to
be efficient as well as how much of the cost each player pays, as illustrated in
Figure 9.9.
We will refer to those mechanisms that do the best the government can
as second-best mechanisms. This is in keeping with our notion of the second
best from our earlier discussions. The second best is not the socially efficient
outcome. But it is the best the government can do given the constraints under
The Need for Information 259
which it operates. In our earlier examples of the second best, the constraints
came from the inefficiency inherent in imposing taxes, moral hazard, or other
concerns. Here the constraints come from lack of information.
We will not fully characterize what the second best looks like in this public
goods game. But, roughly speaking, the examples we’ve seen of mechanisms
that choose a fixed division of the costs describe what the second-best mecha-
nism looks like. The governmentmust accept that, due to a lack of information,
sometimes it will not provide the public good when it would be efficient to do
so or will provide the public good when it is inefficient to do so. Comparing
Figures 9.5 and 9.9, you can see that by changing how the costs are split, the
government can change two things:
1. The valuations for which it fails to achieve efficiency.
2. The distribution of costs between the two players.
The first of these decisions may well be a question that the government
can answer in terms of efficiency. If the government believes it is extremely
unlikely that people have some particular set of valuations, then it should
use a mechanism that leads to the government choosing the wrong policy in
those instances, since those instances are relatively rare. The second question,
however, is about the distribution of welfare. That is a decision not about how
to make the pie larger, but rather, about how to divide it up. We will turn to
questions about how players try to influence such decisions in Chapter 10.
9.3 Regulating a Monopolist
Markets characterized by monopoly power are a classic example of a situation
in which government regulation can improve social welfare. Monopoly power
exists when a single firm controls a market. As you know if you’ve taken
microeconomics, monopolists have incentives to produce too little (relative to
the utilitarian optimum) in order to inflate prices. Doing so gives them higher
profits, but reduces consumer welfare.
There are a variety of reasons an industry might end up with a monopolist
(or, more generally, with a small number of firms exercising oligopoly power).
For instance, a firmmight control amarket because the dominant technology is
its intellectual property. This is often the case, on a temporary basis, in markets
for certain types of medicines. A firm might also control a market because
there are high fixed costs to entering the market, making it too expensive
for competitors to emerge. This is often thought to be the case in certain
“natural monopolies,” such as the provision of utilities like electricity, gas,
and water. Regulating such monopolists is perhaps the paradigmatic example
from economic theory of a Pareto improving policy intervention. And, indeed,
governments do in fact regulate public utilities.
260 Chapter 9
Governments can improve utilitarian social welfare by requiring monopo-
lists to produce more than they otherwise would. Doing so increases consumer
welfare by more than it reduces the monopolist’s profits. The question is: how
much more production should regulators require? In order to answer that
question, the government needs to know the monopolist’s marginal costs of
production. Let’s see why.
Imagine a simple economy with one firm that produces widgets. If the firm
produces qwidgets and sells themat price p, itmakes revenues pq and bears costs
of production cq. (I’m assuming constantmarginal costs of production, c, which
is to say perfectly elastic supply, because it makes the model simple. Nothing
important inwhat I’mgoing to saydepends on constantmarginal costs.)Hence,
the firm’s profits are
π(p, q, c) = q(p − c).
Of course, prices are determined by themarket. We will assume that the firm
must charge the same price to all consumers. Moreover, at price p, demand for
widgets is given by a simple, linear demand function:
D(p) = 100 − p.
That is, if the price per widget is $5, then there is demand for 95 widgets. If the
price per widget is $20, then there is only demand for 80 widgets.
We can invert this demand function to find the price the market will bear,
given the number of widgets produced. If the firm produces q < 100widgets, all
the widgets will be sold as long as the price is such that
D(p) = 100 − p ≥ q.
Rearranging, when q widgets are produced, the highest price the monopolist
can charge and still sell all the widgets is
p∗(q) = 100 − q.
Notice what this implies about the consumer’s welfare (called consumer
surplus in microeconomic parlance). If q widgets are produced, then the price
per widget will be 100 − q. For the qth widget, this is exactly the price that
the marginal consumer is willing to pay. However, for all the other widgets
produced, there were consumers willing to pay more than 100 − q per widget.
Hence, for each of thosewidgets, a consumer ismaking positive surplus (i.e., her
welfare is greater than 0). Indeed, for this reason, we can think of the demand
curve as also representing themarginal consumer surplus.
The Need for Information 261
100
p*(q)
0 100
Quantity
Total
consumer
surplus
Demand
(marginal consumer surplus)
q
D
o
ll
ar
s
Figure 9.10. Consumer surplus given a quantity q.
Figure 9.10 shows how to calculate the total consumer surplus. The downward
sloping line gives demand as a function of the quantity produced. We see that
if the quantity produced is q, then the price will be p∗(q)—the price at which
supply exactly equals demand. The total consumer surplus is represented by
the area of the marked triangle. For the very first widget, someone was willing
to pay 100, but got it for p∗(q) = 100 − q. That consumer made a surplus of
100 − p∗(q) = q. For the next widget, the marginal consumer was willing to pay
a little less, but stillmore than 100 − q. Each subsequent consumer, then, values
the widget slightly less and so makes slightly less surplus. This continues all
the way to the consumer who values the widget at exactly 100 − q and, so,
makes zero surplus. The area of the triangle gives the total surplus welfare that
consumers enjoy by virtue of consuming widgets that they value at more than
100 − q but for which they pay only 100 − q. This area is given by
TCS(q) = 1
2
(
100 − p∗(q)) q.
Using the fact that p∗(q) = 100 − q, the total consumer surplus can be rewritten
TCS(q) = q
2
2
.
9.3.1 Monopolistic Equilibrium
Now let’s think about howmuch themonopolistic firmwill produce if left to
its own devices. The firmmaximizes profits by solving
max
q
q(p∗(q) − c).
262 Chapter 9
100
0 100
Quantity
Firm
profits
Cost of
production
Demand
(marginal consumer surplus)
Consumer
surplus
DW
L
Marginal cost of
production (c)
qM = 100 – c—
2
pM = 100 + c—
2
D
o
ll
ar
s
Figure 9.11. Outcome under a monopolist.
Since p∗(q) = 100 − q, this is equivalent to solving
max
q
q(100 − q − c).
Solving for the first-order condition, the monopolist’s profit-maximizing level
of production is
qM = 100 − c
2
.
This implies that the price under a monopolist is
pM = p∗(qM) = 100 − 100 − c
2
= 100 + c
2
.
Social welfare is profits plus total consumer surplus:
π
(
pM , qM , c
) + TCS (qM) =
(
100 − c
2
) (
100 + c
2
− c
)
+ 1
2
(
100 − c
2
)2
= 3(100 − c)
2
8
.
This sum of firm profits and consumer surplus can be seen graphically in
Figure 9.11.
The Need for Information 263
100
pFB = c
0 100
Quantity
Consumer
surplus
Cost of
production
Demand
(marginal consumer surplus)
qFB = 100 – c
Marginal cost of
production (c)
D
o
ll
ar
s
Figure 9.12. The first best.
9.3.2 Regulation with Full Information
Allowing the monopolist to choose the quantity produced does not
maximize the utilitarian social welfare because the monopolist holds down
production in order to keep prices and profits high. This behavior creates an in-
efficiency, known as deadweight loss, which is represented by the triangle labeled
DWL in Figure 9.11. The deadweight loss exists because, at the monopolist’s
preferred level of production, there are still consumers whose value for widgets
is higher than the firm’s marginal cost of production. Hence, the deadweight
loss represents social welfare that could be created if the firm producedmore.
Suppose a utilitarian welfare maximizing government could regulate the
monopolist, requiring a higher level of production. Such a government would
increase production so that all of the deadweight loss was recovered. That is, it
would make the firm keep producing until the marginal benefits of production
(increased consumer surplus) exactly equaled themarginal costs of production.
Graphically, this means setting the quantity to qFB, represented in Figure 9.12.
At this level of production, the price per widget exactly equals the firm’s mar-
ginal cost of production. So the firm makes exactly zero profits (i.e., revenues
equal production costs). But the consumers enjoy the largest feasible surplus.
There is no deadweight loss.
Formally, the utilitarian government regulates the firm to produce the first-
best quantity of widgets, qFB, which solves
max
q
Firm Profits
︷ ︸︸ ︷
q(p∗(q) − c) +
Consumer Surplus
︷︸︸︷
q2
2
.
264 Chapter 9
100
0 100qH
FB
cH
cL
qL
FB
Quantity
Demand
(marginal consumer surplus)
D
o
ll
ar
s
Figure 9.13. First best for two different marginal costs.
Substituting for p∗(q) = 100 − q and maximizing, the first-best level of produc-
tion is
qFB = 100 − c.
The associated price is
pFB = p∗(qFB) = c.
At the first-best quantity, the price of widgets equals the marginal cost of
production.
9.3.3 Regulation with Uncertainty
Weare interested inwhat happenswhen the government doesn’t have all the
information it needs to optimally regulate thefirm. So, suppose the government
is uncertain of whether the firm has a high marginal cost of production (cH)
or a low marginal cost of production (cL < cH). The government believes the
probability that the firm’s marginal costs are low is λ ∈ (0, 1). Let’s also add one
more constraint. While the government can regulate the firm, it cannot force
the firm to operate at a loss, since the owners can always shut the firm down
instead.
As above, if the government knew the firm’s marginal cost, it would be easy
to implement the first-best policy, illustrated in Figure 9.13. If the firm has
low marginal costs, the government would like to require the firm to produce
qFBL = 100 − cL and if the firm has high marginal costs, the government would
The Need for Information 265
like to require the firm to produce qFBH = 100 − cH . In each case, the firm makes
zero profits and utilitarian social welfare is maximized.
The challenge for the government is figuring out what to do without this
critical piece of information.
CAN THE FIRST-BEST POLICY BE IMPLEMENTED?
One thing the government might do is simply ask the firm whether its mar-
ginal costs are high or low, and then implement the first-best policy assuming
the answer is truthful. But this won’t work. Let’s see why.
Suppose the firmhas highmarginal costs. If it tells the government the truth,
the government will set production at qFBH and the firmwill make zero profits:
π(p = cH , q = 100 − cH , cH) = (100 − cH) (cH − cH) = 0.
If the firm lies and claims it has lowmarginal costs, then the governmentwill set
production at qFBL = 100 − cL. The high-cost firm’s profits from lying, then, are
π(p = cL, q = 100 − cL, cH) = (100 − cL) (cL − cH) < 0.
A high marginal cost firm makes zero profits from telling the truth and
negative profits from lying, so a high marginal cost firm will tell the truth.
This makes sense. Firms want to hold down production in order to increase
prices and profits. The higher the government believes a firm’s marginal costs
to be, the lower it sets production. Hence, all the high marginal cost firm can
achieve by claiming tohave lowmarginal costs is to put itself in a positionwhere
production is even higher and prices even lower. It will not do so.
But what if the firm has low marginal costs? Now, by claiming to have high
marginal costs, the firm can convince the government to reduce production, to
the firm’s benefit. Let’s see this.
If the lowmarginal cost firm tells the truth, the government will set produc-
tion at qFBL and the firmwillmake zero profits. If, instead, the firm claims to have
highmarginal costs, then the government will set production at qFBH = 100 − cH
and the firm’s profits will be
π(p = cH , q = 100 − cH , cL) = (100 − cH) (cH − cL) > 0.
This logic is illustrated in Figure 9.14, which shows that when a firm has low
marginal costs, but production is set at qFBH , the firm makes positive profits.
Hence, a lowmarginal cost firmwill claim to have highmarginal costs.
The analysis above shows that if the government attempts to implement the
first-best policy, all firms will claim to have high marginal costs. When the
firm actually has high marginal costs, the outcome will be socially optimal.
266 Chapter 9
100
0 100qH
FB
cH
cL
qL
FB
Quantity
Profits to type cL
from claiming to
be type cH
Consumer surplus
when type c
L lies
DW
L from cL lie
Demand
(marginal consumer surplus)
D
o
ll
ar
s
Figure 9.14. The first best policy is manipulable by a low marginal cost firm when the
government is uninformed.
However, when the firm actually has low marginal costs, the result will be
underproduction and deadweight loss.
The expected decrease in social welfare (relative to the first best) associated
with this policy is the deadweight loss suffered when the firm has lowmarginal
costs multiplied by the probability that the firm has low marginal costs. The
deadweight loss when the firmhas lowmarginal costs is given by the area of the
triangle in Figure 9.14:
DWL = 1
2
(qFBL − qFBH )(cH − cL) =
(cH − cL)2
2
.
Weighting this deadweight loss by the probability that the firm has low mar-
ginal costs (λ), the expected cost of government uncertainty, in terms of social
welfare, under this policy, is
λ(cH − cL)2
2
.
THE SECOND BEST
The government can design a better mechanism than simply asking the firm
to report its marginal costs and then attempting to implement the first best.
How does it do so?
To induce a firm with low marginal costs to reveal that information, the
governmentmust compensate the firm for the profits it forgoes by not claiming
The Need for Information 267
100
0 100qH
FB
cH
cL
qL
FB
Quantity
Transfer to a firm
claiming marginal
costs of cL
Consumer surplus
if firm type
is c
H
Demand
(marginal consumer surplus)
Consumer surplus
if firm type is cL
D
o
ll
ar
s
Figure 9.15. A mechanism that induces truth telling by making large transfers to firm
claiming to have lowmarginal costs.
to have highmarginal costs. Figure 9.15 illustrates a simple policy that achieves
this goal as follows:
• If the firm claims to have high marginal costs, require production qFBH =
100 − cH .
• If the firm claims to have low marginal costs, require production qFBL =
100 − cL and transfer an amount
t = π(p = cH , q = 100 − cH , cL) = (100 − cH) (cH − cL)
from the consumers to the firm.
This policy makes telling the truth a best response for both types of firms.
Moreover, by eliminating the deadweight loss, this policy leaves the consumers
better off than they otherwise would have been. Let’s see how this works.
A high marginal cost firm that tells the truth makes zero profits. A high
marginal cost firm that claims to have low marginal costs has to produce
qFBL = 100 − cL at price cL (so makes a loss on each sale) and gets a transfer t =
(100 − cH) (cH − cL). So, by claiming to have lowmarginal costs, a highmarginal
cost firm’s payoff is
(100 − cL)(cL − cH) + (100 − cH) (cH − cL) = (cH − cL)(cL − cH) < 0.
Even with the transfer, a high marginal cost firm prefers to truthfully reveal its
costs.
268 Chapter 9
A low marginal cost firm is willing to tell the truth since the transfer it
receives when it reveals itself to have low marginal costs is exactly equal to the
profit it makes by claiming to have highmarginal costs.
If the government can make transfers from consumers to producers cost-
lessly, then this policy gives the firm incentives to truthfully reveal its type
and implements the first-best outcome. But now suppose, as we have in earlier
chapters, that it is costly for the government to make transfers. In particular,
as we have throughout, let’s assume that if the government wants to transfer
a dollar from consumers to the firm, it requires τ > 1 dollars in revenue. By
contrast, we’ll assume that the government can transfer money from the firms
to the consumers without any distortion. This is clearly a simplification, but
there is an intuition for why transfers from firms to consumers should be
less distortionary. The government can use revenue collected from firms as a
substitute for revenue collected using distortionary tools such as income or
sales taxes. Hence, movingmoney from firms to consumers is less distortionary
because it is achieved by reducing distortionary taxes on consumers.
The policy just described, and illustrated in Figure 9.15, depends on large,
distortionary transfers from consumers to low marginal cost firms. Since those
transfers induce their own inefficiency, the government might want to look for
a policy that reduces the size of the transfer it makes to the firm, while still
inducing truthful revelation of marginal costs.
In order to hold down the level of distortionary transfers needed to induce
truth telling by low marginal cost firms, the government must reduce how
profitable it is for a low marginal cost firm to pretend to have high marginal
costs. The government achieves this in two steps. First, it reduces the amount
produced by a firm claiming to have high marginal costs. Second, it makes a
(non-distortionary) transfer from a firm claiming to have high marginal costs
to the consumers equal to the profits the high marginal cost firm would make
under this lower level of production. Together, these two steps leave a high
marginal cost firmwith exactly zero profits (the government can’t transfermore
because it can’t force a firm to operate at a loss) and reduce the attractiveness of
lying for a low marginal cost firm. In so doing, they reduce the distortionary
transfer required to induce truth telling by a lowmarginal cost firm.
Figure 9.16 illustrates this idea. If a firm claiming to have highmarginal costs
is made to produce qFBH , then a low marginal cost firm’s profit from pretending
to have highmarginal costs is the sumof the rectanglesD + E. Suppose, instead,
that production by a firm claiming to have a highmarginal cost is held down to
q′H < q
FB
H . Prior to transfers, this leaves a high marginal cost firm that tells the
truth with profits equal to the rectangle B. Whenever a firm claims to have high
marginal costs, the government transfers B from the firm to the consumers. So,
after transfers, a high marginal cost firm makes zero profits. Prior to transfers,
it leaves a low marginal cost firm that claims to have high marginal costs with
The Need for Information 269
100
100 – q′H
100 – qH
FB
100 – qL
FB
0 100
A
B C
D E
F
G
qH
FBq′H
cH
cL
qL
FB
Quantity
Demand
(marginal consumer surplus)
D
o
ll
ar
s
Figure 9.16. A mechanism that induces truth telling by making smaller transfers to a
firm claiming to have lowmarginal costs, but also inducing some deadweight loss when
the firm claims to have highmarginal costs.
profits equal to the sum of the rectangles B + D. After the transfer of B from
the firm to the consumers, a low marginal cost firm that claims to have high
marginal costs is left with a profit of D. As such, to induce truth telling, the
government need only transferD to a firm claiming to have lowmarginal costs.
By holding down production and making a transfer from firms to consumers
when a firm claims to have high marginal costs, the government reduces the
distortionary transfers it has tomake fromconsumers to lowmarginal cost firms
fromD + E down to justD.
Of course, reducing distortionary transfers in this way comes at a cost.
When the firm actually has high marginal costs, there is deadweight loss from
underproduction. That deadweight loss is represented by the triangle C in
Figure 9.16. The second-best policy induces truth telling while balancing these
benefits and costs.
Let’s see how this works. Building on the argument above, suppose the
government implements the following policy:
• If the firm claims to have high marginal costs, require production q′H <
qFBH and transfer an amount t
′
H = q′H(qFBH − q′H) (i.e., the rectangle B) from
the firm to consumers.
• If the firm claims to have low marginal costs, require production qFBL
and transfer an amount t′L = q′H(cH − cL) (i.e., the rectangle D) from the
consumers to the firm.
We’ve already seen that such a policy will in fact induce truth telling by the
firm.
270 Chapter 9
Now we can solve for the second best. As we’ve already discussed, the trade-
off is this: On the one hand, as q′H gets smaller, the amount that must be
transferred to low marginal cost firms (the rectangle D) decreases. This saves
on distortionary transfers when the firm has low marginal costs. On the other
hand, as q′H gets smaller, the deadweight loss associated with underproduction
when the firm has high marginal costs (the triangle C) gets larger. The second-
best policy will balance these benefits and costs. Let’s see how.
It will be useful to have notation for the first-best outcomes. Referring to
Figure 9.16, when the firm has low marginal costs, utilitarian social welfare
under the first best is
�L = A + B + C + D + E + F.
And when the firm has highmarginal costs, utilitarian social welfare under the
first best is
�H = A + B + C.
Suppose the firm has low marginal costs. Under the policy described above,
the firmwill reveal its true type and productionwill be qFBL . The governmentwill
then transferD to the firm at cost τD to the consumers. Hence, for any given q′H ,
if the firm has lowmarginal costs the total social surplus is
�L + D(1 − τ).
Now suppose the firm has high marginal costs. Here, consumer surplus is
A + B and firm profits are 0. So total social surplus is equal to the first-best
welfare when the firm has high marginal costs minus the deadweight loss
associated with reduced production:
�H − C.
Recall that the probability that the firm has low marginal costs is λ. Hence,
when the level of production for a firm that reports high marginal costs is q′H ,
the expected social welfare from the policy described above is
U(q′H) = λ(�L + D(1 − τ)) + (1 − λ)(�H − C).
We can now substitute in forD = q′H(qFBL − qFBH ) and C =
(qFBH −q′H )2
2 to get
U(q′H) = λ
[
�L + q′H
(
qFBL − qFBH
)
(1 − τ)] + (1 − λ)
[
�H −
(qFBH − q′H)2
2
]
.
Neither �L nor �H are functions of q′H . Maximizing with respect to q
′
H , the first-
order condition characterizing the second-best level of production for a high
The Need for Information 271
marginal cost firm (qSBH ) yields
qSBH = qFBH +
λ
1 − λ(1 − τ)(q
FB
L − qFBH ).
Recall that τ > 1, so the second-best level of production by a highmarginal cost
firm is indeed lower than the first-best level of production. The larger is τ (i.e.,
the more distortionary are transfers from consumers to firms), the lower is the
second-best level of production by a high marginal cost firm, since as τ gets
large, avoiding large distortionary transfers becomes particularly important.
The smaller is λ, the larger is the second-best level of production by a high
marginal cost firm because, when λ is small, the firm is very likely to have high
marginal costs, making it particularly important to avoid the deadweight loss
associated with underproduction.
An important point to see, here, is that the government’s lack of full
information comes at a real cost—both in terms of deadweight loss due to
underproduction and in terms of distortionary transfers by the government
from consumers to producers. Moreover, these transfers from the government
to the low marginal cost firm result in positive firm profits. This fact shows
how the government’s lack of information provides an account of behavior that
may, at first blush, seem puzzling. The government has the legal authority to
regulate monopolies. Yet we often observe the government negotiating with
monopolistic firms over the terms of regulation. Onemight interpret this either
as the government failing to exercise its authority or as evidence ofmalfeasance
(e.g., the firm buying off the government). But our model offers a different
view. When the firm possesses information that the government needs in
order to exercise its regulatory authority effectively, the government cannot
impose the optimal regulation. It must negotiate with the firm to extract the
required information. And those negotiations will result in underproduction in
some circumstances and government subsidization of the monopolist in other
circumstances, not necessarily because of malfeasance or incompetence, but
because of the power of information.
9.3.4 An Informed Regulator
A government might respond to limited information by employing expert
regulators. For instance, a government might seek out regulators who pre-
viously worked in the regulated industry. This provides a rationalization for
the commonly observed “revolving door”—whereby people move back and
forth between employment in some regulated industry and employment in the
agencies that regulate that industry. Of course, using such regulators, who have
their own interests and agendas, comes with risks. To explore such issues, let’s
think about adding an expert to our model.
272 Chapter 9
There is still a monopolistic firm, as above, with either low or high marginal
costs. Now, however, the government appoints an expert regulator. The expert
regulator investigates the firm’smarginal costs.With probabilityμ the regulator
indeed learns the firm’s marginal costs and with probability 1 − μ the regulator
learns nothing. The regulator makes a report to the government. That report
can be either a statement of the firm’s marginal cost or a statement that the
regulator did not learn anything in her investigation. The government, lacking
expertise of its own, does not know whether or not the regulator really learned
the firm’s marginal costs.
Suppose the regulator makes an honest report. Then the government is in
a better position with the informed regulator than without. If the regulator
reveals the firm’s marginal costs, the government can implement the first-best
policy. If the regulator learns nothing, the government can still fall back on
the second-best policy. Hence, at least some of the time, having an honest,
informed regulator makes society strictly better off, and it never makes society
worse off.
The question is, will the regulator tell the truth? To explore this, we want to
think about the incentives of the regulated firm, which might want to try to
corrupt or “capture” the regulator for its own purposes.
REGULATORY CAPTURE
Suppose that the regulator and the firm can collude by plotting for the
regulator to issue a false report to the government. There is a fixed cost to
collusion, k > 0, whichmight represent the risk of being caught. If the regulator
and firm do collude, they split the costs and also split any resulting profits.
It is worth noting that our setup suggests a very stark interpretation—the
firm is bribing the regulator. But matters need not be quite that clear cut. For
instance, a variety of practices, short of bribery,might establish an implicit quid
pro quo between regulators and a regulated industry. The revolving door is an
obvious mechanism by which a quid pro quo might operate. Regulated firms
could create incentives akin to those modeled here simply by structuring an
environment in which regulators believe that their future job prospects depend
on their behavior while in government.
If the government trusts the regulator, when will the firm and the regulator
benefit from colluding?
Suppose the firm has high marginal costs. Under both the first- and second-
best policies, a highmarginal cost firmmakes zero profits. So such a firm has no
incentive to bear the costs of collusion.
What about a lowmarginal cost firm? If the regulator learns nothing (which
happens with probability 1 − μ) and reports that honestly, the low marginal
cost firm will make a profit equal to the rectangle D in Figure 9.17. If the regu-
lator learns the firm’s true marginal costs (which happens with probability μ)
The Need for Information 273
100
100 – qH
FB
100 – qH
SB
100 – qL
FB
0 100
A
B C
D E
F
G
qH
FBqH
SB
cH
cL
qL
FB
Quantity
Demand
(marginal consumer surplus)
D
o
ll
ar
s
Figure 9.17. The second best policy when there is no informed regulator.
and reports that honestly, the firmmakes zero profits. Hence, absent collusion,
the firm’s expected profits are
(1 − μ)D.
If, instead, the firm and the regulator collude, the regulator will simply always
report that the firm has high marginal costs. The government will implement
the first-best policy for a high marginal cost firm—requiring production qFBH
and offering zero transfers. This will result in profits for the low marginal cost
firm equal to the sum of the rectangles D + E in Figure 9.17. Hence, collusion is
worthwhile for the lowmarginal cost firm and the regulator if
D + E − k > (1 − μ)D,
which is equivalent to
k < μD + E. (9.1) In this event, we say that the regulator will be captured by industry. When this happens, the government cannot trust the regulator’s reports, undoing the benefit of using an informed regulator in the first place. AVOIDING CAPTURE If the government wants to gain the benefits of using an informed regulator, it needs to set policy such that the regulator will not be captured—that is, such that Condition 9.1 is not satisfied. In order to do so, it must ensure that 274 Chapter 9 100 100 – qH FB 100 – qH NC 100 – qL FB 0 100 A′ B′ C′ D′ E′ F G qH FBqH NCqH SB cH cL qL FB Quantity Demand (marginal consumer surplus) D o ll ar s Figure 9.18. The optimal policy that avoids collusionbetween thefirmand the regulator. the profits a low marginal cost firm generates by lying are not sufficient to compensate for the costs associated with collusion. To eliminate the incentive to collude, the government can adjust production when the regulator claims to be uninformed and the firm claims to have high marginal costs. This new production level (call it qNCH for “no collusion”) must reduce μD + E so that the firm and regulator do not want to collude. This involves choosing qNCH > q
SB
H , as illustrated in Figure 9.18.
Why does increasing production by the high marginal cost firm reduce
incentives for collusion between the low marginal cost firm and the regulator?
One benefit of collusion is that, by inducing the government to implement the
first-best policy for a high marginal cost firm, collusion provides a profit equal
to the rectangle E that would never be achieved without collusion. Second, by
avoiding the possibility that the informed regulator will reveal that the firmhas
low marginal costs, collusion provides the firm with an extra profit of D in the
event that the regulator is informed. By increasing the amount produced by a
firm claiming to have high marginal costs when the regulator is uninformed,
the government makes E smaller and D larger. That is, comparing Figures 9.17
and 9.18, E′ < E and D′ > D. Since the E/E′ rectangles represent a benefit of
collusion that is realized with certainty, whereas the D/D′ rectangles represent
a benefit of collusion that is realized only probabilistically, the negative effect
on the appeal of collusion associated with moving from E to E′ is larger than
the positive effect on the appeal of collusion associated with moving from D
to D′. Hence, in order to reduce the appeal of collusion, the government wants
qNCH > q
SB
H , so that E
′ < E andD′ > D.
The Need for Information 275
THE IMPACT OF CAPTURE
There is an important point to note here. As we’ve just seen, the government
can set policy so that the firm and regulator do not collude. Nonetheless, even
if the government does so, the possibility of regulatory capture has an effect
on policy and outcomes. In particular, when the government is uninformed,
it will distort policy in a way that leads to more production by firms claiming
to have high marginal costs, because the government knows that firms might
try to capture the regulator. As a result of these government efforts to head off
collusion, distortionary transfers to lowmarginal cost firms are larger than they
otherwise would be. Thus, even if firms and regulators do not regularly collude
with one another, the fact that they could in principle do so has a deleterious
effect on policy.
To see this in the model, let’s calculate the expected social welfare with and
without the possibility of collusion.
Suppose collusion is simply impossible. With probability μ the government
learns the true marginal cost and implements the first-best policy from our
original model, generating social welfare of �H if the firm has high marginal
costs and �L if the firm has low marginal costs. With probability 1 − μ the
government implements the second-best policy from our original model, gen-
erating social welfare of �H − C if the firm has high marginal costs and �L +
(1 − τ)D if the firm has low marginal costs. Hence, expected social welfare if
collusion were impossible is
�H + �L + (1 − μ) (−λC + (1 − λ)(1 − τ)D) .
Now suppose collusion is possible. Again, if the regulator is informed, it will
reveal the truth and the original first-best policy will be implemented. If the
regulator is not informed, the government implements a policy that, if the firm
has high marginal costs, generates a social welfare of �H − C′ and if the firm
has low marginal costs generates a social welfare of �L + (1 − τ)D′. Hence, the
expected social welfare, given the possibility of collusion, is
�H + �L + (1 − μ)
(−(1 − λ)C′ + λ(1 − τ)D′) .
Comparing these, the possibility of collusionmakes social welfare worse if
−λC′ + (1 − λ)(1 − τ)D′ < −(1 − λ)C + λ(1 − τ)D.
This inequality holds. (To see this, recall that qSBH was chosen tomaximize−(1 −
λ)C + λ(1 − τ)D). Thus, even when we don’t see direct evidence of collusive
behavior, the possibility of collusion and regulatory capture may be affecting
the way policy is set and harming social welfare.
276 Chapter 9
9.4 Takeaways
• Identifying optimal policies often requires information that the policy-
maker doesn’t have.
• When relevant information resides with interested parties, the policy-
maker must design incentives for those parties to reveal the informa-
tion. The challenge is that revealing its information may sometimes
lead to disadvantageous policy responses for a given party, giving that
party an incentive to lie or fail to reveal information.
• Lack of information places an additional second-best constraint onhow
much good can be done through policy. As in our earlier examples of
the second best, the government’s limited access to information implies
that policy cannot always get us all the way to Pareto efficiency.
• The possibility of collusion between regulated firms and expert regu-
lators (through bribery, the revolving door, etc.) creates the threat of
regulatory capture. Even if policy is set so that no collusion actually oc-
curs, the threat of collusion due to informational asymmetries distorts
policy.
9.5 Further Reading
Roger Myerson’s “Perspectives onMechanismDesign in Economic Theory: No-
bel Prize Lecture” is deep in content and context about the role of mechanism
design in the theory of incentives.2 Paul Milgrom’s Putting Auction Theory to
Work provides both an interesting informal discussion of the ways in which
auction theory has been used in policy applications and a serious technical
treatment of the important models.
Both the second price auction and the (not budget balanced) mechanism
that induces truth telling in the public goods games are special cases of the
Vickrey-Clarke-Groves mechanism (Vickrey, 1961; Clarke, 1971; Groves, 1973).
Stigler (1972) and Peltzman (1976) are the original treatments of regulatory
capture. The model of regulating a monopolist is inspired by Dal Bó’s (2006)
overview and formal treatment of the relationship between asymmetric infor-
mation and capture. It builds on the classic analyses of Baron and Myerson
(1982) and Laffont and Tirole (1993).
Perhaps the most exciting work going on today on the interplay of policy
and informational problems is in market design. This work addresses problems
such as how to incentivize organ donation and allocate donated organs, how
to match children with schools or doctors with residencies, and a host of other
important topics. Al Roth’sWhoGetsWhat—andWhy is a popular introduction.
You should also read his market design blog.
2http://www.nobelprize.org/nobel prizes/economics/laureates/2007/myerson lecture.pdf
http://www.nobelprize.org/nobelprizes/economics/laureates/2007/myersonlecture.pdf
The Need for Information 277
9.6 Exercises
1. Consider an auction with two bidders. Bidder 1 values the object up for
auction at v1 and bidder 2 values it at v2. If a bidder iwins the auction and
has to pay price p, his payoff is vi − p. If a bidder loses the auction, his payoff
is 0.
The auction is run as an “English Auction.” That is, the auctioneer starts at a
price of 1 and asks who will pay it. After the price is met, the auctioneer
raises the price and asks who will pay that. The item is sold when no bidder
is willing to match the new price. It is sold to the bidder whomet the last
stated price and it is sold at that price.
Each bidder’s strategy can be thought of as a number representing the last
price to which she will say “yes.” Call this the player’s “price limit” and label
player i’s price limit as bi (that is, player i’s strategy says she’ll pay any price
up to and including bi but not more).
(a) Argue that there is at least one b2 such that player 1 choosing b1 > v1 is
not a best response.
(b) Argue that there is at least one b2 such that player 1 choosing b1 < v1 is
not a best response.
(c) Argue that player 1 choosing b1 = v1 is a best response to every b2.
(d) Player 2’s problem is clearly symmetric. So for each player choosing a
price limit equal to her true valuation is a weakly dominant strategy. If
players follow this strategy, which player wins the auction?What price
does the winner pay?
(e) How do your answers to part (d) relate to the outcomes of the “second
price auction” we studied in this text?Would the same or a different
player win?Would that player pay the same or a different price?
2. Suppose there is a population of 20 people. Half of them are healthy and half
of them are sick. Each individual knows whether she is healthy or sick.
If a healthy person receives health care, her payoff is 10. If she does not
receive health care, her payoff is 7. The price of providing health care to a
healthy person is 3.
If a sick person receives health care, her payoff is also 10. If she does not
receive health care, her payoff is 0. The price of providing health care to a
sick person is 5.
Let’s assume that health care can only be procured with health insurance.
An individual cannot buy her own health care other than by buying
insurance.
278 Chapter 9
Suppose a not-for-profit insurance company is selling health care coverage.
The first goal of the insurance company is to cover as many people as
possible. Conditional on this, its goal is to charge as little as possible to sick
people for their insurance. However, nomatter what, it is not allowed to lose
money.
(a) Suppose the insurance company knows if people are healthy or sick.
What price will it charge sick people?What price will it charge healthy
people?
(b) Now suppose the insurance company can’t observe whether people are
healthy or sick.
i. Why won’t it work for the insurance company to simply ask people
whether they are sick or healthy and then charge them accordingly?
ii. Suppose, then, that the insurance company charges everyone the
same price. What price must it charge to break even, if everyone buys
insurance?
iii. At that price, who will buy insurance?Will the insurance company
make or lose money?
iv. Given this, what price will the insurance company in fact charge?
Who will buy insurance?
(c) The phenomenon described in your previous answers is called the
problem of adverse selection—because the pool of insurance buyers ends
up being the sick, the price has to be so high that it erodes the insurance
value. It was a major concern in the debates surrounding the Affordable
Care Act because there was worry that young, healthy people would
refuse to buy health insurance, despite the act’s requirement that they
do so. The solution in the Affordable Care Act is to fine people who don’t
buy health insurance.
i. Suppose the insurance company charges a price p ∈ (3, 5). What is the
smallest possible fine, f ∗(p), the government can impose for not
buying insurance, such that everyone buys insurance?
ii. What is the lowest price, p, and associated fine, f ∗(p), such that
everyone buys insurance and the insurance company at least breaks
even?
3. Consider a public goods game with two players in which each player i
chooses effort ei and the total public goods produced are e1 + e2. Player 1
bears costs e21. Player 2 bears costs c × e22. The parameter c is equal to either 1
or 2. Player 2 knows the true value of c, but the government is uncertain as
to the true value of c.
The Need for Information 279
Given knowledge of the true c, the first-best efforts are eFB1 = 1 and eFB2 = 1c .
We are going to assume that the government can simply force people to
choose whatever effort it wants them to take.
(a) Suppose the government asks Player 2 to report c and then implements
the first best, naively assuming that Player 2 told the truth.
i. Will a Player 2 with c = 1 tell the truth (i.e., report c = 1) or lie (i.e.,
report c = 2)?
ii. Will a Player 2 with c = 2 tell the truth (i.e., report c = 2) or lie (i.e.,
report c = 1)?
(b) Suppose the government can now offer transfers from Player 1 to Player 2
conditional on Player 2’s report of her c. Further assume that such
transfers are inefficient—a transfer of t to Player 2 costs Player 1 an
amount τ t, with τ > 1. Finally, suppose the probability that c = 1 is 12 .
i. If the government wants to elicit truth telling as cheaply as possible,
will it offer transfers to Player 2 following a report of c = 1, c = 2, or
both?
ii. What is the smallest such transfer it can offer that elicits truth telling?
(c) Continue to suppose the probability that c = 1 is 12 . What is the expected
utilitarian payoff (as a function of τ ) if the government pursues the
smallest transfer policy that elicits truth telling. (Hint: Calculate the
utilitarian payoff if it turns out that Player 2 has c = 1. Calculate the
utilitarian payoff if it turns out that Player 2 has c = 2. Thenmultiply
each of these by 12 and sum to find the expected utilitarian payoff.)
(d) Continue to suppose the probability that c = 1 is 12 . Without any
information, the best policy the government can pursue is e1 = 1 and
e2 = 23 . Such a policy yields an expected utilitarian payoff of
2
(
1 + 2
3
)
− 12 −
(
1
2
× 1 + 1
2
× 2
) (
2
3
)2
= 5
3
.
For what values of τ is the expected utilitarian outcome better if the
government offers the best transfer scheme that elicits truthful
revelation of c instead of implementing this best uninformed policy?
(e) What do your answers to these questions tell us about the effect of lack of
information on the government’s ability to achieve good policy
outcomes?
4. A local government is trying to decide whether to build a school that will
jointly serve two neighborhoods. The school will cost onemillion dollars to
build. Neighborhood 1 values the school at value v1 dollars and
280 Chapter 9
neighborhood 2 values the school at v2 dollars. The government does not
know these valuations, though it knows that each is somewhere between 0
and onemillion. Assume all players have quasi-linear preferences.
(a) For which pairs of valuations is the utilitarian optimum to build the
school and for which pairs of valuations is the utilitarian optimum not
to build the school?
(b) Suppose the government proposes the followingmechanism. Each
neighborhood will say an amount it values the school. The
neighborhoods can say any number they like between 0 and onemillion,
they need not tell the truth. Call the statement from neighborhood one
s1 and the statement from neighborhood two s2. If the sum of the two
statements is greater than or equal to onemillion, the school will be
built, with neighborhood 1 paying $600,000 and neighborhood 2
paying $400,000. If the two statements sum to less than onemillion, the
school will not be built.
i. Assume players play weakly dominant strategies. For which pairs (if
any) of true valuations, v1 and v2, will the school be built?
ii. Are there any pairs of true valuations, v1 and v2, where the policy that
will be followed as a result of such behavior by the neighborhoods
(build or don’t build) is inefficient (i.e., not the utilitarian optimum)?
(c) Suppose the government proposes the followingmechanism. Each
neighborhood will say an amount it values the school. The
neighborhoods can say any number they like between 0 and onemillion,
they need not tell the truth. If the sum of the two statements is less than
onemillion, then the school is not built. If the sum of the two
statements is greater than or equal to onemillion, the school will be
built, but in this mechanism, the price charged to each neighborhood
can be a function of the stated valuations of the two neighborhoods.
i. Identify a formula for the price (a function of the stated valuations of
the two neighborhoods) the government can charge neighborhood 1
when the school gets built, such that, for any v1, it is a best response for
neighborhood 1 to state its true valuation regardless of what
neighborhood 1 expects neighborhood 2 to say. Give a brief, informal
explanation of why this works.
ii. What, if anything, is wrong with amechanism that uses this formula
to determine the price?
(d) Briefly explain how your answers to (b) and (c) point to a fundamental
tension between lack of information and efficient policy.
The Need for Information 281
5. Return to the game in Figure 6.6. Imagine that the government wants to
achieve the utilitarian optimum and can force U to choose a level of
investment, e, but can’t forceD to change the price it offers. Further,
suppose the government doesn’t know c, only U knows it.
(a) Suppose the government simply asks U what c is. U can choose, as an
answer, any positive number. The government then naively assumes that
this answer is the true c and imposes the utilitarian optimal level of
investment given that c. Informally (i.e., nomath necessary), will the c
that U tells the government be larger than, smaller than, or equal to the
true c?Why? Briefly explain how your answer points to a tension
between lack of information and efficient policy choice.
(b) What cwill U report to the government?
10
Influence over Elected Officials
Elections are the first line of defense against excessive rent seeking in democra-
cies. They serve this function in at least two ways. First, elections allow voters
to select politicians motivated and able to pursue the voters’ interests. Second,
they create incentives for politicians to do so. Madison put it eloquently in
Federalist No. 57:
The aim of every political constitution is, or ought to be, first to obtain
for rulers men who possess most wisdom to discern, and most virtue to
pursue, the common good of the society; and in the next place, to take the
most effectual precautions for keeping themvirtuouswhilst they continue
to hold their public trust.
Madison, of course, believed that achieving these goals requires more than just
elections. He advocated for a whole suite of institutional checks and balances,
most notably the separation of powers, to keep politicians “virtuous whilst they
continue to hold their public trust.” But there can be no question that electoral
accountability plays a central role. As Madison wrote in Federalist No. 51:
In framing a government which is to be administered by men over men,
the great difficulty lies in this: you must first enable the government to
control the governed; and in the next place oblige it to control itself.
A dependence on the people is, no doubt, the primary control on the
government.
This is a lofty vision, especially in light of our often cynical view of electoral
politics. Leaving aside issues of fraud and violence that plague elections in
much of the world, even in the best of circumstances, elections can struggle
to establish “dependence on the people.” Electoral concerns seem, at times, to
drive politicians to pander to particularistic interests. Moreover, the realities of
campaigning can give undo influence to organized ormoneyed interests. Yet, at
the same time, democratic elections do establish a relationship of accountabil-
ity between the government and the governed. The question is, to what extent
does that accountability relationship result in improved governance outcomes?
In this chapter, we explore these issues through several models of electoral
politics.
Influence over Elected Officials 283
10.1 Particularistic Interests
We’ve discussed a variety of examples of inefficiency resulting from policies
targeted to benefit some particular group of citizens at the expense of society
at large. The home mortgage deduction benefits homeowners at the expense
of economic efficiency. Professional licensing benefits incumbent members
of a profession at the expense of new entrants and consumers. Political pork
benefits the members of a particular legislative district at the expense of the
rest of the taxpaying public. Low gasoline taxes benefit both transportation and
agricultural interests at the expense of the environment. And so on. InChapters
4.2.3 and 8.3 we saw various reasons that distributive politics might end up
favoring certain groups over others. Here, we explore another possibility, rooted
in electoral politics.
Politicians are motivated to win elections. If a politician’s electoral prospects
are more responsive to the welfare of one group of citizens, that politician
has incentives to bestow benefits on that group at the expense of other, less
responsive groups.
This kind of logic is not new, nor is it only for the cynical. In 1840, future
President Lincoln coauthored a confidential memo giving the Whig Party’s
local electoral committees instructions for targeting responsive voters:1
After due deliberation, the following is the plan of organization, and the
duties required of each county committee.
1st. To divide their county into small districts, and to appoint in each a
sub-committee, whose duty it shall be tomake a perfect list of all the voters
in their respective districts, and to ascertain with certainty for whom they
will vote. If they meet with men who are doubtful as to the man they will
support, such voters should be designated in separate lines, with the name
of the man they will probably support.
2nd. It will be the duty of said sub-committee to keep a CONSTANT
WATCH on the DOUBTFUL VOTERS, and from time to time have them
TALKED TO by those IN WHOM THEY HAVE THE MOST CONFIDENCE,
and also to place in their hands such documents as will enlighten and
influence them.
Theremight be a variety of reasons that a particular group is more electorally
responsive than another. Let’s consider a few.
Many voters are concerned primarily with ideological issues that correspond
to the platform of one party (or, in other settings, one ethnic group, religion,
etc.). It would be essentially impossible for the other party to win the support of
suchvoters.Hence, strongly partisan voters are typically thought to be relatively
unresponsive to distributive issues. By contrast, other voters have little concern
1See Collected Works of Abraham Lincoln. Volume 1. University of Michigan Digital Library
Production Services. http://quod.lib.umich.edu/l/lincoln/lincoln1/1:214?rgn=div1;view=fulltext
http://quod.lib.umich.edu/l/lincoln/lincoln1/1:214?rgn=div1;view=fulltext
284 Chapter 10
about broad ideological matters, but instead are focused on a single issue. For
instance, in local elections, teachers may care primarily about school budgets
and policy. Hence, a candidate for mayor might be able to win the support of a
teachers’ union by choosing an education policy of which the union approves,
independent of any other policy position. Such single-issue voters are highly
responsive.
Institutional factors can also affect responsiveness. For instance, in the
United States, many functions of local government are carried out by so-called
special purpose governmental units. Berry (2009, pp. 26–27) explains:
Most special districts perform a single function. . . . Almost any service
provided by a municipality can be provided by a special district govern-
ment. The special district familiar tomost Americans is the school district.
Although school districts are themost numerous, they represent less than
one-third of all special districts. Among the 35,000 nonschool special
districts in existence as of 2002, some of the most common functions
included providing fire protection, water, sanitation, parks, and libraries.
These special purpose governments are important. For instance, the com-
bined revenues of all special district governments in the United States are
roughly the same as the combined revenues of all city governments and are
significantly larger than the combined revenues of all county governments.
Most special purpose government officials are elected. And, interestingly, many
special purpose governments do not hold their elections on election day in
November. As a consequence, the voters who turn out for such elections
are primarily those with a direct stake in whatever domain the special pur-
pose government controls. If only these voters turn out, only they can be
responsive.
Legislative districting creates yet another institutional source of non-
responsiveness. From the perspective of the electoral fortunes of, say, amember
of the United States House of Representatives, the voters in his or her district
are responsive to pork-barrel projects brought to the district. But voters from
other districts are not responsive. This means that each member of Congress
has incentives to target only the voters in his or her district.
Finally, as we discussed in Chapter 4.2.3, concentrated interests are better
able to organize themselves to take action than are diffuse interests. Thus, we
might expect that concentrated interests are more responsive to issues about
which they care than are diffuse interests.
Now that we’ve seen that voter responsiveness might vary for a host of
reasons, let’s consider how it affects policy in a simple model inspired by Dixit
and Londregan (1996).
Two candidates, a and b, seek office. There are three groups of voters—
the a-partisans (group A), the b-partisans (group B), and the independents
(group I). The independents make up a share α of the electorate, while the
Influence over Elected Officials 285
a- and b-partisans each make up a share 1−α2 . No group is a majority on its own
(i.e., α < 1/2). A candidate wins if she gets a majority of votes.
At the beginning of the election, each candidate proposes a platform, x,
which represents the policies she will pursue if elected. Each candidate can
propose one of three possible platforms:
1. Under the efficient platform, xE, each group has a payoff equal to 1.
2. Under a partisan-biased platform (call this xA for candidate a and xB for
candidate b), the relevant partisans get a benefit of π , while all other
voters get 0.
3. Under the independent-biased platform, xI , the independents get a
benefit of π , while all other voters get 0.
Assume that 1 < π < max
{
1
α
, 21−α
}
, so that a biased platform is not a utilitarian
optimum, but is preferred to the efficient platform by the privileged group.
After observing the platforms, the voters decide for which candidate to vote.
The independent voters’ payoffs come only from the platform payoffs just
described. But the partisan voters also care about the identity of the politician
in office—if a group’s preferred candidate is elected, the members of that group
get an extra benefit η > 0. If voters are indifferent, they flip a coin.
Suppose candidates care only about winning election. What do equilibrium
policies look like?
The probability of winning, given platforms, depends on how biased the
supporters are in favor of their preferred candidate (i.e., the size of η). Hence,
there are two cases, represented separately in the following two tables (best
responses are in bold):
xE xI xB
b’s platform
η > 1 η < 1
xE
xI
xA
a’s platform
1–
2
, 1–
2
1–
2
, 1–
2
1–
2
, 1–
2
0, 1 1, 0
0, 1 0, 1
1, 01, 0
xE xI xB
b’s platform
xE
xI
xA
a’s platform 1–
2
, 1–
2
1–
2
, 1–
2
1–
2
, 1–
2
1, 01, 0
0, 1
0, 1
0, 1
1, 0
If partisans are highly attached to their preferred candidates (η > 1), in
equilibrium both candidates propose a platform targeted at the independent
voters. If partisans are more weakly attached to their preferred candidates
(η < 1), in equilibrium policy is efficient. The logic is straightforward.
When attachments are weak, if (say) candidate a attempts to lure the inde-
pendent voters by proposing xI , candidate b can win the election by proposing
286 Chapter 10
the efficient policy and gaining the support of both groups A and B. Hence,
in equilibrium, both candidates propose the efficient policy, preserving their
electoral bases and competing for the independent voters.
By contrast, when attachments are strong, each candidate knows that no
matter what, she will hold onto the support of her partisans and cannot gain
the support of the other candidate’s partisans. Only the independent voters are
responsive. So each candidate has an incentive to target policy to benefit the
independent voters.
The model, while simple, highlights an important point. Politicians, moti-
vated by the desire to hold office, will pursue policies that benefit those citizens
whose votes are responsive to policy choice. If a politician is certain that some
group of voters will always support her or will never support her, she has little
incentive to provide policy benefits to that group. Hence, in policy domains
characterized by groups of highly responsive and unresponsive voters, policy
will be biased away from efficiency and towards the interests of the responsive
voters.
This simple insight provides leverage onmany of our examples of inefficient
policy choice. If homeowners are particularly responsive to the home mort-
gage deduction, sugar producers are particularly responsive to sugar subsidies,
public sector workers are particularly responsive to public sector wages, and
taxi drivers are particularly responsive to limits on ride sharing, then electoral
considerations will drive politicians to target policies in those areas towards
those particularistic interests.
Themodel is also consistent with empirical evidence. For instance, Berry and
Gersen (2010, 2011) study a change to theCalifornia Electoral Code in the 1980s
allowing school boards to shift from off-cycle (i.e., not in November) to on-
cycle elections. As we’ve already discussed, off-cycle elections tend to attract
only single-issue voters. If voters don’t come to the polls, they certainly are
not responsive to policy. Thus, the model would lead us to expect that, when
a district moves to on-cycle elections, policy might become less targeted to
single-issue education voters (e.g., teachers) because other voters become more
responsive. And, indeed, this is what happened in California. When a school
district moves from off-cycle to on-cycle elections, turnout roughly doubles
on average. Moreover, policy becomes less favorable to teachers—for instance,
teachers’ salaries decreased by about $1,000 on average in on-cycle districts.
10.2 Special Interests and Campaign Donations
Of course, groups motivated to influence policy have tools at their disposal
beyond the vote. Perhaps most importantly, they can use money to influence
elected officials’ policy choices.
Influence over Elected Officials 287
Themost disturbing possibility is that theremight be a quid pro quo between
politicians and organized interests—campaign donations in exchange for a
politician taking policy actions that he or she otherwise would not have taken.
But things need not be as nefarious as all that for money to matter for policy.
Consider two other possibilities.
First, money might not buy policy concessions, but it might buy access—a
politician may not be willing to change her behavior for a donor, but might
be more open to giving a donor an opportunity to make a case. If there
are circumstances in which new information or argument could persuade a
politician to change his or her position, having such access could push policy
outcomes in a donor’s favor even without any quid pro quo.
Second, money might be useful for winning elections. For instance, imagine
that politicians are precommitted (perhaps by their personal ideology or party
affiliation) to a policy platform, so money can’t possibly change their behav-
ior. Money might still matter for policy outcomes if voters are responsive to
campaigning (e.g., advertisements, speeches), so that having access to resources
helps politicians win election. Organized interests might then donate to a
politician whose ideology matches their own preferences in order to help her
gain office. Nothing untoward is going on—campaign donations don’t lead the
politician to pursue any policy she wouldn’t otherwise have pursued. Nonethe-
less, by helping candidates that are already sympathetic to its interests win
election, an interest group does in fact use campaign contributions to secure
policies fromwhich it benefits.
If you believe either of these latter two stories, youmight be inclined to think
that the influence of money on politics is relatively unproblematic. In the first
story, the politician is only changing her mind when convincing information
or argument is presented. And, in the second story, campaign donations might
be viewed as an expression of citizens’ intensity of preference.
But let’s remember the model of interest group organization from
Chapter 4.2.3. There we saw that concentrated interests will have an easier
time organizing to influence policy than will diffuse interests. Hence, even
if campaign contributions only work through legitimate channels, they will
nonetheless distort policy outcomes in favor of concentrated interests at the
expense of diffuse interests. Ifmoney buys access, in those circumstances where
information or argument could shift policy, organized interests will have the
opportunity to make their case, while diffuse interests will not. Similarly, if
money helps win campaigns, candidates who favor policies that benefit orga-
nized interests will have access to greater campaign resources and, thus, will win
elections more often than candidates who favor diffuse interests. Indeed, as a
result, we may simply not observe many candidates who advocate for policies
that benefit diffuse interests.
288 Chapter 10
There is considerable debate about the extent to which campaign money
influences policy outcomes.On the onehand, by somemeasures, there is an aw-
ful lot of money in politics. For instance, Bombardini and Trebbi (2011) report
that during the elections for the 106th Congress, the top 50 donor industries
gave total campaign donations of almost $370 million. By the election of the
109thCongress, the amount had risen to almost $445million. Ifmoney doesn’t
matter for policy, why are industries making these donations?
But, staggering as these numbers may seem, there is an argument that they
are actually quite small. This argument derives from the so-called Tullock
Paradox. Tullock (1972) points out a puzzle that emerges if we view campaign
donations as an investment in policy outcomes. Ansolabehere, de Figueiredo,
and Snyder (2003, p. 110) summarize Tullock’s argument:
In 1972, when Tullock raised this question, campaign spending was about
$200 million. Assuming a reasonable rate of return, such an investment
could have yielded at most $250–300 million over time, a sum dwarfed
by the hundreds of billions of dollars worth of public expenditures and
regulatory costs supposedly at stake.
And, they argue, the puzzle has only grown since the 1970s. I can do no better
than to quote Ansolabehere, de Figueiredo, and Snyder (2003, pp. 110–111):
[A]ll defense contracting firms and individuals associated with those firms
gave approximately $10.6 million to candidates and parties in 1998 and
$13.2 million in 2000. The U.S. government spent approximately $134
billion on defense procurement contracts in fiscal year 2000 (U.S. Census
Bureau, 2000). Firms, individuals and industry associations of the oil and
gas industry gave $21.6 million to candidates and party organizations
in 1998 and $33.6 million in 2000. The Energy Information Adminis-
tration (1999) of the U.S. Department of Energy values subsidies to the
energy industry in 1999 at $1.7 billion. In agriculture, crop producers and
processors contributed $3.3million to candidates and parties in 2000; U.S.
commodity loans and price supports equaled $22.1 billion that year (U.S.
Department of Agriculturewebsite). Dairy producers, who since 1996have
had to have subsidies renewed annually, gave $1.3 million in 2000 and
received price supports worth almost $1 billion in the Farm Security and
Rural Investment Act of 2002. In the case of sugar producers, Stratmann
(1991, p. 615) estimates that a “$3,000 sugar PAC contribution maps into
a yes vote with almost certainty.” Without sugar industry contributions,
he further estimates, the final vote on the sugar amendment to the 1985
agriculture bill would have been 203–210, effectively ending the sugar
subsidy. With contributions, the subsidy survived: the final vote was
267–146. A U.S. General Accounting Office (1993) study values that the
Influence over Elected Officials 289
annual transfer from consumers to sugar producers and processors at
$1.1 billion a year from 1989 to 1991. In other words, $192,000 worth of
contributions in 1985 bought more than $5 billion worth of value for the
sugar industry over a five-year period.
The discrepancy between the value of policy and the amounts con-
tributed strains basic economic intuitions. Given the value of policy at
stake, firms and other interest groups should give more. The figures above
imply astronomically high rates of return on investments.
Ansolabehere, de Figueiredo, and Snyder make sense of these findings by
noting that campaign donations have a relatively small effect on electoral
outcomes. As a result, they suggest, no matter which of the stories above you
believe, donations will have relatively little impact on policy outcomes. If there
is a quid pro quo (for policy concessions or access), donors have relatively
little leverage over politicians because donations are not particularly valuable
to politicians. And if money is simply a way of helping sympathetic candidates,
it is relatively ineffective. In any case, the policy returns a donor can hope to
garner are small. Indeed, on Ansolabehere, de Figueiredo, and Snyder’s view,
campaign donations are better understood as pure entertainment consumption
by donors, rather than anything to do with shifting policy outcomes.
Bombardini and Trebbi (2011) take a different view of the evidence and its re-
lationship to the Tullock Paradox. They point out that organized interests have
at least two ways to influence politicians: money and votes. Whatever role you
believe money plays in politics, the ability to directly deliver votes could serve
as a substitute for campaign donations. They argue that perhaps the amount
of campaign donations is small relative to the size of government, not because
there isn’t competition among interest groups to shape policy outcomes, but
because that competition involves both money and votes. If this is correct,
by ignoring the value of votes, Ansolabehere, de Figueiredo, and Snyder are
overestimating the implicit rate of return from campaign contributions.
To illustrate this argument, Bombardini and Trebbi (2011, p. 588, footnote 2)
offer the following quotation from Arizona Senator Dennis DeConcini:
If I get a contribution from, say, Allied-Signal, a big defense contractor, and
they’ve raisedmoney forme. And then they come in and say, “Senator, we
need legislation thatwould extend some rule of contracting that’s good for
us.” They lay out the case. My staff goes over it. I’m trying to help them.
Why am I trying to help them? The cynic can say: “Well, it’s because they
gave you 5,000 bucks. And if you ran again, they’ll give you another 5,000
bucks.” Or is it because they have 15,000 jobs in Arizona and this will help
keep those jobs in Arizona? Now tome, the far greater motivation is those
jobs, because those are the people that are going to vote for me. But I can’t
ignore the fact that they have givenmemoney.
290 Chapter 10
Bombardini and Trebbi go on to provide a variety of evidence to support
the claim that both votes and money matter. Perhaps most compellingly, they
show two facts. First, within a Congressional district, the largest donors tend
to be medium-sized industries. Second, a given industry tends to give its largest
donations in those districts where it is ofmedium size. They argue that the logic
underlying both facts is the same. Industries don’t give donations in districts
where they are very small employers. In such districts, it would be too expensive
to try to wield influence. Industries also don’t give donations in districts where
they are huge employers. In those districts, they can provide so many votes
that they don’t need to give large donations—for example, the auto industry
may not need to make large donations to have influence in Michigan politics.
Significant campaign donations make sense for industries that can provide
some votes, but need to top those votes off with donations to have an impact
on policy outcomes.
Using this approach, Bombardini and Trebbi estimate a rate of return for
campaign donations, correcting for the ability to deliver votes. Doing so yields a
much more reasonable estimate than the numbers presented by Ansolabehere,
de Figueiredo, and Snyder might suggest. In particular, they report that the
average rate of return to campaign donations is about thirteen cents on the
dollar. With this more plausible number, it again becomes reasonable to think
that interest groups may indeed be competing with one another for influence
over policy outcomes, using both votes and money as tools to achieve their
goals.
10.3 Electoral Accountability
The previous two sections discussed how electoral politicsmay create incentives
for inefficient policy targeting or distortionary uses of money in politics. Prob-
lematic as such incentivesmay be, voters’ ability to hold politicians accountable
through elections also plays an indispensable role in creating the conditions for
good governance.
If retaining office depends on achieving good outcomes for voters, then
policymakers seeking reelection may be willing to take actions that they find
personally costly but which benefit voters. Elections can, thus, create incen-
tives for politicians to identify good policies, forgo corruption, choose policies
preferred by voters even when they are not preferred by the politicians, and
so on. In these ways, elections fulfill part of Madison’s vision, by fostering a
“dependence on the people” and, thereby “keeping [politicians] virtuous.”
Elections also give voters an opportunity to identify and retain politi-
cians with characteristics—for example, managerial skills, policy positions,
honesty—that the voters value. Such electoral selection affects governance out-
comes by allowing voters to screen for high quality or good leaders. In this
Influence over Elected Officials 291
way, elections fulfill Madison’s goal “to obtain for rulers men who possess most
wisdom todiscern, andmost virtue to pursue, the commongoodof the society.”
In light of this, in this section we explore a basic model of electoral account-
ability and related empirical evidence. We do so with an eye toward answering
several questions:
1. What are the mechanisms by which elections improve voter welfare?
2. What features of an electoral environment seem to increase incentives
for politicians to act on behalf of voters?
3. Are stronger electoral incentives always beneficial to voters?
In our model of electoral accountability, there are three players: an incum-
bent, a challenger, and a voter. Each politician may be high quality or low
quality. You can think of quality as reflecting the politician’smanagement skills,
knowledge of good public policy, or the ability of the politician’s advisors and
subordinates. Each politician is of high quality with probability p ∈ (0, 1) and
is of low quality with probability 1 − p. A politician’s quality is her private
information.
In the first period, the incumbent chooses a level of effort to devote to policy,
e1 ∈ [0, 1]. The effort cannot be observed by the voter. Then a policy outcome is
determined.
The policy outcome can be good or bad. The difference between high and
low quality incumbents is that high quality incumbents always achieve a good
outcome, while low quality incumbents only achieve a good outcome with
probability e1. You can think of this assumption in a couple of ways. High
quality incumbents might always know what good policy is, while low quality
politicians have to invest considerable effort and resources to try to identify
good policies. Or high quality politicians might have good control over their
staffs, so that their policy ideas are implemented faithfully, while low quality
politiciansmight need to work hard to have any hope that their policy ideas are
correctly implemented.
After the first-period policy outcome is determined, the voter forms beliefs
about how likely the incumbent is to be high quality. Then the voter chooses to
reelect the incumbent or replace the incumbentwith the challenger (whom the
voter believes is of high quality with probability p).
In the second period, the winner of the election chooses a new level of effort,
e2 ∈ [0, 1], and anewpolicy outcome is determined.Once again, if the politician
in office in the second period is of high quality, then the policy outcome is good
for certain. If the politician in office in the second period is of low quality, then
the policy outcome is good with probability e2. The game ends after the second
period.
Payoffs are as follows. A politician gains a benefit B, with 0 < B < 1, for each
period she is in office. In a period in which she is in office and chooses effort
292 Chapter 10
e, she suffers a cost e2. The voter cares only about policy outcomes, gaining a
benefit of 1 in any period in which the policy succeeds and a benefit of 0 in any
period in which the policy fails.
Let’s solve this game from the end. In the second period, regardless of which
politician is in office, she has no incentive to exert any effort, since there is not a
future election. Thus, any equilibrium involves zero effort in the second period.
Now consider the voter’s reelection decision. Given that the winner of the
election will choose effort e2 = 0, the probability of a good outcome in the
second period is simply the probability that the winner is high quality. Thus,
the only thing the voter cares about in the election is whether the first-period
incumbent is more or less likely than the challenger to be high quality. If the
first-period incumbent ismore likely than the challenger to be high quality, the
voter reelects the incumbent. Otherwise, the voter replaces the incumbentwith
the challenger.
Given the voter’s reelection rule, the critical question is how the voter forms
his beliefs about how likely the incumbent is to be high quality. Without going
into the technical details, there is a simple intuition. If the incumbent is of
high quality, then the outcome will be good for certain. If the incumbent is
of low quality (and chooses effort e1 < 1), then there is some chance of a bad
outcome. Thus, if the voter observes a bad first-period outcome, he is certain
the first-period incumbent is of low quality. If the voter observes a good first-
period outcome, he is not sure whether the first-period incumbent is of low or
high quality, but his assessment of the probability that the incumbent is of high
quality goes up.2 Thus, the voter will reelect the incumbent if the outcome is
good and replace the incumbent with the challenger if the outcome is bad.
In light of this, how will the incumbent behave in the first period? Recall, a
high quality incumbent succeeds for sure, so has no reason (or need) to exert
effort. But if the incumbent is low quality, then hard work could help her
achieve a goodpolicy outcome and reelection. This is how the accountability re-
2Formally, we apply Bayes’ rule: The probability of some eventX given another event Y (written
Pr(X|Y)) is
Pr(X|Y) = Pr(Y|X)Pr(X)
Pr(Y|X)Pr(X) + Pr(Y|notX)Pr(notX) .
So, if the voter believes a low quality incumbent will choose effort e1, then the voter believes that
the probability that the incumbent is high quality, given a good outcome, is
Pr(High Ability|Good Outcome) =
Pr(Good Outcome|High Ability)Pr(High Ability)
Pr(Good Outcome|High Ability)Pr(High Ability) + Pr(Good Outcome|Low Ability)Pr(Low Ability)
= 1 × p
1 × p + e1 × (1 − p)
.
It is straightforward that this is greater than p, so following a good outcome, the voter prefers to
reelect the incumbent.
Influence over Elected Officials 293
lationship creates incentives for a politician to take costly effort that benefits the
voter. Of course, the incumbent balances the benefits of increasing her chances
of reelection against the costs of effort. She solves the following problem:
max
e1
e1B − (e1)2.
Solving, the first-period effort by a low quality incumbent is
e∗1 =
B
2
.
The overall probability of a good outcome in the first period is
Pr(Good Outcome) = p + (1 − p)B
2
.
10.3.1 Rewards of Office
One fact is immediate from this model. All else equal, the greater are the
rewards to holding office (i.e., the higher is B), the more costly effort the voter
is able to extract from the (low quality) incumbent and the better the expected
policy outcome. This claim is consistent with some existing evidence. In Italy,
mayors of larger towns (more than 5,000 residents) are paid significantly more
than mayors of smaller towns. This kind of institutional variation in salaries
provides a nice way to make an all-else-equal comparison of mayors with
different benefits of holding office. Small towns and large cities are different in
lots of ways, so one cannot simply compare the performance of their mayors
and assume any difference is due to the fact that mayors of large cities are
paid more. But, on average, towns just below and just above the 5,000 resident
threshold are likely to be quite similar. So if we compare the performance of
mayors in these two kinds of towns, we are coming close to isolating just the
effect of salary differences. Gagliarducci and Nannicini (2011) do precisely this
and find that, indeed, better paid mayors perform better. They decrease per-
capita taxes and tariffs, while leaving the level of government expenditures
unchanged.
10.3.2 Term Limits
A closely related implication of the model is that the behavior of politicians
depends on whether or not they can stand for reelection. In the first period,
reelection is possible and, so, electoral accountability creates incentives for
effort by incumbent politicians. In the second period, the politician in office
cannot stand for reelection and shirks nomatter her quality.
de Janvry, Finan, and Sadoulet (2011) study this issue in the context of Brazil.
In the early 2000s the Brazilian national government created a program to
294 Chapter 10
help keep children in school. Under the program, poor parents were offered a
fairly large cash reward if their children did not drop out. Overall, the program
was a success—decreasing drop out rates among those who had access to
the program by about 8%. However, de Janvry, Finan, and Sadoulet find that
differentmunicipalities had very different results. The program performed 36%
better in municipalities where the mayor was up for reelection compared to
municipalities where the mayor could not seek reelection due to term limits,
suggesting that reelection incentives played an important role incentivizing
good implementation of the policy.
Finan and Ferraz (2011) also use Brazilian data to study the effects of term
limits on corruption. The Brazilian central government randomly audited a
collection of municipalities to assess the gap between grants to the municipal-
ity by the central government and actual spending by the municipality. The
difference between these two numbers reflects resources wasted (or stolen) by
the local government. Finan and Ferraz find that term-limitedmayors are about
2 percentage points more corrupt than non-term-limitedmayors.
10.3.3 Incentives and Screening
Elections, in this model, play two roles in improving government perfor-
mance. The first, which we’ve already discussed, is to create incentives for
politicians to exert costly effort for the benefit of the voters. These incentives
come from the fact that the incumbent knows she can only gain reelection by
achieving a good outcome. Elections also play a second role—they help voters
screen politicians, retaining incumbents they believe are of high quality and
replacing incumbents they believe are of low quality.
Alt, Bueno de Mesquita, and Rose (2011) separately estimate the magnitudes
of these two effects of elections on the quality of governance. They do so for
governors of American states, exploiting the fact that states vary in their term
limit laws. Some states have two-term term limits, some have one-term term
limits, some have no term limits, and individual states have changed their term
limit laws over time.
This variation in term limit laws sets up two comparisons, each of which
isolates one of the two effects. A first-term governor who is eligible to run again
and afirst-termgovernorwho is term-limitedhave eachwonelectiononly once,
and sohave each faced the same selectionpressures.However, the governorwho
is eligible to run againhas stronger incentives toworkhard to impress voters and
gain reelection. Comparing the performance of these two types of governors,
thus, provides an estimate of the incentive effect.
A first-term, term-limited governor and a second-term, term-limited gover-
nor both face the same weak incentives. However, they differ in terms of the
amount of electoral selection they have survived. Comparing the performance
Influence over Elected Officials 295
of these two types of governors, thus, provides an estimate of the electoral
selection effect.
Alt, Bueno de Mesquita, and Rose estimate these two effects using data from
the American states from 1950 to 2000. They use within-state variation (i.e.,
states that changed term-limit rules) to identify the different effects of incen-
tives and selection. Their results suggest that, all else equal, economic growth
is higher and taxes, spending, and borrowing costs are lower under reelection-
eligible incumbents than under term-limited incumbents (incentives), and un-
der second-term, term-limited incumbents than under first-term, term-limited
incumbents (electoral selection). Moreover, according to their estimates, these
two effects of elections on the quality of governance are of roughly equal
magnitude.
10.3.4 Voter Information
Voter access to information about incumbent performance might also affect
the power of electoral incentives and the quality of electoral selection. Voter
information flows from a variety of sources—the news media, rival candidates,
government transparency initiatives, and so on. Let’s start by looking at a
simple extension of our model that allows for variation in voter information.
We will then discuss some evidence.
Keep the same model as above, with one change. When the policy fails, the
voter definitely learns that it failed. However, when the policy succeeds, the
voter only learns that fact probabilistically. In particular, following a good out-
come, the voter observes what he perceives as a good outcome with probability
π ∈ (1/2, 1) and observes what he perceives as a bad outcome with probability
1 − π . An increase in π is equivalent to an increase in voter information.
In thismodel, the behavior of politicians in the secondperiod is just as above.
The voter’s behavior is also unchanged. It is still the case that the voter thinks
the incumbent is more likely to be high quality following a perceived good
outcome andmore likely to be low quality following a perceived bad outcome.3
3LetH denote high quality, L denote low quality,G denote a good outcome, and B denote a bad
outcome. If the voter believes a low quality incumbent will choose effort e1, then the voter believes
that the probability that the incumbent is high quality, given a good outcome, is
Pr(H|G) = Pr(G|H)Pr(H)
Pr(G|H)Pr(H) + Pr(G|L)Pr(L) =
πp
πp + e1π(1 − p)
.
It is straightforward that this is greater than p, so the voter wants to reelect the incumbent following
a good outcome.We also have
Pr(H|B) = Pr(B|H)Pr(H)
Pr(B|H)Pr(H) + Pr(B|L)Pr(L) =
(1 − π)p
(1 − π)p + (1 − e1 + e1(1 − π))(1 − p)
.
It is straightforward that this is less than p, so the voter wants to replace the incumbent following a
bad outcome.
296 Chapter 10
Given this, the incumbent believes that shewill be reelected if and only if the
voter perceives a good outcome. So if a low quality incumbent chooses effort e1,
she believes that she will be reelected with probability πe1.
As before, the low quality incumbent has incentives to exert effort to try to
keep her job. But now the benefits of effort are somewhat reduced, since she
is not certain that the voter will correctly perceive her successes. A low quality
incumbent solves the following problem:
max
e1
πe1B − (e1)2.
Maximizing, first-period effort by a lowquality incumbentwhen voter informa-
tion is imperfect (labeled eπ1 ) is
eπ1 =
πB
2
.
The better the voter’s information (the closer π is to 1), the stronger are
the incumbent’s incentives for effort. The intuition is straightforward. When
the voter’s information about policy success or failure is noisy, effort by the
incumbent translates less directly into reelection than when policy success or
failure is observed perfectly by the voter. As a result, the incumbent has weaker
electoral incentives than in the baseline game where the voter always correctly
perceived the outcome:
eπ1 =
πB
2
<
B
2
= e∗1.
CHALLENGERS
One possible source of voter information is electoral challengers. A chal-
lenger has strong incentives to point out areas in which an incumbent politi-
cian’s policies have not succeeded. Moreover, if voters know challengers have
incentives to point out policy failures, they can infer from challenger silence
on some issue that the incumbent probably had policy success. Hence, the
presence of electoral challengers has the potential to improve voter information
in a way very similar to that modeled above.
Gordon and Huber (2007) compare the behavior of judges in Kansas elected
under two different systems. In some Kansas districts, judges run against
challengers in competitive elections. In other Kansas districts, judges run in
so-called retention elections—voters do not vote for the incumbent or a chal-
lenger, they just vote up or down on the incumbent. The previous paragraph
suggests that voter information is stronger in competitive elections and, thus,
that incumbents have stronger incentives in such systems.
Influence over Elected Officials 297
This is indeed what Gordon and Huber find. Judges facing competitive
elections behave differently than judges facing retention elections. Kansas has a
guideline-based system for sentencing that depends on the severity of the crime
and the criminal history of the defendant. Each criminal case is classified into a
particular group based on these criteria. Using case-level data that controls for
which sentencing group a case falls in (so comparing judicial behavior for very
similar kinds of crimes), and a rich set of additional case-level controls, Gordon
and Huber show that judges facing competitive rather than retention elections
sentence defendants more harshly, incarcerating defendants about 16% more
frequently. Assuming Kansas voters like strict law enforcement, this suggests
that the presence of challengers increases the extent to which government
officials take actions that represent the voters’ interests. (We will consider an
alternative interpretation in Section 10.3.5.)
MEDIA COVERAGE
Perhaps the most compelling evidence on the link between voter informa-
tion and electoral accountability comes from Snyder and Strömberg (2010).
Theymeasure the amount of information voters have about their congressional
representative using the congruence between congressional districts andmedia
markets. Here’s the idea. Imagine you live in a midsized city with a local daily
newspaper. Suppose, further, that your city and your congressional district are
basically the same. Then your local newspaperwill cover your local congressper-
son closely—your congressional district is highly congruent with your media
market. Suppose, now, that you live in a town 30miles outside of that city. Your
daily newspaper may still be the city’s paper. But that newspaper is not terribly
interested in reporting on your congressperson, since he or she represents
relatively few of the newspaper’s readers. Your congressional district is not very
congruent with your media market. Snyder and Strömberg claim that changes
in a localities congruence is a source of fairly random variation in the extent
to which voters have information about their congressperson’s performance.
Their idea is, if arguments like those above are correct, congruence should
correlate with performance.
Figure 10.1 documents the various relationships that Snyder and Strömberg
find. Panel (a) shows that congruence does in fact predict news coverage of a
congressperson. Each subsequent panel is then consistentwith ourmodel. First,
panels (b) and (c) show that congruence leads to increased voter information—
the more congruent a congressional district (the horizontal access) the more
likely the voters are to have readnews coverage of their congressperson (panel b)
and to correctly answer survey questions about their congressperson (panel c).
Panels (d) and (e) show that increased congruence leads congresspeople to be-
have in ways that are more representative of the interests of their constituents.
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Influence over Elected Officials 299
Representatives frommore highly congruent districts aremore likely to stand as
a witness before congressional committees on behalf of their districts (panel d)
and less likely to vote in lockstep with the national party (panel e). Finally,
panel (f) shows that this increased effort on the part of politicians in more
congruent districts seems to translate into better outcomes for the district—the
more congruent the congressional district with its media market, the more per
capita federal spending flows to the district.
These pictures tell the basic story of how increased voter information can
translate into better incentives and better outcomes. Snyder and Strömberg
(2010) also do a lot of work to show that these relationships are not simply
spurious correlations. For instance, they find these results even when con-
trolling for characteristics of the district—indeed, they can show that when a
locality gets redistricted such that it becomes more (or less) congruent with its
media market, both the behavior of the congressperson and the level of federal
spending directed to the locality change in the expected way. So the results are
not, for instance, confounded by problems like big cities happening to both
attract more federal spending and bemore congruent.
VOTER RESPONSIVENESS
Berry and Howell (2007) present a different kind of evidence about the link
between voter information and electoral accountability. They do not exam-
ine whether better voter information results in better governance outcomes.
Rather, they investigate whether voter behavior becomes more responsive to
governance outcomes when voters have better information. They find that the
answer is yes.
Beginning in 2000, South Carolina instituted a school accountability system
whereby the public was informed about school-level standardized test scores.
During the 2000 school board elections, the raw test scores were reported to the
public. However, for the 2002 school board elections and beyond, instead of raw
test scores, the public was simply told whether each school was in one of four
broad categories. Since schools fell into the same category, this change in the
reporting system diminished the public’s ability to distinguish good outcomes
(improved test scores) from bad outcomes. In the 2000 election, the public
could observe an improvement of any magnitude. In 2002, the public could
only observe improvements that were large enough to move a school from one
category to another. Thus, as in our model, in 2002, there might have been
some policy successes (improvements in scores) that were observed as failures
(no change in category).
Berry and Howell find that this decrease in voter information had an
impact on voters’ ability to use information about outcomes to make electoral
decisions. In the 2000 election, improvements in test scores relate positively
300 Chapter 10
and significantly to electoral support for incumbent school board members.
However, in elections following the 2002 changes in reporting systems, im-
provements in test scores no longer have any correlation with electoral support
for incumbent school board members. Diminishing voter information made it
impossible for voters to provide incumbent politicians with strong incentives
for good performance.
10.3.5 The Risk of Electoral Pandering
We’ve seen important ways in which stronger electoral incentives can bet-
ter align incumbent behavior with voter preferences. However, this need not
always be the case. Sometimes increased electoral incentives actually distort
the behavior of politicians away from voter interests. One interesting type
of situation in which such distortions can occur is when politicians have an
incentive to “pander.” The technicalities of a pandering model are a bit too
involved for our discussion here, but let me walk you through some intuitions
and then discuss a bit of evidence.
To make things really stark, imagine a model with a voter and an incumbent
who perfectly shares the voter’s preferences. So, in the absence of electoral
incentives, the incumbent would behave precisely as the voter wants her to.
The distortion comes from the fact that the voter faces two kinds of uncer-
tainty. First, the voter is uncertain of the right policy choice. Suppose there are
only two possible policies: A and B. The voter thinks that the right policy is
probably A, but he isn’t certain. (Since, all else equal, the voter would choose
policy A, refer to A as the “popular” policy.) Second, the voter is uncertain of
how competent the incumbent is. A competent incumbent always knows what
the right policy is. An incompetent incumbent has more information than the
voter—enough that she should choose B if her information says to do so—but
is not perfectly informed.
The voter, for his part, will reelect the incumbent only if he thinks the
incumbent is more likely to be competent than is the challenger. Given this,
how should the incumbent behave?
If the incumbent’s information indicates that policy A is the right policy,
the incumbent’s choice is clear—by choosing A she chooses the policy that
both she and the voter believe is right. If the incumbent’s information indicates
that policy B is the right policy, things are more complicated. Choosing policy
B, which the voter thinks is unlikely to be the right policy, carries some
electoral risk for the incumbent. To see this, suppose the voter believes that the
incumbent will follow her information. (This is what the voter would like the
incumbent to do, even if she turns out to be the incompetent type, because even
the incompetent type has pretty good information.) If the incumbent chooses
policy B, the voter knows that one of two things is true. Either the correct policy
is in fact B and the incumbent got the policy choice right. Or the correct policy
Influence over Elected Officials 301
is A and the incumbent got the policy choice wrong, which can only happen
if the incumbent is incompetent. As such, upon observing the policy choice
B, the voter starts to think it more likely that this was the right policy. But,
since the voter started with the belief that Bwas unlikely to be the right policy,
when he sees the incumbent choose B, he also starts to think the incumbent is
more likely to be incompetent. This increased concern about incompetence can
lead the voter to prefer the challenger. Thus, the incumbent has an incentive to
pander—that is, even a competent incumbent who knows the right policy is B
might choose themore “popular” policy,A, in order to avoid being perceived as
incompetent.
These kinds of pandering incentives come directly from the desire for re-
election. Thus, those features of the electoral environment that, in our earlier
model, enhanced incentives, here can make voters worse off by increasing
pandering. For instance, pandering can only exist with relatively informed
voters. If all the voters observe is whether the government performs well or
poorly, then the incumbent has incentives to choose policies that are likely to
succeed. It is only the fact that voters can directly observe the substantive policy
choice that creates incentives to pander. Similarly, the incentives to pander are
strongest when the incumbent faces a competitive election. If the incumbent
is term limited, or doesn’t face a serious challenger, then convincing the voter
that she is or is not competent doesn’t matter for her future payoffs, so she has
no incentive to pander. It is only when reelection is possible and contested that
pandering becomes attractive.
Depending on how one thinks about the right sentencing behavior, one
can view the evidence from Gordon and Huber (2007) discussed above as
suggesting that judges pander to law-and-order voters only when they face
serious electoral incentives. Similarly, Canes-Wrone and Shotts (2004) show
that presidents propose budgets that are more in line with public opinion
when two conditions hold: (i) the presidential election is close at hand, and
(ii) presidential approval is such that the election is expected to be competitive.
As with Gordon and Huber, one can interpret this finding as evidence of
pandering to the public when electoral incentives are strong or as evidence of
increased responsiveness to the legitimate demands of the voterswhen electoral
competitiveness is high. Nonetheless, it is important to bear inmind that those
forces that increase electoral incentives can increase or decrease the quality of
governance, depending on whether you believe politicians achieve reelection
by implementing good policy or by pandering to public opinion.
10.4 Takeaways
• Electoral concerns create incentives to target policy to benefit citizens
whose political support is likely to be responsive to that policy. This can
302 Chapter 10
lead to policy distortions that favor concentrated interests, single-issue
voters, non-partisan voters, and so on.
• There are a variety of ways in which interest groups might use money
to affect electoral and policy outcomes—a quid pro quo between a
policymaker and donor, using money to buy access to policymakers,
or using money to help allied candidates win elections. There is some
controversy over the extent to which money in fact influences policy
outcomes.
• Electoral accountability plays at least two roles in affecting the quality
of governance in a democracy: (i) the desire to gain reelection creates
incentives for incumbents to take actions that they believe will please
voters, and (ii) elections serve as a selection mechanism whereby voters
replace incumbents whom the voters believe are of low quality on some
dimension (e.g., competence, honesty, ideological fidelity with voters).
• Several factors affect the magnitude of incentives created by elections:
benefits of office, term limits, voter information, the presence of chal-
lengers, and so on.
• Sometimes the incentive effect of elections can backfire by encouraging
pandering. When incumbents believe that good policy outcomes are
the path to reelection, factors that increase electoral incentives improve
governance. However, when incumbents believe that pandering is the
path to reelection, factors that increase electoral incentives reduce the
quality of governance.
10.5 Further Reading
The model of electoral targeting is inspired by Dixit and Londregan (1996).
There are many models similar to the model of electoral accountability (for
a couple examples, see Ashworth and Bueno de Mesquita (2006) and Besley
(2006)). Ashworth (2012) provides a stellar overview of the theoretical and
empirical literatures. For models of pandering, have a look at Canes-Wrone,
Herron, and Shotts (2001) and Maskin and Tirole (2004). Scott Gehlbach’s
terrific Formal Models of Domestic Politics provides a more advanced, textbook
treatment of the various types of models discussed in this chapter.
10.6 Exercises
1. Based on the analysis in this chapter, offer two arguments in favor of term
limits for elected politicians and two arguments against.
Influence over Elected Officials 303
2. The following is a common puzzle discussed by election observers. Often,
some identifiable group of voters almost always votes for one political
party over the other (e.g., African Americans vote overwhelmingly for
Democrats and southern fundamentalist Christians vote overwhelmingly
for Republicans). Yet, the argument goes, that political party often does
little to help that loyal group of voters once in office. With reference to the
analysis in Section 10.1, provide a potential explanation for this
puzzle.
3. Based on the analysis in Section 10.2, provide an assessment of the likely
impact on the quality of public policy of significant restrictions on
campaign donations and outside expenditures on campaigns.
4. Consider the model from Section 10.3. But suppose the voter has an affinity
for the incumbent, so that if the incumbent is reelected, the voter gets an
additional payoff of α. (This could be because the incumbent is charismatic,
because the voter and incumbent are from the same political party or
ethnicity, etc.)
From the analysis in footnote 2, if the voter believes that low ability
incumbents choose effort e1, then, conditional on seeing a good outcome,
the voter believes the incumbent is of high ability with probability
p
p+e1(1−p) > p. If the voter observes the bad outcome, he is certain the
incumbent is low ability.
(a) What is the expected utility of electing the challenger?
(b) If the voter believes low ability incumbents choose effort e1, what is the
expected utility of reelecting the incumbent after seeing a good
outcome?
(c) What is the expected utility of reelecting the incumbent after seeing a
bad outcome?
(d) If the voter believes low ability incumbents choose effort e1, for what
values of α does the voter reelect the incumbent nomatter what? For
what values of α does the voter reelect the incumbent only following a
good outcome?
(e) If α is such that the voter reelects the incumbent nomatter what, what e1
will the incumbent choose?
(f) What does this imply about the effect of voter affinities for one
candidate over the other on electoral accountability?
(g) We can think of higher levels of voter affinity as corresponding to less
competitive elections. Does this model suggest that competitive
elections are good or bad for accountability?
304 Chapter 10
5. (This problem is due to Scott Ashworth.) An elected official must decide
whether to behave or to be corrupt. If he is corrupt, then he gets a private
benefit worth B, while he gets no private benefit from behaving. After the
official makes his choice, he stands for reelection.Winning the election is
worth R > B to the official. The voter strictly prefers for the politician to
behave rather than act corruptly.
(a) Suppose the voter does not have any information about the official’s
corruption choice prior to voting. Is there any reelection rule that (if
anticipated by the politician) induces good behavior by the official? If
yes, what is it? If no, why not?
(b) Now assume that there are n newspapers, each of which can report on
corruption if and only if it happens. (Corruption is perfectly observed by
the reporters.) A newspaper that reports on corruption gets a boost in
sales, giving it a benefit ofM. The voter observes the newspaper reports
before voting. Is there a reelection rule that (if anticipated by the
politician) induces good behavior by the official? If yes, what is it? If no,
why not?
(c) Now assume that the official can offer bribes to the newspapers after he
chooses to be corrupt. Both B andM are measured in dollars, with
B > M. Newspapers care only about profits. Howmuch does the official
have to offer in bribes to get away with corruption? Howmany
newspapers are needed to deter corruption?
(d) What does this imply about the market structure of the media and
democracy?
11
Institutions, Incentives, and Power
Bueno de Mesquita et al. (2003) tell the following story of Leopold II. Leopold
was the king of Belgium from 1865 through 1909. Beginning in 1885, he was
also the private owner of the Congo Free State—an area of land in Africa more
than seventy-five times the size of Belgium.
Leopold faced very different political constraints in the two polities of which
he was the leader. His governance of Belgium, a constitutional monarchy, was
constrained by elected parliaments and cabinets. Moreover, the government
of Belgium was chosen by majority rule from a voting population that, at the
beginning of his reign, had over 100,000 members and, by the end of his reign,
was made up of all of Belgium’s adult male citizens.
Leopold held the Congo Free State as his personal property. He controlled
the Congo with a mercenary army—the Force Publique. The members of the
Force Publique were the only constituency to which Leopold was accountable
in Africa. The easiest way to stay in power was by extracting and distributing
private goods to his cronies.
This case is interesting becausewe observe one person, simultaneously facing
two different sets of institutions. So how did Leopold behave as leader of each
place?
As the constitutional monarch of Belgium, Leopold was generally viewed as
one of the great reformers of his day. He advocated for universal male suffrage,
gaveworkers the right to unionize and strike, instituted child labor laws, funded
large public works projects (including road and railroad construction), and
took measures to diminish unemployment. Under his leadership, Belgium
experienced prosperity and rapid economic growth. All told, Leopold was
regarded as a progressive and highly successful leader in Belgium.
Leopold’s story is quite different in the Congo. He ran the Congo as an
extractive slave state, first focusing on ivory and later on rubber. Leopold
restricted foreign access to the Congo and allowed the Force Publique to enslave
the native population. Work and compliance were enforced through torture,
mutilation, and murder. The Force Publique was given enormous financial
incentives to maintain Leopold’s leadership, in the form of commissions based
on the amount of rubber its slaves produced. Estimates vary as to how many
people weremurdered during Leopold’s genocidal rule over the Congo. The low
306 Chapter 11
end of estimates are on the order of twomillion, with some scholars putting the
number as high as fifteenmillion.
Under one set of institutions, Leopold was a noted progressive. Under an-
other set of institutions, the self-same Leopold was one of the great genocidal
murderers of modern history—on par with Stalin, Hitler, Pol Pot, and Mao.
Certainly other factors, like racism, play a role in explaining Leopold’s hor-
rendous crimes in Africa. But, it seems likely that the unconstrained political
environment in Congo was an important factor in Leopold’s decision to imple-
ment horrific policies that benefited himself and his cronies while decimating
millions of lives.
In this final chapter, we will think at a general level about how such differ-
ences in political institutions affect the incentives of political leaders who wish
to stay in office. Following the analysis in Bueno de Mesquita et al. (2003), we
will describe institutions according to two features:
1. The size of the selectorate: The proportion of the population that has
some chance of playing a role in the selection of the leader.
2. The size of thewinning coalition: The portion of the selectorate needed
to keep a leader in power.
Our standard notions of regime type can be located within this selec-
torate/winning coalition typology. In a democracy, the selectorate is citizens
with voting rights and awinning coalition is somemajority or plurality of those
citizens (depending on the exact electoral rules). In a Soviet-style autocracy, the
selectorate is the members of the party and a winning coalition is made up
of some central committee of those party members. In a junta or monarchy,
the selectorate is a group of elite military officers or nobles and clergy, while a
winning coalition is some small critical group of those elites.
We will study a model of a leader choosing between two kinds of policies:
providing public goods (i.e., good public policy) and providing private goods to
the members of the leader’s winning coalition. Think of public goods as things
like economic growth, peace, or solving social dilemmas. Think of private goods
as corruption, direct transfers of wealth, patronage, and so on.
We will assume that leaders are primarily motivated by the desire to remain
in office. Then we will examine how different institutions (i.e., different sizes of
the selectorate and winning coalition) affect incentives to provide public and
private goods.
The motivating idea is this: in order to stay in office, a leader must prevent
challengers from recruiting away winning coalition members. So, in small
winning coalition systems, a leader needs to keep relatively few people happy to
retain power. It is relatively inexpensive to do so by providing private goods for
the members of the winning coalition. Indeed, within such a system, money
Institutions, Incentives, and Power 307
spent on providing public goods for the population (beyond those that the
members of the winning coalition themselves demand) is, speaking politically,
a waste of resources that could potentially be exploited by challengers. That is,
in small winning coalition systems, bad policy is good politics.
The incentives are different in large winning coalition systems. In those
systems, it is very expensive to provide private goods to all the members of
the winning coalition, because there are so many of them. Hence, in a large
winning coalition system, the most effective way to stay in power is to provide
public goods for everyone. That is, within a largewinning coalition system, good
policy is good politics.
This logic predicts some interesting things. First, we should expect better
policy outcomes in large winning coalition systems. Second, and more surpris-
ingly, we should expect the survival of leaders to be negatively related to the
quality of public policy in small winning coalition systems. That is, autocratic
leaderswhoprovide badpolicy outcomes are expected to survive inoffice longer
because bad policy is good politics. The opposite is expected in large winning
coalition systems. Bueno de Mesquita et al. show patterns in data that are
broadly consistent with this second prediction.
Let’s now turn to a model that captures these intuitions.
11.1 A Selectorate Model
There are two politicians: an incumbent leader, L, and a challenger, C. There
is also a selectorate, made up of S individuals. The incumbent leader starts the
game with a preexisting winning coalition of sizeW < S.
The government has resources, R. (For technical convenience, assume R > S.)
Each politician proposes a policy, which is an amount of public goods (g) to be
provided and an amount of private goods (x) to be provided to eachmember of
the politician’s winning coalition. (For simplicity, I assume eachmember of the
winning coalition gets the same private goods.) Eachmember of the selectorate
then chooses which politician to support. The incumbent leader loses power if
and only if two things happen:
1. The challenger gets the support of a group of at least sizeW.
2. The leader loses the support of at least onemember of her winning
coalition.
The price of a unit of public goods is p, so g units of public goods costs p × g
dollars. Private goods are measured directly in dollars. Policy proposals must
have a balanced budget. So any proposal, (g, x), must satisfy
pg + Wx ≤ R.
308 Chapter 11
Payoffs are quasi-linear. Suppose a member of the selectorate, i, receives pri-
vate goods xi and public goods g. Her payoffs are linear in xi and are increasing,
but with decreasingmarginal returns, in g. In particular, let’s assume the utility
from some amount of public goods, g, is the natural log of g (denoted ln g). This
is a simple functional form that captures the idea that payoffs are increasing in
public goods, but with decreasingmarginal returns. Thus, her payoffs are
Ui(xi, g) = xi + ln g.
The payoff to a politician who is not in office is 0. The payoff to a politician
who is in office includes a benefit from holding office, B > 0, and a benefit
fromany resources not spent onpolicy, u(R − pg − Wx), where u is an increasing
function. Thus, the politician who wins leadership has payoffs
B + u(R − pg − Wx).
I make one further assumption. The incumbent leader is committed to the
members of her winning coalition. If she retains office, any member of her
winning coalition who supported her remains in the winning coalition. The
challenger cannot make a similar commitment. It is not until the challenger
takes office that the members of the selectorate learn who will be in the
challenger’s inner circle—that is, the winning coalition. From the perspective
of a selectorate member, each member of the selectorate is equally likely to end
up in the challenger’s winning coalition, should the challenger take power.
11.1.1 Equilibrium
I focus on a Nash equilibrium in which both politicians attempt to secure
the support of exactly W people and in which each member of the selectorate
supports the politician whose platform he or she prefers.1
Suppose the incumbent proposes (gL, xL) and the challenger proposes
(gC, xC). Who will the members of the selectorate support?
If the incumbent retains office, a member of the winning coalition makes
a payoff of xL + ln gL, while a member of the selectorate not in the winning
coalition makes a payoff of ln gL. If the challenger wins, each member of the
selectorate ends up in the new winning coalition with probability WS . So the
expected payoff to a member of the selectorate from the challenger winning
is WS × xC + ln gC. Given this, a member of the incumbent’s winning coalition
1This last restriction is the common assumption that players don’t play weakly dominated
strategies. It rules out equilibria in which I support a politician I dislike because I knowmy support
has no effect on the outcome. That is, it rules out certain kinds of coordination traps.
Institutions, Incentives, and Power 309
continues to support the incumbent if
xL + ln gL ≥ W
S
× xC + ln gC, (11.1)
while a member of the selectorate not in the incumbent’s winning coalition
supports the incumbent if
ln gL ≥ W
S
× xC + ln gC. (11.2)
The incumbent leader has an advantage over the challenger in holding on
to the support of the members of her winning coalition—she can guarantee
them continued access to private goods, while the challenger cannot because
he cannot commit to themakeup of his winning coalition. Given this, we want
to see whether there is any offer a challenger can make that will allow him to
unseat the incumbent.
The most attractive proposal a challenger can make to the members of the
selectorate is to spend the entire budget, R, and to divide it between public and
private goods in a way that maximizes a selectorate member’s expected utility
(remembering that the selectorate members do not know if they will end up
in the winning coalition should the challenger win). This proposal solves the
following:
max
(g,x)
W
S
x + ln g subject to pg + Wx = R. (11.3)
Notice, from the budget constraint, we have the following condition:
pg + Wx = R ⇒ x = R − pg
W
.
This says that, given that the challenger is going to spend the whole budget,
the choice of howmuch to spend on public goods (g) tells you, through simple
accounting, how much she will spend on private goods (x). Hence, she really
just has tomake one choice: howmuch to spend on public goods. In ourmodel,
we can see this by substituting x = R−pgW into Equation 11.3. This transforms the
two-dimensional maximization problem subject to a budget constraint into a
simple one-dimensional problem of howmuch to spend on public goods:
max
g
W
S
× R − pg
W
+ ln g.
Using the fact that the derivative of ln g with respect to g is 1g , the following
first-order condition gives the challenger’s optimal spending on public goods
310 Chapter 11
(labeled gC):
1
gC
= p
S
⇒ gC = S
p
.
Substituting back into the budget constraint tells us how much the challenger
will propose to spend on private goods for her winning coalition. Putting this
all together, the challenger’s best policy proposal is
gC = S
p
xC = R − S
W
. (11.4)
This implies that, for any member of the selectorate, the expected payoff from
the challenger winning is
W
S
× R − S
W
+ ln S
p
= R − S
S
+ ln S
p
.
Let’s label this payoff, which is the best expected payoff that the challenger can
offer to members of the selectorate in exchange for their support, as U
C
.
To stay in office, the incumbent leader has to provide the members of her
winning coalition with a better payoff than the challenger can offer. Assume,
for the moment, that everyone not in the winning coalition will support the
challenger. Then each member of the winning coalition is pivotal—if any
member leaves the winning coalition, the incumbent leader falls. As such, the
leader must offer a package (gL, xL) that convinces eachmember of the winning
coalition that having her in office is better than having the challenger in office.
That is, (gL, xL) must satisfy
xL + ln gL ≥ UC and pgL + WxL ≤ R.
The leader can in fact make a proposal that will keep her in office. Why is
this? The members of the leader’s winning coalition understand that if they
stick with her, they get to stay in the winning coalition, so they get the private
goods she offers for certain. If they defect to the challenger, they may or may
not end up in the newwinning coalition, so theymay ormaynot get the private
goods. Thus, it is clear from Condition 11.1, if the incumbent leader offered the
same proposal as the challenger, the incumbent’s existing winning coalition
members would support her.
Of course, the incumbent leader will not make the same proposal as the
challenger. She wants to remain in power as cheaply as possible, since she gets
to keep any resources she doesn’t allocate to public or private goods. As we
just said, all else equal, the leader’s existing winning coalition members strictly
prefer her to the challenger because they are certain to remain in her win-
ning coalition if she wins. Hence, the leader can retain her winning coalition
Institutions, Incentives, and Power 311
members’ loyalty even if she offers them somewhat less than the challenger
is offering to his winning coalition (whose membership is uncertain). Let’s see
exactly what the incumbent leader offers.
Suppose the leader were going to propose spending a total amount � on
providing public and private goods. She wants to use those resources to make
the members of her winning coalition as happy as possible. Doing so will allow
her to keep � as small as possible while still staying in office. To do so, she
maximizes the winning coalitionmembers’ utility, given a total expenditure �.
That is, the leader solves
max
x,g
x + ln g subject to � = Wx + pg.
Just as we did for the challenger, we can use the budget constraint to reduce
this to a one-dimensional problem, since whatever share of � the incumbent
doesn’t spend on public goods, she spends on private goods for her winning
coalition members. (She then keeps R − � for herself.) The budget constraint
implies that x = �−pgW . Hence, the incumbent’s maximization problem can be
rewritten
max
g
� − pg
W
+ ln g.
The first-order condition for this problem is
p
W
= 1
gL
⇒ gL = W
p
.
For any amount � ≥ W that the leader spends, she will divide it as follows:
gL(�) = W
p
xL(�) = � − W
W
. (11.5)
Notice, if � < W, our formula in Equation 11.5 calls for an x < 0. Since this is
not allowed, the leader is stuck at what is called a “corner solution.” Thatmeans
that if she spends � < W, she will allocate it all to public goods, providing no
private goods to her winning coalition.
The analysis above already reveals two important pieces of intuition. First,
when the winning coalition is small, private goods are shared among a small
group of people. Hence, the incumbent has particularly strong incentives to
allocate a lot of her spending to private goods (i.e., xL is decreasing in W). As
the winning coalition gets larger, the leader spends more and more resources
on public goods. Indeed, if the winning coalition gets large enough relative to
the budget allocated (W > �), the leader provides only public goods, spending
nothing on private goods for the winning coalition.
312 Chapter 11
Second, compare the incumbent leader’s division of resources in
Equation 11.5 to the challenger’s division of resources in Equation 11.4.
The incumbent allocates a bigger portion of the resources she spends to private
goods than does the challenger. (You can see this clearly if you consider the
case of � = R.) This is because the incumbent’s winning coalition members
know for certain that theywill be in her winning coalition in the future. Hence,
they place greater value on private goods. But the challenger’s supporters don’t
know if they will end up in her winning coalition or not. So they put less value
on private goods andmore value on public goods.
Now the incumbentmust decide howmuch to spend in total. She will spend
just the amount needed to keep her in office. Call this amount �∗. Let’s assume
that U
C
> ln Wp , so that the incumbent leader must spendmore thanW to keep
the winning coalition happy. This implies that �∗ > W, so the leader’s optimal
allocation between public and private goods is given by Equation 11.5. Using
this fact, the minimal �∗ that keeps the members of the incumbent leader’s
winning coalition loyal satisfies
�∗ − W
W
+ ln W
p
= UC.
Rearranging, the incumbent’s total spending is
�
∗ = W
(
U
C + 1 − ln W
p
)
. (11.6)
11.1.2 Outcomes and Institutions
What do we learn from this analysis? Let’s start by studying the amount that
is spent by the government. If we substitute the definition of U
C
into �∗ (recall
U
C = R−SS + ln Sp ), we find that the incumbent leader spends
�
∗ = W
(
R
S
+ ln S
W
)
.
Differentiating with respect to W shows that total government spending is
increasing in the size of the winning coalition.2 The larger the size of the
winning coalition, the more of the budget the leader spends and the less
she misappropriates. Hence, for leaders, small winning coalition systems are
better than large winning coalition systems in that they offer the leader more
opportunities for personal corruption.
2 d�∗
dW =
R
S + ln SW − 1. Since we have R > S > W, the first term is greater than 1 and the second
term is positive. Together, then, the first two terms are greater than 1, so the whole derivative is
positive.
Institutions, Incentives, and Power 313
To see what drives this fact, it helps to study the policy choices. Recall, from
above, that the per-person level of private goods is
xL(�∗) = �
∗ − pgL
W
.
Substituting for �∗ and for gL(�∗) = Wp , we get
xL = R
S
+ ln S
W
− 1.
Thus, the per-person public and private goods provided by the incumbent
leader are
gL = W
p
xL = R
S
+ ln S
W
− 1.
The level of public goods provided is increasing in the size of the winning
coalition and the level of private goods provided to members of the winning
coalition is decreasing in the size of the winning coalition.
As the size of the winning coalition increases, it becomes more expensive
to provide private goods. So, increasingly, as the winning coalition gets large,
the cheapest way for the leader to make the members of the winning coalition
happy is to provide public goods.3 When the winning coalition is small, it is
quite cheap to provide private goods. Hence, in small winning coalition sys-
tems, the leader provides lots of private goods and relatively few public goods.
These results highlight another important point—public goods are all that
matter to a member of society who is not in the winning coalition. Large
winning coalitions create incentives for leaders to provide public goods rather
than private goods. Hence, for a person not in the winning coalition, large
winning coalitions are better.
Taken together, all of these results suggest the following point. In large
winning coalition systems, good policy is good politics. In small winning
coalition systems, bad policy is good politics. Governments are not benevolent
social welfare maximizers. Leaders are not inherently motivated to achieve
Pareto improvements. Rather, political leaders have their own preferences and
incentives. The desire to stay in office is a powerful source of such incentives. So
leaders pursue policies that benefit those people who are in a position to keep
them in office. If that group of people has preferences that are broadly similar
to most of society (i.e., if most of society is in the selectorate and the winning
coalition is large), then leaders have incentives to pursue policies that are pretty
benevolent. If that group of people has preferences that are quite different from
3Indeed, as we discussed earlier, if the winning coalition is really big, the leader provides no
private goods at all to themembers of the winning coalition.
314 Chapter 11
most of society, then leaders have incentives to pursue policies thatmaywell be
quite bad for society.
There could be many reasons why the winning coalition ends up being
small—autocratic institutions, widespread inattention by voters, special inter-
ests capturing control of the political process, and soon. In this sense, the lesson
of the selectoratemodel is similar to the lesson of ourmodel, fromChapter 10.1,
of elected incumbents who target policy to the interests of responsive voters.
All of this is to say that politics act as a real and important constraint
on whether or not the social dilemmas we discussed in Part II get solved. If
the institutions of government create incentives such that the government is,
broadly speaking, working for the people, then policy is likely to be good. If the
institutions of government create incentives such that the government is not,
broadly speaking, working for the people, then rational politicians are likely
to choose policies that are not good for society, but rather are good for their
political coalition.
If this argument is right and the social dilemmas discussed throughout this
book are important, then we should expect the quality of political institutions
to have a big impact on the type of policy pursued and the welfare outcomes for
society. In the remainder of this chapter, we explore whether this is the case in
a couple of settings.
11.2 Institutions and Development
The selectorate model provides a formalization of the idea that political insti-
tutions play an important role in determining whether governments pursue
good or bad public policy. Given the arguments of the rest of this book—that
good public policy plays an important role in determining citizen welfare—
you might wonder whether there is any systematic evidence of a link between
the quality of political institutions and welfare. In this section, we will look
briefly at some evidence on this question, focusing especially on whether good
governance institutions lead to economic growth.
Answering this question is tricky. Consider the simplest comparison you
might make to assess the answer—comparing economic outcomes in countries
with good institutions to economic outcomes in countries with bad institu-
tions. Unfortunately, even if you controlled for lots of other things in that
comparison, you would not convincingly answer the question. Suppose you
found a correlation between good institutions and good economic outcomes.
You would not know whether the good institutions caused the economic
outcomes or whether a good economy causes good institutions. Perhaps, for
example, as the economy grows, people become more educated, and more
educated people demand better government institutions. To make things even
more complicated, there could be no causal relationship between the two at
Institutions, Incentives, and Power 315
all. Perhaps there is some third factor—say climate or ethnic fractionalization—
that creates the correlation by affecting both institutions and the economy.
Given these deep causal inference problems, if one wants to figure out the
relationship between good institutions and economic outcomes, one has to be
a bit more clever.
One way to start to see that governance institutions really might matter for
growth is to think anecdotally about some more convincing comparisons. As
Acemoglu, Johnson, and Robinson (2005) discuss, prior to the late 1940s, North
and South Korea shared a common history and culture. They were also quite
similar economically, with the north the more industrially developed of the
two. But afterWorldWar II, the two parts of Korea ended up with very different
political systems—North Korea came under Communist control, while South
Korea’s nationalist government aligned with the West. Starting in the late
1960s, South Korea had one of the highest growth rates in modern history,
while the North Korean economy basically failed to grow at all. By the year
2000, South Korea’s per capita GDPwasmore than sixteen times North Korea’s.
Government institutions seem to matter. Although even here the inference
is questionable. After all, the two Koreas differ in many ways (beyond polit-
ical institutions) in the postwar period. For instance, their different political
alignments resulted in different military alliances, trading partners, diplomatic
relationships, and so on.
11.2.1 Settler Mortality, Institutions, and the Economy
If you want to assess the impact of institutions on economic outcomes, you
have to find a way to set up a comparison that is something like an experiment.
That is, you need some countries to get good institutions and other countries to
get bad institutions for reasons not having to do with their current or expected
future economic outcomes. This is a tough challenge. Perhaps themost famous
research attempting to do so is Acemoglu, Johnson, and Robinson (2001).
Here is their idea. European colonialists established different kinds of institu-
tions in different places. One source of variation was simply the home country
of the colonist—the French set up different institutions from the British or the
Dutch. Another source of variationwaswhether the colonists planned to live in
the colony. In places where the colonists themselves planned to live, they set up
European-like governance institutions. In places where the colonists planned
to establish, say, extractive colonies, but did not plan to live, they established
much less enlightened institutions. (Remember the story of King Leopold.) So,
Acemoglu, Johnson, and Robinson reason, where colonists planned to live was
an important source of variation in the quality of governance institutions at the
time of colonization.
Institutions are sticky. A country that gets good institutions at the time
of colonization tends to have good institutions later, and likewise with bad
316 Chapter 11
institutions. This suggests that settlement patterns at the time of colonization
exert an influence on the quality of institutions, even today.
If colonial settlement patterns were unrelated to factors that affect contem-
porary economic outcomes, then we have something like the experiment we
want. But is this true? Surely the settlers chose to stay in locations with lots
of natural resources and good economic prospects, factors that might carry
through to economic growth today.
Acemoglu, Johnson, and Robinson argue that a major determinant of set-
tlement patterns at the time of colonization was the disease environment.
Colonists did not want to settle in locations rife with malaria and yellow fever,
as they would not survive. Further, they argue, the diseases that constituted the
major risks to colonists at the time of settlement are unlikely to have a serious
impact on economies today because those diseases have either been eradicated
or effectively controlled. As such, they argue, the bit of variation in settlement
patterns that is due to the disease environment at the time of colonization
might have affected institutions, while having no other relationship to current
economic outcomes. That variation is like an experiment—countries that have
good institutions because of their deep historical disease environments and
countries that have bad institutions because of their deep historical disease
environments can be compared to learn about the effect of institutions because
deep historical disease environment is “as if random” (i.e., assigned almost as if
for an experiment) relative to modern economic outcomes. We’ll come back
to how airtight this argument is later. For now, though, let’s look at a little
data.
At a very simple level, if Acemoglu, Johnson, and Robinson’s argument
is right, we should see a relationship between historic disease environments
and modern economic outcomes. Figure 11.1 shows that relationship. The
horizontal axis is a measure of settler mortality. The vertical axis is a measure of
per-capita income in 1995. Each point is a country. (They are labeledwith three-
letter country codes.) There is clearly a negative relationship—the less pleasant
a location was to settle, the worse its economy today.
This simple picture doesn’t tell the whole story. In particular, it leaps directly
from settler mortality to modern economic outcomes. What we really want to
see is a two-step relationship. First, settler mortality at the time of colonization
should predict worse institutions today. Second, we want to isolate the bit of
variation in institutions today that is due to settler mortality and see that it is
associated with worse economic outcomes today.
Figure 11.2 shows the first step. On the horizontal axis, again, is a measure
of settler mortality. On the vertical axis is a measure of the quality of modern
institutions—inparticular, ameasure ofwhether the government respects prop-
erty rights (higher numbersmean better institutions). Again, the relationship is
clearly negative.
Institutions, Incentives, and Power 317
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Figure 11.1. Log settler mortality at time of colonization against log 1995 GDP per
capita. This figure uses Acemoglu, Johnson, and Robinson’s (2001) data to replicate their
Figure 1.
Showing the second of these relationships is a bit more involved, since you
must isolate the bit of variation in the quality of institutions that is due to
settler mortality and then relate just that bit of variation to GDP. The details of
how one does this are not important for us.4 What is important is that, having
done so, Acemoglu, Johnson, and Robinson find the expected relationship—
good institutions seem to lead to better economic outcomes. In particular,
their estimates suggest that moving from the twenty-fifth percentile (roughly
Nigeria) to the seventy-fifth percentile (roughly Chile) in quality of institutions
yields a sevenfold increase in GDP.
Of course, there are reasons you might be skeptical of this interpretation.
First, since the evidence is historical and across many countries, there are in-
evitably somemeasurement concerns (Albouy, 2012). Second, it seems possible
that settler mortality has ways to affect economic outcomes today besides
just institutions. For instance, Glaeser et al. (2004) point out that, along with
good institutions, colonists who actually settled in the colonies brought along
their human capital. If human capital leads to investment in infrastructure,
health, more human capital, or what have you, it could have a persistent effect
4If you are interested in this kind of empirical research, you should read Angrist and Pischke
(2008).
318 Chapter 11
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Figure 11.2. Log settler mortality at time of colonization against modern expropriation
risk (higher expropriation risk means more respect for property rights). This figure uses
Acemoglu, Johnson, and Robinson’s (2001) data to replicate their Figure 3.
on the economy. Hence, Glaeser et al. argue, one cannot be certain that the
relationship between settler mortality and modern economic outcomes is due
to institutions. Nonetheless, Acemoglu, Johnson, and Robinson provide some
really interesting, if inevitably limited, evidence. In the next section, we will
look at some more evidence of a link between institutions, policy choices, and
welfare.
11.3 Foreign Aid
We have looked at both a model and some evidence related to two key claims.
First, that government policy actually matters for outcomes we care about.
Second, that the type of incentives created for policymakers by political insti-
tutions affect the kind of policies made and, thus, the welfare outcomes for
citizens. In this section we will look at both of these questions again, within
the context of a particular policy domain, foreign aid.
In our discussion of foreign aid, let’s start with the traditional account of how
aid works. This is the account typically given by development specialists and
others who advocate foreign aid as a (at least partial) solution to global poverty.
We will then turn to some critiques from within the tradition of development
Institutions, Incentives, and Power 319
economics. Finally, we will think about a political economy account of the
politics of foreign aid policy, using the selectorate model to motivate our
discussion.
11.3.1 Poverty Traps and Foreign Aid
In Chapter 5.2 we discussed the standard account of the role of foreign aid,
based on the theory of poverty traps (Sachs, 2006; Collier, 2007). Poor countries
lack human capital, infrastructure, health, and a variety of the other features
of a congenial investment environment. As such, they cannot attract foreign
investment. This inability to attract capital leads poor countries to become ever
poorer, making it even harder to invest in human capital, infrastructure, and
so on. Poverty creates a vicious cycle. And so, poor countries are caught in a
poverty trap, unable to develop and grow precisely because they are poor. This
problem, the argument goes, is only exacerbated by globalization. As capital
becomes increasingly mobile, the disadvantages of those countries that cannot
attract foreign investment are magnified.
Foreign aid is thought to be a solution to poverty traps. Aid can be used by
poor countries to invest in the infrastructure andhumancapital needed tomake
poor countries more attractive destinations for foreign capital. Once foreign
investment begins to flow to the country, wealth will increase. This allows for
further investment in infrastructure and human capital, which then attracts
even more investment. Aid is intended to break the vicious cycle of poverty,
replacing it with a virtuous cycle of investment and growth.
On this account, a country is not expected to depend on aid for the long
term. Rather, like in the case of the Tennessee Valley Authority creating an
agglomeration economy in manufacturing, aid is meant to be a short- to
medium-term measure that allows a big push in infrastructure and human
capital investment. This big push ismeant to shift the country into the virtuous
cycle of economic growth, eventually eliminating the need for foreign aid.
11.3.2 Does Foreign Aid Work through Poverty Traps?
Perhaps the most prominent critic of the poverty traps view of foreign aid is
the development economist William Easterly.5 Easterly rejects the poverty trap
view, primarily on empirical grounds, and suggests a different model for how
foreign aid could be effective.
He starts by pointing out that it is very difficult to find any evidence of even a
correlation between foreign aid and future economic growth. Any relationship
that has been found, Easterly notes, is highly fragile to both specification of the
statistical model (e.g., whether or not to control for domestic economic policy)
5See, for example, Easterly (2003, 2006) and Easterly and Pfutze (2008).
320 Chapter 11
and to the inclusion of newdata (e.g., asmore years become available). The first-
order fact one notices from the data is essentially no relationship between aid
and growth.
Easterly further questionswhether poverty traps exist at all. There is no doubt
that there are some very poor countries. But that is not evidence of a poverty
trap. A poverty trap requires two things to be true: (i) the poor get poorer
over time because the rich can attract investment while the poor can’t, and
(ii) poverty is a persistent trait of a country (i.e., certain countries are caught in
poverty). Easterly questions whether either of these features of the poverty trap
model actually describes the world. He points to the following evidence. From
1950 to 2001, the growth rates of the richest 8% of countries and poorest 20%
of countries were indistinguishable (both around 2.5%). If one looks only from
1985 to 2001, then the poorest 20% of countries grew more slowly. However,
if one accounts for both their poverty prior to 1985 and the quality of their
government institutions prior to 1985, the quality of government was a better
predictor of low growth than was initial poverty. And of the 28 countries that
constitute the poorest 20% in 1950, eleven were no longer among the poorest
20% in 1985.
Taken together, Easterly argues, this kind of evidence calls into question
whether poverty traps exist. Poor countries seem not to be stuck in a cycle of
negative growth relative to rich countries. And, to the extent that there is any
evidence that they are (e.g., by looking only from 1985 on), the reason seems
to be because of bad governance, not poverty traps. Moreover, poverty does not
seem to be persistent. There are always poor countries. But the identity of the
poor countries changes over time.
Given that Easterly does not believe poverty traps exist, it is not surprising
that he is unpersuaded by the argument for big push foreign aid as a solution to
poverty. After all, the argument for big push foreign aid hinges on the existence
of poverty traps. And, indeed, Easterly presents some evidence to suggest that
foreign aid programs designed to address poverty traps do not work. From 1950
to 2001, among the poorest 20% of countries, those that received aid failed
to grow at a faster rate than those that did not. There was a huge aid push
in Africa during this period. For instance, in the 1990s the average African
country received aid equal to 15% of GDP. Yet during this same time, economic
growth in Africa plummeted. And of the 88 countries that received aid between
1965 and 1995, only 6 had economic growth of more than a dollar per dollar
of foreign aid. Notice, even if aid sparks no growth, mechanically there is
economic growth of a dollar per dollar of aid (since a dollar of aid itself increases
GDP by a dollar). The 6 countries that had growth in excess of a dollar per dollar
of aidwereHong Kong, China,Morocco, Tunisia, Sri Lanka, andMalta—not the
countries evoked by the poverty traps story.
Institutions, Incentives, and Power 321
None of this evidence, on its own, settles the matter. For instance, perhaps
aid recipients failed to grow faster than non-aid recipients because they were
in worse economic shape to begin with. More generally, a critical question that
such facts don’t address is whether those countries that received aidwould have
faired even worse absent aid. But taken together, Easterly’s evidence certainly
raises some questions about how common poverty traps are and how much
good aid is in fact doing.
11.3.3 Effective Aid?
Empirical scholarship is divided on the question of the efficacy of aid.6
The most heralded study purporting to show aid’s positive effects on eco-
nomic growth is Burnside and Dollar (2000), which finds that multilateral aid
is correlated with economic growth in countries that have good economic
policies (e.g., trade openness) in place. However, Easterly (2003) claims that
these findings are highly sensitive to empirical specification and disappear with
the addition of more years of data. Indeed, such non-robustness characterizes
much of the literature (Roodman, 2007). Moreover, none of these studies has a
source of variation in aid that is sufficiently close to random to justify a causal
interpretation one way or the other.
Among studies with more convincing causal interpretations, the evidence
remains equivocal.On thepositive side,Galiani et al. (2014) show that countries
that just qualify for aid have higher growth rates than similar countries that just
fail to qualify for aid. Werker, Ahmed, and Cohen (2009) show mixed effects
of aid flows from wealthy OPEC countries to poor Muslim countries resulting
from shocks to world oil prices—they find no effect on growth, a positive
effect on consumption, and a negative effect on savings. Other studies find that
aid has a variety of deleterious effects. Djankov, Montalvo, and Reynal-Querol
(2008) report that receiving aid is associated with a decrease in democratic
governance. Svensson (2000) shows a positive relationship between aid and
corruption. Rajan and Subramanian (2011) find that aid reduces the growth
of export industries. And Nunn and Qian (2014), Crost, Felter, and Johnston
(2014), and Dube and Naidu (2015) use a variety of clever sources of variation to
show that aid appears to have increased conflict in several countries.
Easterly reads this evidence, on balance, as suggesting that aid does more
harm than good. His explanation is that the foreign aid system is broken. Aid
agencies have bad incentives—they do things that get noticed, whether or not
they make a difference. International institutions and governments rely on
incorrect theories of poverty traps and state building to motivate unrealistic,
utopian visions of the effects of aid. As a result, aid ends up doing little to relieve
suffering andmuch to prop up dictators and kleptocrats in poor countries.
6See Qian (2015) for an overview on which the summary below is based.
322 Chapter 11
Sowhat are we to do?On Easterly’s view, there are a few simple steps. The first
step is to accept that aid cannot change societies, economies, or governments.
Economic growth, in Easterly’s view, must come from homegrown develop-
ment of markets and entrepreneurship. This cannot be done for people; it must
arise organically.
A second step is to stop giving aid to corrupt leaders. Aid directed in this way
does not help the poor. It simply allows bad leaders to steal money, use it to stay
in power, and continue to implement bad policies.
Third, aid should be given to relieve the suffering associated with great
poverty. Rather than attempting to transform societies or economies, we should
use aid for the more modest purpose of making people’s lives less miserable.
Inherent in this goal is givingmoney to local, direct service organizations doing
measurable and accountable good on the ground, rather than to dictators.
Easterly’s recommendations strike me as sensible. (I’m not a development
specialist, so there’s no reason you should care about my opinion.) But I also
believe his analysis misses a critical piece of the puzzle. In particular, he seems
both outraged and puzzled as to why rich governments have persisted in
pursuing failed aid policies—policies that prop up dictators, hurt the poor, and
fail to achieve their stated goals—for so long. I think his puzzlement derives
from the fact that this may not be a question for a development economist, but
rather for a political economist. So at the risk of appearing just a little too cynical
for my own good, I want to think for a moment about the political economy of
foreign aid.
11.3.4 A Political Economy of Foreign Aid
Let’s apply the intuitions about leader incentives from the selectorate model
to the politics of foreign aid (Bueno de Mesquita and Smith, 2007, 2009).
Perhaps governments are following what, from Easterly’s perspective, are failed
foreign aid policies, not because they do not understand the development
economics, but because those policies, while not economically optimal, are
politically optimal. Here’s what I mean.
Imagine two countries, A and B. The leader of country A offers the leader
of country B some resources (which we can call foreign aid) in exchange for
country B making a policy concession of some sort. Think of the United
States offering Egypt aid in exchange for maintaining peace with Israel or
offeringColombia aid in exchange for crackdowns ondrug cartels. The leader of
country B can accept the aid and make the policy concession, or she can reject
the aid and notmake the policy concession. Each leader faces domestic political
competition as in the selectorate model.
Without solving a whole newmodel, let’s think about the incentives at work
here, given what we know about selectorate politics.
Institutions, Incentives, and Power 323
When will country A’s leader be willing to trade aid for policy? The cost
to country A’s leader is that resources spent on foreign aid could have been
used to provide public and private goods to her winning coalition. Hence,
foreign aid potentially opens up an opportunity for her challenger. The benefit
to country A’s leader is that the foreign aid expenditures induce country B to
enact a pro-A policy. This policy, presumably, is a public good for the citizens of
country A. The larger the winning coalition of country A, the more valuable it
is for country A’s leader to provide public goods to her citizens. This suggests
the following. First, aid-for-policy deals are more attractive to the leader of
country A when the amount of aid needed to buy the policy concession from
country B is small. Second, aid-for-policy deals are more attractive to the leader
of country A the larger A’s winning coalition is.
Now think about country B. Country B’s leader will accept an aid-for-policy
deal as long as the aid more than compensates for the costs of the policy
concessions. How costly the policy concessions are depends on at least two
factors. First, howbad the policy change is for countryB. Second, howmuch the
leader of country B cares about implementing suboptimal policies. The larger
country B’s winning coalition is, themore costly the leader of country B finds it
to make a policy concession. Hence, the amount of aid A will have to provide
to get an aid-for-policy deal from B is increasing in the size of B’s winning
coalition.
Taken together, this story about aid-for-policy deals has some interesting
implications. Letme startwith some empirical implications and then talk about
the implications for social welfare. Three empirical predictions follow from the
argument above:
1. Aid will primarily be provided by countries with large winning coali-
tions, since policy concessions are particularly valuable to them.
2. Most aid will go to countries with small winning coalitions, since they
are the cheapest to buy off.
3. While aid will go to small winning coalition countries more often than
to large winning coalition countries, when it does go to a large winning
coalition country, the aid package will be unusually large, since such
countries are expensive to buy off.
The data, sadly, turn out to be supportive of all three of these predictions.
Bueno de Mesquita and Smith (2009) find the following in data on aid from
countries within the OECD. The larger the winning coalition of an OECD
country, the more likely it is to give aid (point 1). Controlling for poverty and
need, the larger the winning coalition of a country (i.e., the more democratic
it is), the less likely it is to receive aid (point 2). Conditional on receiving an aid
package, large winning coalition countries receive a larger number of dollars
(point 3).
324 Chapter 11
The empirical findings in Bueno de Mesquita and Smith (2007, 2009) are
certainly not slam-dunk convincing. In particular, they do little to isolate causal
relationships in the data and one could certainly tell other stories for some
of the findings. That said, the theory yields some subtle and counterintuitive
implications that seem to be borne out in the data. Further, there is other evi-
dence, less directly tied to this particular theory, but more convincing causally,
that also suggests politics play an important role in determining foreign aid
policy. In perhaps themost important such study, Kuziemko andWerker (2006)
uncover political motivations in foreign aid by exploiting a natural experiment
in the value of the concessions a recipient country can offer a donor. The
variation comes from the interaction of two sources—rotating membership
of the non-permanent members of the United Nations Security Council and
variation in the importance of the issues facing the security council in any
given year. The idea is that a vote on the security council (which might be
boughtwith a foreign aid package) is of greater valuewhen there are high-stakes
issues before the council. And, indeed, Kuziemko andWerker find that countries
receive more foreign aid when they have a vote on the security council in high-
stakes years, suggesting that foreign aid is being used, at least in part, to buy
votes in the United Nations.
Having looked at a bit of evidence, let’s now turn to the implications of this
theory for social welfare.
Start by asking who benefits from aid-for-policy deals, on this political econ-
omy account. Clearly, the leaders of both country A and country B benefit.
If they didn’t, they wouldn’t agree to the deal in the first place. The donor
country’s leader benefits because she gets a policy concession that isworthmore
to her than are the resources spent on foreign aid. The recipient country’s leader
benefits because she gets resources that are more valuable to her (presumably
for providing private goods for herself and her coalition partners) than the lost
public goods associated with the policy concessions. Finally, the citizens of the
donor country also benefit from the aid-for-policy deal. The citizens of that
country (which typically has a large winning coalition) have a leader who is
concerned with providing public goods. That leader was willing to make the
deal precisely because the public goods associated with the recipient country’s
policy concessions were more valuable than whatever public goods could have
been purchased with the aid money.
Only one group, on this account, is hurt by the aid-for-policy deal—the
citizens of the recipient country! Remember, a key prediction of the political
economy model of aid is that aid flows primarily to dictators, since they are
relatively inexpensive to buy off. The citizens of recipient countries, thus,
typically have leaders who are not motivated to pursue good policy, but rather
to provide private goods to a small group of critical supporters (precisely as
Deaton and Easterly both note). Hence, aid-for-policy deals result both in costly
Institutions, Incentives, and Power 325
policy concessions and resources flowing to dictatorial leaders who use those
resources to stay in office. Both of these make the citizens of aid recipient
countries worse off.
You may have thought Easterly’s take on foreign aid was discouraging. But
the political economy view is even more so. It suggests that rich governments
may be giving aid to dictatorial governments, not because they don’t under-
stand how to use aid properly, but because they are using aid as a political tool.
The leaders of democratic countries have incentives to improve the welfare of
their citizens, since it is their citizens who keep them in office. They do not have
clear incentives to improve the welfare of citizens of other countries. Hence,
they use foreign aid as a tool to buy policy concessions. And because dictatorial
leaders are cheaper to buy off than are democratic leaders, foreign aid resources
flow to dictators, actually hurting the citizens of the country receiving aid.
I tell you this story not to induce despair, but because it lets us end on
an absolutely critical point for thinking about politics and policymaking. If
you want to understand and lead policy debates, politics matter. It will not
do to come in with some first-best (or even second-best) theory of policy
interventions and assume that, once you explain it to them, politicians will
do the optimal thing. Politicians and other policymakers are embedded within
strategic environments and are driven by their own interests and incentives.
If you want to move policy in some direction, you must take those political
constraints seriously in selecting your goals, in deciding for what policies to
advocate, and in formulating a strategy for getting your ideas implemented.
11.4 Takeaways
• Different political institutions create different incentives for political
leaders. Leaders have incentives to pursue policies that benefit the peo-
ple on whom they depend to remain in power.
• Institutions thatmake leaders’ hold onpower contingent on the support
of a small group make bad policy good politics. Institutions that make
leaders’ hold on power contingent on the support of large groups of
citizens make good policy good politics.
• The fact that a leader has incentives to provide good policy for her own
citizens does not mean that she has incentives to provide good policy
around the globe. So, for instance, democratic leaders are willing to
pursue foreign aid policies that secure policy concessions that benefit
their own citizens at the expense of the citizens of the recipient country.
This phenomenon is exacerbated by the fact that autocratic leaders
don’t depend on providing good policy to stay in power and, so, are
cheaper to buy policy concessions from than are democratic leaders.
326 Chapter 11
• When thinking about how to achieve policy change, or the likely effects
of a policy change, it is critical to think about how the institutions of
government affect the incentives of the leaders who must adopt and
enforce the policies.
11.5 Further Reading
Bruce Bueno de Mesquita, Alastair Smith, Randolph M. Siverson, and James D.
Morrow’sThe Logic of Political Survival is the fullest articulationof the selectorate
model. Bueno de Mesquita et al. (2001) is a non-technical introduction. Daron
Acemoglu and James A. Robinson’sWhy Nations Fail is an exhaustive treatment
of the roll of political institutions in economic development. For a different
tradition of thinking about institutions and development, see Douglass C.
North and Robert P. Thomas’s classic The Rise of theWesternWorld andDouglass
C. North, John J. Wallis, and Barry R.Weingast’s Violence and Social Orders.
For accessible treatments of the foreign aid debate, compare Jeffrey Sachs’s
The End of Poverty, Paul Collier’s The Bottom Billion,William Easterly’s TheWhite
Man’s Burden, and Bruce Bueno de Mesquita and Alastair Smith’s The Dictator’s
Handbook. As I mentioned in the text, Qian (2015) provides an overview of
empirical studies of the effects of foreign aid, focusing on the economics
literature.
11.6 Exercises
1. The United States’ government gives over $1 billion per year in aid to Egypt’s
government. Moreover, U.S. law forbids the continued flow of aid from the
United States to a country whose government has been formally found to
have been overthrown by a coup. Yet, following the 2013 coup in Egypt that
overthrew a democratically elected government, theWhite House stated:
The law does not require us to make a formal determination as to
whether a coup took place, and it is not in our national interest tomake
such a determination.
Give an account of this policy decision based on the selectorate model.
2. Historically, when a democracy defeats another country in war and has the
opportunity to set up a new government in that country, the victorious
democracy rarely sets up a democratic government in the defeated country.
(TheMarshall Plan is a famous exception.) It is muchmore common for the
victorious democracy to set up some form of autocracy in the defeated
country.
Institutions, Incentives, and Power 327
(a) From the perspective of the selectorate model, whymight this be?
(b) Suggest some way that a citizen of a democracy who was interested in
spreading democracy to other countries might work to encourage
his/her government to behave differently after war.
3. Recall from the analysis of the selectorate model that total spending by the
leader is
�
∗ = W
(
R
S
+ ln S
W
)
.
If we differentiate this with respect to the size of the selectorate, we get
d�∗
dS
= W(S − R)
S2
,
which is negative since R > S. This implies that, holding fixed the size of the
winning coalition, the leader is better off with a larger selectorate.
(a) Give an intuition for why this is the case.
(b) What does this imply about howwe should expect to see
non-democratic leaders shape their political institutions?
4. Even though only the members of the leader’s winning coalition are
relevant to her decisionmaking, the leader in the selectorate model
nonetheless provides some public goods.
(a) Why is this the case?
(b) This suggests that better policy outcomes could be achieved by
increasing the importance of public goods to members of the winning
coalition (even without changing their importance to citizens in
general). Identify two policies that outside forces could pursue that
might have this effect.
(c) The amount of public goods the leader provides is decreasing in p, the
price of public goods. Identify two policies outside forces might pursue
that would decrease p.
Summing Up Constraints on
Good Governance
In Part III we’ve seen that we should not expect the government to function
as a Pareto improving machine. Indeed, this is precisely why we need to study
the political economy of public policy. If the government were simply in the
business of identifying and implementing second-best policy interventions,
politics wouldn’t muchmatter for policy.
We examined two types of governance constraints. First, we considered tech-
nological constraints—limits on the ability of even a benevolent government
to implement optimal policy. These include the ability of the governed to adapt
their behavior to avoid policy interventions, commitment problems and other
dynamic constraints inside government, and lack of information.We can think
of the government’s limited ability to overcome each of these challenges as
another set of second-best constraints that affect the extent towhich policy can
improve social welfare.
Next we considered incentive constraints—facts about the institutions of
government that shape the kinds of policies that are in policymakers’ interests
to pursue. We focused on incentives that come from policymakers’ desire to
maintain power. These include incentives derived from the electoral process—
such as the incentive to target responsive voters, the need to raise money,
and the accountability relationship. Our analysis highlighted features of the
electoral environment that improve both incentives and selection, but also
showed that there are sometimes trade-offs and risks of perverse effects (e.g.,
strengthening incentives can lead to pandering). Finally, we considered a more
general model of incentives in democratic and autocratic regimes. Broadly
speaking, in institutions where leaders require the support of a large number
of citizens to retain power, good policy is good politics. But in institutions
where leaders’ hold on power depends on a small number of supporters, good
policy is bad politics. By taking this model into the realm of foreign aid we saw
how the interaction of leaders who themselves face different types of domestic
constituencies make these politics, and their welfare implications, even more
complex.
I purposefully did not provide an in-depth treatment of particular gov-
ernance institutions—the legislature, courts, bureaucracy, executive, central
Constraints on Good Government 329
bank, and so on. Such institutions also shape incentives and impose important
constraints. Understanding these institutions is essential. But, as I stated at the
outset, I have tried to focus on high level technological and incentive problems.
The particulars of institutional incentives is a big topic, best left to a book
dedicated to that topic.
Concluding Reflections on Politics and Policy
In the event that you haven’t been paying attention, this book has, broadly
speaking, attempted to convey three messages. In Part I we explored the nor-
mative foundations of policy, discovering howdifficult it is to say anything con-
clusive aboutwhat good public policy is. In Part II we developedmodels to learn
about some fundamental dilemmas of social life.We found that if we arewilling
to embrace a weak form of consequentialism—defining a good policy change as
one thatmakes somepeople better off andnooneworse off—then externalities,
coordination problems, and commitment problems all create opportunities for
a variety of policies to do a lot of good. Finally, in Part III we started to take
seriously the politics of policymaking. Governments are not Pareto improving
machines. Policies are made by individuals with their own beliefs, interests,
and goals operating in highly constrained and strategic political environments.
For reasons having to do with fundamental technological constraints and the
incentives created by the institutions of government and the desire for power,
sometimes policymakers take actions that benefit society and sometimes they
take actions that do not benefit society. Often, whether a policy is a good idea—
in the sense of addressing a social dilemma—is neither here nor there with
respect to whether that policy will be pursued or implemented.
The realization that policymaking is so fundamentally political can sit un-
comfortably with the traditions of policy analysis and policy education, which
tend to focus on technocratic concerns such as cost-benefit analysis, program
evaluation, and public administration. Once we accept that the merits of a
policy are, at best, but one input into the highly political policymaking process
we are left wondering, what role is there for traditional policy analysis? And are
traditional approaches likely to lead to good outcomes?
These questions can be unsettling. After all, if policymaking is all about
politics, and politics follows its own strategic logic revolving around the pursuit
of power, what is the point of spending all this effort trying to understand
and articulate good policies? Why did we bother with Part II? We could have
jumped right from Chapter 1 (there is no such thing as good policy) straight to
Chapter 11 (policymakers don’t really care about doing good anyway) and
been done with it. As the economist Dani Rodrik put it in an influential and
thoughtful essay, “If politicians’ behavior is determined by the vested interests
towhich they are beholden, economists’ advocacy of policy reforms is bound to
332 Concluding Reflections
fall on deaf ears. The more complete our social science, the more irrelevant our
policy analysis.”1 I want to conclude with just a few thoughts on these issues.
There are, of course, important roles for traditional policy analysis. Let me
suggest two.
First, in plenty of settings, politicians want to pursue something at least
approximating an optimal policy. In such happy circumstances, when leaders’
incentives and the principles of good policymaking coincide, policymakers are
in need of technocratic advice of the sort traditional policy analysis provides.
Second, ideas themselves are powerful. It is important for informed people to
shout good policy ideas from the mountain tops, even if they often fall on the
deaf ears of political leaders. At least someof the time, good ideas changeminds.
If enough people come to believe in a particular idea, political incentives can
shift.Whoknows, in another couple of generations,wemight yet see politicians
embrace fighting global warming through a carbon tax or paying for a sustained
effort to avoid asteroid-inducedmass extinction.
All of that said, my own view is that, if you want to lead policy change
(whether from within government or from without), depressing though it
may be, it is almost always a mistake to embrace traditional policy analysis
while ignoring the politics of the policymaking process. There is a dangerous
tendency to think of the second-best policy as the optimal policy given all the
constraints except those that come from the policymaking process itself. But
politics are a fundamental constraint onwhat policy outcomes are possible. The
real second best is the optimal policy, given all the constraints—technological,
informational, economic, and political.
We need some idealists fighting for good, if perhaps infeasible, ideas. But we
also need practical policymakers and policy entrepreneurs, willing to rigorously
think throughwhat can actually be achieved and how to achieve it. This kind of
thoroughgoing policy analysis requires not only understanding what problems
need addressing and what policies might work to address them. It requires
taking seriously political constraints that can fundamentally change our notion
of good policy.
Often what seems the second-best policy is not politically feasible. As we
discussed at the very outset of this book, absent political considerations, a
carbon tax coupled with an offsetting reduction in some other distortionary
tax seems an obvious, Pareto improving response to global warming. But once
we consider the need for a policy reform to have a coalition of political support,
both in the short and long run, a cap-and-trade system without a revenue
generating auction may be preferable. The fact that the benefits of increased
efficiency are left with the regulated firms (a concentrated interest), rather than
1Dani Rodrik. “The Tyranny of Political Economy,” Project Syndicate, February 8, 2013.
http://www.project syndicate.org/commentary/how economists killed policy analysis by dani
rodrik
http://www.projectsyndicate.org/commentary/howeconomistskilledpolicyanalysisbydanirodrik
http://www.projectsyndicate.org/commentary/howeconomistskilledpolicyanalysisbydanirodrik
Concluding Reflections 333
transferred to the diffuse citizenry, may make cap-and-trade more politically
feasible than a carbon tax in the short run, since the regulated firms have a
reason to support reform. Moreover, a cap-and-trade system creates a natural
constituency for the long-run sustainability of reform in at least two ways.
First, firms that reduce emissions below the amount allowed by their permits
can bank the surplus for future use or sale. Firms with a significant amount
of carbon permits banked would strongly oppose any attempt to undo reform,
since such regulatory rollback would reduce the value of their banked assets.
Second, the presence of a market gives a new set of previously irrelevant actors
an interest in the sustainability of the reform—financial services companies
and others involved with the actual operation of the market. For both of these
reasons, cap-and-trade creates a natural coalition to ensure long-run viability
(recall our discussion of dynamic consistency). A carbon tax, by contrast, has no
natural constituency beyond environmentalists, making it vulnerable to repeal
by policymakers looking to score political points through tax cutting.
Policies, even once put into law, are implemented and enforced by political
actors whose incentives can distort the policy inmyriad ways. These incentives
must also be taken into consideration when evaluating the likely effects of a
policy. Failure to do so can lead one to support policies that end up having
little, or even deleterious, effects.We saw an example of this in our discussion of
foreign aid. That analysis suggested that advocates for increased foreign aidmay
bedoingmoreharm than good for theworld’s poor. Foreign aid, if implemented
properly,mightwell address poverty traps or, at least, relieve intensemisery. But
political leaders, following their political incentives, may use foreign aid in a
way that systematically harms aid recipients—propping up autocratic leaders
who pursue policies that hurt their own people but help the donor nations.
Finally, the study of political economy opens up the possibility of a whole
new set of policy concerns. Political incentives and political institutions are
themselves key determinants of whether leaders make and enforce good poli-
cies. Hence, the design and adoption of political institutions that give leaders
good incentives is a fundamental policy issue in its own right, one with which
anyone concerned with good governance and good policy must grapple.
Understanding politics, then, is essential to understanding policy. Politics is
a central determinant of the types of policies that can and do get implemented.
Frustrating and limiting as it may seem at times to talk about politics when you
want to talk about policy solutions, no thoroughgoing analysis of public policy
can ignore something so fundamental. It is my hope that the tools in this book
will help you bring the insights of political economy to bear on your own policy
concerns. It is my belief that doing so will lead to a more rigorous and realistic
analysis and, ultimately, more effective policy responses to society’s woes.
PART IV
Appendices on Game Theory
A
Utility, Strategic-Form Games, and
Nash Equilibrium
A rational person in a supermarket deciding what kind of bread to buy has a
pretty easy problem. She has preferences over the different breads, over money
spent, and soon. All shehas to do is think about some simple trade-offs (perhaps
one type of bread is more delicious than another, but also costs more) and buy
the bread that she most prefers, given the prices. This is a classic, non-strategic,
rational choice problem. It is not strategic because the outcome for the decision
maker (what bread she gets, how much she spends) does not depend on the
behavior of anyone but herself. It is a rational choice problem because she has
rational preferences and acts based on them.
Much of what is interesting about the social world is not like buying a loaf of
bread.Most interesting situations are situations of strategic interdependence. That
is, situations inwhich the outcome for one persondepends not only onher own
behavior, but also on the behavior of others.
Understanding such strategic interdependence is critical for identifying op-
portunities for public policy to do good in the world. It is also essential for
understanding some of the challenges that limit the extent to which policy-
makers do so. Unfortunately, analyzing situations of strategic interdependence
can be complicated because a person’s actionsmay depend onwhat she believes
others will do. Game theory is the mathematical tool that we use to structure
our thinking about such situations. It is used extensively throughout this book.
Game theory is a powerful and flexible tool that can be used to study
quite complicated strategic environments—environments with many players,
asymmetric access to information, a variety of kinds of uncertainty, and so on.
Our goal, however, is not to learn game theory for game theory’s sake. Rather,
our purpose is to learn just enough game theory to grasp the social dilemmas
and governance challenges that are the core substantive concerns of this book.
So these appendices are limited to two relatively simple classes of games, which
will be sufficient for our purposes.
Before we get to game theory, however, we need to say a little bit more about
our model of rational decisionmakers.
338 Appendix A
A.1 Utility
In Chapter 2 I describe a rational person as someone whose preferences are
complete and transitive. For now, let’s stick with that.
Preferences are a bit unwieldy to work with, if only because you have to
constantly write this symbol, �. Happily, it turns out that the preferences of
a rational individual can be represented in amuchmore user-friendly way, with
numbers.
Suppose a person has rational preferences over a set of alternatives, A. That
means the person can take all the alternatives in A and line them up in order
of preference (there might be some stacks, representing indifference). Suppose
we line them up from least preferred to most preferred. If we then assign
each alternative a number in ascending order (giving the same number to all
alternatives in an indifference stack), we have constructed a utility function.
Person i’s utility function is any function that assigns a number to each alter-
native and satisfies the following condition: person i’s utility from alternative x
is greater than her utility from alternative y if and only if x �i y and her utility
from alternative x is equal to her utility from alternative y if and only if x ∼i y.
Utility functions are useful because it is easier to work with numbers than it is
to work with preference relations. Typically, we will write person i’s utility from
alternative x as ui(x), which, again, is just a number.
One point is worth noting. There are many utility functions that represent
a given preference. If i prefers x to y, then this utility function represents that
preference:
ui(x) = 10 ui(y) = 1
and so does this utility function:
ui(x) = 1,000,000 ui(y) = −132.42323.
This is because, as we’ve defined them thus far, all the information a utility
function communicates is ordinal (about the order of preference) not cardinal
(about the magnitude of preference). Importantly, this means that the notion
of utility that we’ve used to define rationality is fundamentally different from
the notion of utility that underlies utilitarianism—for utilitarianism to make
sense, utilities need to be comparable across individuals (i.e., need to be on
a common scale), whereas even within an individual’s preferences, let alone
across individuals, the scale is meaningless for our ordinal notion of utility.
A.1.1 Expected Utility
Sometimes we want to be able to think about the preferences of rational
people who face some uncertainty. (We talk about this in our discussion of
Strategic-Form Games 339
preferences behind the veil of ignorance in Chapter 1.) Consider, for example, a
rational person deciding whether or not to carry an umbrella without knowing
for certain whether it is going to rain. Such a person faces four possible out-
comes:
1. No Umbrella, No Rain (NN)
2. Umbrella, No Rain (UN)
3. No Umbrella, Rain (NR)
4. Umbrella, Rain (UR)
Presumably it is unpleasant to get wet and also a little annoying to carry an
umbrella around. So, if such a person knew it wasn’t going to rain, she would
not carry an umbrella. And if she knew it was going to rain, she would carry an
umbrella (assuming getting wet is more annoying than carrying an umbrella).
But she doesn’t knowwhether or not it will rain. All she knows is the probability
it is going to rain according to the weather report.We need a way tomodel how
she uses her information about the probability of rain and her preferences over
these four possible outcomes to make a decision.
Our standard utility functions, unfortunately, are not up to the task of
addressing this issue. That is because, in order to answer questions like “how
high does the probability of rain need to be for me to be willing to carry an um-
brella?” we need some information about the cardinality of my preferences—
how intensely do I dislike being wet relative to my annoyance at carrying an
umbrella?
To think about such choices, we model a decision maker choosing between
alternatives that are themselves lotteries. A lottery is a probability distribution
over various possible outcomes. For instance, suppose the probability of rain
is p. Then a decision maker choosing whether or not to carry an umbrella is
choosing between the following two lotteries:
Lottery 1 (don’t carry an umbrella): “No Umbrella and Rain” with
probability p and “No Umbrella and No Rain” with probability 1 − p.
Lottery 2 (carry an umbrella): “Umbrella and Rain” with probability
p and “Umbrella and No Rain” with probability 1 − p.
In order to deal with preferences over lotteries, we need people’s preferences
to have a little more structure than just being complete and transitive. In
particular, suppose their preferences satisfy two additional requirements:
1. Continuity: Suppose there are three lotteries L1,L2, and L3 such that
person i has preferences
L1 �i L2 �i L3.
340 Appendix A
Then there exists a probability p such that person i is indifferent
between lottery L2 and a new lottery that gives lottery L1 with
probability p and lottery L3 with probability 1 − p.
2. Independence: Suppose there are three lotteries L1,L2, and L3 and
person i has preference
L1 �i L2.
Then for any probability p, person i prefers a new lottery that gives
lottery L1 with probability p and lottery L3 with probability 1 − p to a
new lottery that gives lottery L2 with probability p and lottery L3 with
probability 1 − p.
I’m not going to go into technicalities, but it turns out that if preferences
over lotteries are complete, transitive, continuous, and independent, then pref-
erences can be described by a von Neumann-Morgenstern (vnm) utility function,
which has the following property. For each possible outcome, the vnm utility
function assigns a number, just like a normal utility function. If you want
to know whether a person prefers one lottery to another, you compare their
expected utilities. You find a person’s expected utility for a lottery bymultiplying
the utility associated with each outcome by the probability of that outcome
occurring, and then summing.
Let’s go back to our rain example and assume some person, i, has preferences
described by the following vnm utility function:
ui(NN) = 9 ui(UN) = 6 ui(NR) = 0 ui(UR) = 3.
Suppose the probability of rain is 13 . If person i carries an umbrella she faces
the following lottery: the outcome is UN with probability 23 and the outcome is
URwith probability 13 . So her expected utility from carrying an umbrella, given
that the probability of rain is 13 , is
EUi
(
Umbrella|1
3
)
= 2
3
× 6 + 1
3
× 3 = 5.
If she chooses not to carry an umbrella, she faces the following lottery: the
outcome isNN with probability 23 and the outcome isNRwith probability
1
3 . So
her expected utility from not carrying an umbrella, given that the probability
of rain is 13 , is
EUi
(
NoUmbrella|1
3
)
= 2
3
× 9 + 1
3
× 0 = 6.
Strategic-Form Games 341
Given that the probability of rain is 13 , person i prefers not to carry an umbrella,
since an expected utility of 6 is greater than an expected utility of 5.
Notice, we can also now ask the more general question, “how high must the
probability of rain be in order for person i to carry an umbrella?” To answer this
question, we solve for the probability of rain that makes the expected utility
of carrying an umbrella higher than the expected utility of not carrying an
umbrella. Suppose the probability of rain is some number p between 0 and 1.
This implies the probability of no rain is 1 − p. Given this, person i’s expected
utility of carrying an umbrella is
EUi
(
Umbrella|p) = (1 − p) × 6 + p × 3 = 6 − 3p.
(Notice, for p = 13 , this equals 5, as we found above.) Her expected utility from
not carrying an umbrella is
EUi
(
NoUmbrella|p) = (1 − p) × 9 + p × 0 = 9 − 9p.
(Again, for p = 13 this equals 6, as we found above.)
Person i prefers to carry an umbrella if and only if the expected utility of
carrying an umbrella is greater than the expected utility of not carrying an
umbrella, given that it rains with probability p:
6 − 3p > 9 − 9p.
Rearranging, this holds if p > 12 . So, in this particular case, person i prefers to
carry an umbrella if the probability of rain is greater than one-half.
There is nothing special about a probability of rain equal to one-half. That
just happened to be the threshold for carrying anumbrella in this example. Sup-
pose, for instance, that another person, j, has a vnm utility function given by
uj(NN) = 12 uj(UN) = 6 uj(NR) = 0 uj(UR) = 3.
Person j’s expected utility from carrying an umbrella, given a probability of rain
p, is
EUj
(
Umbrella|p) = (1 − p) × 6 + p × 3 = 6 − 3p.
Person j’s expected utility from not carrying an umbrella is
EUj
(
NoUmbrella|p) = (1 − p) × 12 + p × 0 = 12 − 12p.
So person j prefers to carry an umbrella if
6 − 3p > 12 − 12p.
342 Appendix A
Rearranging, this holds if p > 23 . Person j, who really values not carrying an
umbrella on sunny days, only carries an umbrella if he believes the probability
of rain is at least two-thirds.
It is worth noting that a vnm utility function does let us compare the
relative value of alternatives within an individual’s preferences. That is, it lets
us make statements like, “I care more about avoiding getting wet than about
the annoyance of carrying an umbrella.” But even this isn’t strong enough to
provide a foundation for utilitarianism. For that, we need to be able to compare
strength of preference across people. That is why we rely on quasi-linearity for
much of the book.
A.2 Games in Strategic Form
Now that we have a technology for modeling payoffs let’s turn to game theory.
Wewill start by focusing on games in strategic form. Such games are described by
three components:
1. Players: The collection of people playing the game.
2. Strategies: For each player, a list of things that player can do in the
game.
• Wewill call a collection (or, more correctly, a profile) of
strategies—one for each player—an outcome of the game. The
idea is, if you know how everyone will play, you knowwhat
will happen in the game.
3. Payoffs: A description of each player’s preferences over the set of
possible outcomes.
It will help to look at some examples.
A.2.1 Where to Eat?
Suppose a married couple, Ethan and Rebecca, are deciding where to eat.
They have two options: a delicious pork restaurant or a not-so-delicious vege-
tarian restaurant. Sadly, they are both coming straight from work and their cell
phones are dead, so they can’t talk. Each must simply go to a restaurant and
hope the other has chosen the same place.
A strategy for each player is simply a choice of restaurant. Thus, the strategies
available to each player are pork (P) or vegetarian (V). An outcome of the game is
a strategy profile (one strategy for each player). Let’s write a strategy profile as a
pair, with Ethan’s strategy first. There are four possible outcomes of this game:
(P,P), (P,V), (V,P), and (V,V).
Strategic-Form Games 343
V
1, 1
P
Rebecca
P
V
Ethan
4, 3
3, 40, 0
Figure A.1. Where to eat?
T
–1, 1
H
Kid 2
H
T
Kid 1
1, –1
1, –1–1, 1
Figure A.2. Matching pennies.
The last thing we need to describe our game is payoffs. As it turns out, Ethan
loves pork. Rebecca, being a rabbi, prefers to eat vegetarian. However, they love
each other, so themost important thing to each of them is to eat together. Their
payoffs are given by the following vnm utility functions:
uE(P,P) = 4 uE(P,V) = 1 uE(V,P) = 0 uE(V,V) = 3
uR(P,P) = 3 uR(P,V) = 1 uR(V,P) = 0 uR(V,V) = 4
These payoffs reflect two things. Each player prefers to go to his or her less-
preferred restaurant with the other than to go to his or her more-preferred
restaurant alone. That said, conditional on both being together, Ethan would
prefer they were eating pork and Rebecca would prefer they were eating vege-
tarian. And, conditional on eating separately, they agree that Ethan should eat
pork and Rebecca should eat vegetarian.
It is sometimes useful to represent a simple game like this as a matrix.
In Figure A.1, Ethan’s strategies are the rows and Rebecca’s strategies are the
columns. The payoffs in each cell represent Ethan’s and Rebecca’s payoffs (with
the row player’s always written first) from the outcome associated with that
cell’s strategy profile.
A.2.2 Matching Pennies
There are two kids, 1 and 2. Eachhas a penny. Simultaneously, each kid shows
heads (H) or tails (T). If the pennies match, kid 1 wins and gets to keep both
pennies. If the pennies don’t match, kid 2 wins and gets to keep both pennies.
Each kid cares only about money. This game is represented in the matrix in
Figure A.2.
344 Appendix A
A.2.3 Cleaning an Apartment
There are two roommates, 1 and 2. They must each decide how hard to work
on cleaning up their apartment. Each will choose a level of work. Call Player i’s
level of work si and assume that si is chosen from the set of real numbers greater
than or equal to zero. The total cleanliness of the apartment is
π(s1, s2) = s1 + s2 +
s1 × s2
2
.
This says that the harder each works, the cleaner the apartment will be. More-
over, the third term (s1 × s2/2) indicates that the harder Player 1 works, the
more effective Player 2’s effort and vice versa.
To see this last point, suppose s1 = 1. If Player 2 increases her effort from 1 to
2, total cleanliness goes from
π(1, 1) = 1 + 1 + 1 × 1
2
= 2.5
to
π(1, 2) = 1 + 2 + 1 × 2
2
= 4.
So,when s1 = 1, an increase in effort by Player 2 from1 to 2 increases cleanliness
by 4 − 2.5 = 1.5.
Now suppose s1 = 2. If Player 2 increases her effort from 1 to 2, total cleanli-
ness goes from
π(2, 1) = 2 + 1 + 2 × 1
2
= 4
to
π(2, 2) = 2 + 2 + 2 × 2
2
= 6.
Here an increase in effort by Player 2 from 1 to 2 increases cleanliness by 6 − 4 =
2. Player 2’s increase in effort makes more of a difference for total cleanliness
when Player 1 is working harder. We refer to situations like this as Player 1’s
effort and Player 2’s effort being complements.
Players enjoy a clean apartment. However, the players also suffer costs for
their individual effort. To capture these costs in a simple model, let’s assume
that if Player iworks si, she suffers costs s2i .
Given all this, Player 1’s payoff from an outcome (s1, s2) is
u1(s1, s2) = π(s1, s2) − (s1)2 = s1 + s2 +
s1 × s2
2
− (s1)2
xiafm
Highlight
Strategic-Form Games 345
and Player 2’s payoff is
u2(s1, s2) = π(s1, s2) − (s2)2 = s1 + s2 +
s1 × s2
2
− (s2)2.
There are an infinite number of outcomes in this game, so we can’t represent
it in a matrix. Nonetheless, it is a perfectly well-specified game that we might
want to analyze.
A.2.4 Choosing a Number
There are two players who have $10 to split. Each bids a number between 0
and 10, inclusive. Call Player 1’s bid s1 and Player 2’s bid s2. If the two bids sum
to 10 or less (i.e., s1 + s2 ≤ 10), then each player receives his or her bid. If the two
bids sum to more than 10, then each player receives nothing. Each player cares
only about his or her individual, monetary payoffs.
Player 1’s payoff from any outcome (s1, s2) is
u1(s1, s2) =
⎧
⎨
⎩
s1 if s1 + s2 ≤ 10
0 if s1 + s2 > 10.
Player 2’s payoff from any outcome (s1, s2) is
u2(s1, s2) =
⎧
⎨
⎩
s2 if s1 + s2 ≤ 10
0 if s1 + s2 > 10.
Again, this game has an infinity of possible outcomes, so we cannot represent it
in a matrix.
A.3 Nash Equilibrium
Situations of strategic interdependence are complicated—for both the players
and the analyst. In this section, we develop the main tool we use for figuring
out what might happen in such situations:Nash equilibrium.
Recall that a strategy profile is a collection of strategies, one for each player
in the game. A Nash equilibrium is a strategy profile that meets a particular
condition. I’m going to start by telling you the condition and what it means.
Later we’ll turn to the question of why you should care about or believe in Nash
equilibrium as a prediction of what will happen in a game. But first things first,
let’s define a Nash equilibrium.
Intuitively, a strategy profile is a Nash equilibrium if no individual has a
unilateral incentive to change her behavior. What does that mean? A strategy
profile lists what each player will do in the game. The profile is a Nash equilib-
rium if each individual is taking an action that leads to an outcome that is as
346 Appendix A
good for her as possible, holding all other players’ behavior fixed. Now let’s be a
little more formal.
• Suppose our game hasN players.
• The set of all possible strategies for a Player i is Si.
• A particular strategy for Player i is si ∈ Si.
• A strategy profile, (s1, s2, . . . , sN), is a list of strategies, one for each
player. We will sometimes notate this strategy profile as s, where s =
(s1, s2, . . . , sN).
• We will sometimes want to be able to talk about the list of strategies
for everyone but some Player i. We will notate this reduced profile as
s−i = (s1, . . . , si−1, si+1, . . . , sN).
• We will often, then, reconstruct the full profile by combining the
reduced profile and themissing player’s strategy, writing s = (si, s−i).
• Player i’s utility (or payoff) from the strategy profile s = (s1, s2, . . . , sN) is
ui(s).
To make this notation clearer, let’s do an example.
EXAMPLE A.3.1 (BIDDING FOR $10 WITH 3 PLAYERS)
Consider a game with three players. Each gets to name a real number from
0 to 10. Call the number a player chooses her bid. If the three bids sum to 10
or less, each player gets a dollar amount equal to her bid. If the three bids sum
tomore than 10, each player gets nothing. Each player has utility equal to the
money she receives.
We can apply the notation above to this game.
• There are three players, soN = 3.
• For any player, i, the set of strategies is Si = [0, 10]; that is, the real
numbers from 0 to 10.
• Aparticular strategy for a Player i is just one of these real numbers.
• A strategy profile takes the form of three numbers, a bid by Player
1, a bid by Player 2, and a bid by Player 3. For instance, s = (1, 4, 7)
is a strategy profile.
• We could also consider that strategy profile without Player 2’s
strategy. Then we would have s−2 = (1, 7). Similarly, that strategy
profile without Player 1’s strategy is s−1 = (4, 7) and without
Player 3’s strategy is s−3 = (1, 4).
• We can reconstruct the full profile by saying s = (s2, s−2) =
(4, (1, 7)).
(Continued on next page)
Strategic-Form Games 347
• Player i’s utility from an outcome s = (s1, s2, s3) is
ui(s) =
⎧
⎨
⎩
si if s1 + s2 + s3 ≤ 10
0 if s1 + s2 + s3 > 10.
Having established this notation, we can now formally define Nash equilib-
rium.
DefinitionA.3.1. Consider a gamewithN players. A strategy profile s∗ =
(s∗1, s
∗
2, . . . , s
∗
N) is aNash equilibrium of the game if, for every player i,
ui(s
∗
i , s
∗
−i) ≥ ui(s′i, s∗−i)
for all s′i ∈ Si.
This formalizes the intuitive definition I gave above. A strategy profile gives a
strategy for each player: (s∗1, s
∗
2, . . . , s
∗
N). This profile is a Nash equilibrium if every
player, i, wants to play s∗i , assuming everyone else plays according to the strategy
in s∗. That is, no player has a unilateral incentive to change her behavior.
As a quick aside, it isworthnoting thatwehave actually definedwhat is called
a “pure strategyNash equilibrium.” The phrase “pure strategy” refers to the idea
that players take some action for certain—they don’t randomize among various
strategies. For instance, in the bidding game, each player chooses one real
number.We don’t consider the possibility that a playermight use a strategy like
“flip a coin and bid 2 if it comes up heads and bid 7 if it comes up tails.” (Such a
strategy, constructed by playing some pure strategy with some probability and
another pure strategy with some probability, is called a “mixed strategy.”) Since
we only study pure strategyNash equilibria in this book, I don’t qualify the term
Nash equilibriumwith the phrase “pure strategy,” though if you go on to study
more game theory, you will see that terminology.
A.4 Why Nash Equilibrium?
There are several reasons that Nash equilibrium is an appealing prediction for
how people will behave in strategic situations. Let me suggest a few.
A.4.1 No Regrets and Social Learning
Perhaps the most appealing feature of Nash equilibrium is that it satisfies
a sort of “no regrets” criterion. Suppose players use strategies that are part of
348 Appendix A
a Nash equilibrium. Then no player looks at the outcome of the game and
believes she made amistake or wishes she had done something different.
This is an important and appealing stability property. Imagine a group of
players playing a game in the same society over time. Suppose the players start
at some random strategy profile and then adjust their behavior according to
a simple social learning procedure. For instance, suppose at some iteration, t,
each player chooses the behavior that would have made her best off in the
previous iteration, t − 1, given what all the other players did in iteration t − 1.
That is, she naively chooses her action today to make her payoff as high as
possible, assuming no other players change their behavior from yesterday. If
players find themselves, at some point, at a Nash equilibrium, no individual
has an incentive to change her behavior in the next iteration or any iteration
thereafter. By the definition of a Nash equilibrium, every individual is max-
imizing her payoff, given what everyone else did. Hence, under this kind of
social learning story, once thepeople in a society find themselves playing aNash
equilibrium in a particular game, they will keep playing it forever. It is a stable,
or self-reinforcing, pattern of behavior.
Relatedly, if some strategy profile is not a Nash equilibrium, then at least one
player is making a mistake, given what everyone else is doing. Such a person
will therefore change her behavior in the next iteration—that is, the non-Nash
profile is not stable. Now, nothing guarantees that a process of adjustment
like this will lead to a Nash equilibrium. This kind of social learning process
may remain unstable forever—with people adjusting their behavior in every
iteration. But if behavior ever does settle down to something stable, that stable
behavior will be a Nash equilibrium.
A.4.2 Self-Enforcing Agreements
Another appealing feature is that you can think of a Nash equilibrium as a
self-enforcing agreement. Suppose you and I are in some interaction with one
another.Wewant to reach a deal about howwewill behave, butwe cannotwrite
a binding contract that will be enforced by a court. For instance, suppose you
are my research assistant. I am deciding whether to write you a good letter of
recommendation, and you are deciding whether to work hard on my research
project. In such a situation, all you and I can do ismake an agreement and hope
that the other person honors it. If you agree towork hard in exchange for a good
letter and then I write you a bad letter, there is nothing you can do. Similarly, if
I write you a good letter in exchange for hard work, and then you shirk, there is
nothing I can do.
We can describe the interaction over which we are trying to make an
agreement as a game. It might look something like the situation modeled in
Figure A.3 (though I hope not).
Strategic-Form Games 349
Shirk
0, 4
Work hard
RA
Good letter
Bad letter
Professor
4, 3
1, 23, 1
Figure A.3. Professor and research assistant game.
In such a situation, any agreement that you and I will find credible must
be self-enforcing—that is, each of us must individually want to honor the
agreement.What is a self-enforcing agreement that wewould all actually honor
upon playing this game? It is a Nash equilibrium. If we agree to play a Nash
equilibriumprofile, thenwewill actually bewilling to do so, since the definition
of a Nash equilibrium is that, given what you are doing, the thing I’m supposed
to do is, in fact, inmy interest and vice versa. If, however, we try to agree to play
a profile that is not a Nash equilibrium, it is not self-enforcing. At a profile that
is not aNash equilibrium, at least one of us has an incentive to change behavior.
A.4.3 Analyst’s Humility
Finally, for an analyst, there is one more reason to like Nash equilibrium as a
prediction. Suppose you predicted the outcomeof a gamewould be someprofile
that is not aNash equilibrium. Implicitly, youwould be asserting that you know
things about the environment that the players themselves do not know.
Why is this? You apparently have information that supports the conclusion
that a non-Nash profile will be played. The players must not have this same
information. A non-Nash profile is a profile where at least one player would be
better off changing behavior. Thus, if the players had your information, at least
one of themwould alter her behavior and your prediction would be wrong.
While it is not impossible to imagine situations where the analyst believes
she knows things about the game that the players in the game don’t know, as
a general matter this seems a strange assumption. After all, you are just sitting
around solving the game. The players are living it. Who do you think you are?
A.5 Solving for Nash Equilibrium
Okay, we’ve defined a Nash equilibrium and talked about why it may be the
right prediction for what will happen in games. Now let’s talk about how to
actually find a Nash equilibrium.
The basic tool for solving for a Nash equilibrium is called a player’s best
response to the other players’ strategies. A best response by Player i to a profile
of strategies for all the other players is a strategy for Player i that maximizes her
payoff, given what all the other players are doing.
350 Appendix A
Definition A.5.1. A strategy, si, is a best response by Player i to a profile of
strategies for all the other players, s−i, if
ui(si, s−i) ≥ ui(s′i, s−i)
for all s′i ∈ Si.
Notice, there neednot be a unique best response to a givenprofile of strategies
by others. Given what everyone else is doing, Player i may have multiple
strategies that are optimal. An example will help to fix ideas.
EXAMPLE A.5.1 (BIDDING OVER $10 WITH 3 PLAYERS)
Recall the game from Example A.3.1.
Consider Player 1’s best response to the profile of strategies for Players 2 and
3, (9, 9). In this scenario, regardless of what Player 1 bids she will get a payoff
of 0. Hence, any bid is a best response for Player 1.
Now consider Player 1’s best response to a profile of strategies for Players 2
and 3, (3, 3). If Player 1 bids an amount of money less than or equal to 4, she
gets that amount of money. If she bids an amount of money greater than 4,
she gets nothing. Hence, her unique best response to (3, 3) is to bid exactly 4.
Wewould like to be able to think about Player i’s best response to any possible
profile of strategies for the other players. To do this, wewill think about Player i’s
best response correspondence. Player i’s best response correspondence is amapping
that tells you Player i’s best responses to any given profile of strategies for the
other players.
DefinitionA.5.2. Player i’s best response correspondence, BRi, is amapping
from profiles of strategies for all players other than i into subsets of Si
(Player i’s set of possible strategies) satisfying the following condition: For
each s−i, the mapping yields a set of strategies for Player i, BRi(s−i), such
that si ∈ BRi(s−i) if and only if si is a best response to s−i.
We’ve worked through these pretty unpleasant definitions because they
provide us with a straightforward way to solve for Nash equilibria. A Nash
equilibrium is a strategy profile, s∗, where each Player i’s strategy, s∗i , is a best
response to what the other players are doing, s∗−i. Thus, if we can figure out each
player’s best response correspondence, it will be easy to find Nash equilibria.
Let’s do this in a bunch of examples so you can see what I’m talking about.
A.6 Nash Equilibrium Examples
In this section, we will work our way through the examples of strategic-form
games from Section A.2, solving for Nash equilibria in each of them.
Strategic-Form Games 351
V
1, 1
P
Rebecca
P
V
Ethan
4, 3
3, 40, 0
Figure A.4. Where to eat?
A.6.1 Where to Eat?
Recall the game about where a married couple should eat represented in
Figure A.4. Let’s solve for each player’s best responses. Suppose Ethan believes
Rebecca will play P. Then his payoff from playing P is 4 and his payoff from
playing V is 0. So he wants to play P. Now suppose Ethan believes Rebecca will
play V. Then his payoff from playing P is 1 and his payoff from playing V is 3.
So he wants to play V. Given this, Ethan’s best response correspondence is
BRE(P) = P BRE(V) = V.
The logic for Rebecca is the same:
BRR(P) = P BRR(V) = V.
A Nash equilibrium in this game is a strategy profile (s∗E, s
∗
R), such that s
∗
E is a
best response for Ethan to s∗R and s
∗
R is a best response for Rebecca to s
∗
E. There are
four possible strategy profiles—(P,P), (P,V), (V,P), (V,V). Which of these is a
Nash equilibrium?
First consider (P,P). If Rebecca plays P, then Ethan’s best response is BRE(P) =
P. So Ethan is playing a best response to Rebecca’s strategy. Similarly, if Ethan
plays P, then Rebecca’s best response is BRR(P) = P. So Rebecca is playing a best
response to Ethan’s strategy. Thus, this profile is a Nash equilibrium.
Next consider (P,V). If Rebecca plays V, then Ethan’s best response is
BRE(V) = V. So Ethan is not best responding to Rebecca’s strategy. Thus, this
profile is not a Nash equilibrium. Ethan would be better off by unilaterally
changing his behavior to V. (It turns out, Rebecca would also be better off
unilaterally changing her behavior.)
Next consider (V,P). This also is not a Nash equilibrium. If Rebecca is playing
P, then Ethan’s best response is BRE(P) = P, so Ethan could make himself better
off by unilaterally changing his behavior to P. (Rebecca could also unilaterally
make herself better off.)
Finally, consider (V,V). If Rebecca plays V, then Ethan’s best response is
BRE(V) = V. So Ethan is best responding toRebecca’s strategy. Similarly, if Ethan
plays V, then Rebecca’s best response is BRR(V) = V, so Rebecca is also best re-
sponding to Ethan’s strategy. Hence, this strategy profile is a Nash equilibrium.
352 Appendix A
Figure A.5. Matching pennies.
T
–1, 1
H
Kid 2
H
T
Kid 1
1, –1
1, –1–1, 1
This list is exhaustive. The game has two (pure strategy) Nash equilibria. In
one (delicious) equilibrium, both players eat pork. In the other (regrettable)
equilibrium, both players eat vegetarian.
A.6.2 Matching Pennies
Recall the matching pennies game represented in Figure A.5:
Once again, it is not hard to calculate best responses.
BR1(H) = H BR1(T) = T
and
BR2(H) = T BR2(T) = H.
These best responses say that kid 1 always wants to try to match kid 2,
while kid 2 always wants to do the opposite of what kid 1 did. From these best
responses it should be clear that there are no (pure strategy) Nash equilibria
of this game. In any profile in which both players are doing the same thing—
(H,H) or (T,T)—kid 2 is not playing a best response. In any profile in which
the two players are doing different things—(H,T) or (T,H)—kid 1 is not best
responding.
This implies that our Nash equilibrium concept fails to make a prediction for
what will happen in this game. An expanded notion of Nash equilibrium that
allowed for mixed strategies (i.e., kids randomize between heads and tails) does
make a prediction for this game. You might not be surprised to learn that, in
such an equilibrium, each kid will flip her coin.
A.6.3 Cleaning an Apartment
In our cleaning an apartment game, two roommates (1 and 2) each chose
how hard to work at cleaning the apartment. The choices are labeled s1 and s2.
The total cleanliness of the apartment is π(s1, s2) = s1 + s2 + s1×s22 . Player i’s cost
of work is s2i . Player 1’s payoff from a profile (s1, s2) is
u1(s1, s2) = π(s1, s2) − (s1)2 = s1 + s2 +
s1s2
2
− (s1)2
Strategic-Form Games 353
BR1(0.5) BR1(3) BR1(6)
Utility u1(s1, 6)
u1(s1, 3)
u1(s1, 0.5)
s1
Figure A.6. Player 1’s best responses to three of Player 2’s possible strategies.
and Player 2’s payoff is
u2(s1, s2) = π(s1, s2) − (s2)2 = s1 + s2 +
s1s2
2
− (s2)2.
Before we solve for the players’ best response correspondences, let’s draw a
player’s payoffs. The three curves in Figure A.6 each represent Player 1’s utility
as a function of her effort choice, s1 (which increases as we move from left to
right on the horizontal axis). There are three curves because I’ve drawn Player
1’s utility as a function of s1 for three different values of s2 (s2 = 0.5, s2 = 3, and
s2 = 6).
Finding a player’s best response correspondence, here, is mathematically a
bit different from in our previous two games. In this game, there are literally
an infinite number of things the other player can do. A player’s best response
correspondence must tell her what her best strategy is for any possible strategy
by the other player.
Graphically, it is clear what Player 1’s best response correspondence looks
like. For each s2, we find the s1 that maximizes Player 1’s utility. These best
responses are shown in Figure A.6 for three values of s2.
More generally, we can find Player 1’s best response to a choice s2 by maxi-
mizing Player 1’s utility function, treating s2 as fixed.Wedo so by taking the first
derivative, with respect to s1, and setting it equal to zero. The first derivative is
∂u1(s1, s2)
∂s1
= 1 + s2
2
− 2s1.
354 Appendix A
The term1 + s22 represents Player 1’smarginal benefit from increased effort—that
is, how much an incremental increase in her work increases cleanliness. The
term−2s1 represents Player 1’smarginal cost from increased effort—that is, how
much an incremental increase in her work increases her personal costs.
Player 1’s best response to s2 can be found by setting this derivative equal
to zero—that is, setting the marginal benefits equal to the marginal costs. So if
some s′1 is a best response to s2 itmust satisfy the following first-order condition:
1 + s2
2
= 2s′1.
Rewriting this in terms of best responses, we have that for any s2
1 + s2
2
= 2 × BR1(s2).
This can be rewritten
BR1(s2) =
1
2
+ s2
4
.
A similar argument shows that
BR2(s1) =
1
2
+ s1
4
.
What, then, is aNash equilibriumof this game?At aNash equilibrium, Player
1 is playing a best response to Player 2 and vice versa. That is, if (s∗1, s
∗
2) is a Nash
equilibrium, we need the following to hold:
s∗1 = BR1(s∗2) =
1
2
+ s
∗
2
4
and
s∗2 = BR2(s∗1) =
1
2
+ s
∗
1
4
.
Hence, we have a system of two equations and two unknowns. If we solve for
the unknowns, we will have a Nash equilibrium.
To find a pair that satisfies these two requirements, we can substitute. In
the first expression, we can replace s∗2 with
1
2 +
s∗1
4 , since we know that in an
equilibrium, this is what s∗2 must equal. Doing so, we can rewrite the first
condition as
s∗1 =
1
2
+
1
2 +
s∗1
4
4
.
Strategic-Form Games 355
0
1
2–
3
2–
3
BR1(s2) = +
1–
2
s2–
4
BR2(s1) = +
1–
2
s1–
4
0 1
s2
s1
Figure A.7. Best responses in the apartment cleanup game.
Solving for s∗1, we get
s∗1 =
2
3
.
Given this, it is not difficult to find Player 2’s equilibrium strategy:
BR2(s
∗
1) =
1
2
+
2
3
4
= 1
2
+ 1
6
= 2
3
.
Thus, the unique Nash equilibrium of this game is both players choosing effort
equal to 23 .
Above, we solved for the Nash equilibrium algebraically. But we can also
see it graphically, by plotting each player’s best response correspondence. In
Figure A.7, the horizontal axis is Player 1’s effort and the vertical axis is Player 2’s
effort. You read the figure as follows. To find Player 1’s best response to some s2,
move horizontally rightward from s2 (on the y-axis) to the line labeled BR1(s2),
then drop down vertically to the x-axis to find the s1 that is a best response
for Player 1 to that s2. To find a best response for Player 2 to some s1, move
vertically upward from that s1 (on the x-axis) to the line labeled BR2(s1), then
move horizontally leftward to the y-axis to find the s2 that is a best response for
356 Appendix A
Player 2 to that s1. A Nash equilibrium is a point where each player is playing
a best response to the other—that is, where the best response correspondences
intersect. Hence, the only Nash equilibrium is
(
2
3 ,
2
3
)
.
A.6.4 Choosing a Number with Two Players
Let’s turn to the easier “choosing anumber” game—the onewith twoplayers.
Each player bids a number between 0 and 10, inclusive. Call Player 1’s bid s1
and Player 2’s bid s2. If the two bids sum to 10 or less, then each player receives
the dollar value of his or her bid. If the two bids sum to more than 10, then
each player receives nothing. Each player cares only about his or her individual,
monetary payoffs.
Player i’s payoff from any profile (s1, s2) is
ui(s1, s2) =
⎧
⎨
⎩
si if s1 + s2 ≤ 10
0 if s1 + s2 > 10.
Let’s think about Player 1’s best response correspondence. First, suppose
Player 2 makes a bid s2 < 10. If Player 1 bids s1 > 10 − s2, she makes zero. If
Player 1 bids s1 ≤ 10 − s2, she makes s1. Hence, Player 1 maximizes her payoff
by choosing s1 = 10 − s2. Next, suppose Player 2 bids s2 = 10. Then, for any bid,
Player 1 makes a payoff of 0. Hence, any bid is a best response to s2 = 10. So
Player 1’s best response correspondence is
BR1(s2) =
⎧
⎨
⎩
10 − s2 if s2 < 10 Any s1 ∈ [0, 10] if s2 = 10. Player 2’s best response correspondence follows the same logic: BR2(s1) = ⎧ ⎨ ⎩ 10 − s1 if s1 < 10 Any s2 ∈ [0, 10] if s1 = 10. To find the Nash equilibria of this game, we look for pairs (s∗1, s ∗ 2), such that s∗1 ∈ BR1(s∗2) and s∗2 ∈ BR2(s∗1). Let’s start by ruling out some profiles. Consider a profile, (s1, s2), such that s1 + s2 < 10. No such profile is a Nash equilibrium because if the two bids do not sum to at least 10, then one player could unilaterally increase her bid a little bit and improve her payoff. Next, consider a profile such that 10 < s1 + s2 < 20. Such a profile also can- not be a Nash equilibrium. Since s1 + s2 < 20, at least one of s1 or s2 is less than 10. For the sake of argument, suppose s2 < 10. Then Player 1’s unique best response is BR1(s2) = 10 − s2. But, since s1 + s2 > 10 we know that Player 1 is
Strategic-Form Games 357
0
10
BR1(s2)
BR2(s1)
0 10
s2
s1
Figure A.8. The best responses in the two player number bidding game. Intersections of
the best response correspondences are Nash equilibria.
actually choosing s1 > 10 − s2, which is not a best response. So this profile is
not a Nash equilibrium. Substantively, if the sum of the bids is greater than 10
and at least one player is bidding less than 10, then the other player couldmake
herself better off by decreasing her bid so that the bids sum to 10. Doing so, she
moves from a payoff of 0 to a positive payoff.
Now consider a profile such that s1 + s2 = 10. Any such profile is a Nash
equilibrium. If s2 < 10, then Player 1 is best responding by playing 10 − s2. If
s2 = 10, then any bid by Player 1 is a best response, including 0. Similarly, if
s1 < 10, then Player 2 is best responding by playing 10 − s1 and if s1 = 10, then
any bid by Player 2 is a best response, including 0.
The only profile left to consider is (10, 10). If Player 2 bids 10, then Player
1 is indifferent over all her possible bids, so 10 is a best response. Similarly, if
Player 1 bids 10, then Player 2 is indifferent over all his possible bids, so 10 is a
best response. Hence, at (10, 10), both players are best responding.
This analysis implies that the full set of Nash equilibria of this game is
• Any pair (s∗1, s∗2) satisfying s∗1 + s∗2 = 10
• (10, 10).
We can see these equilibria graphically by drawing the two best response
correspondences, as in Figure A.8. The horizontal axis is Player 1’s bid and
358 Appendix A
the vertical axis is Player 2’s bid. The solid line is Player 1’s best response
correspondence. Hence, for any s2, moving over to the solid line and dropping
down to the horizontal axis tells you the s1 (or set of s1’s) that is a best response
by Player 1 to that s2. For any s2 less than 10, this identifies a unique best
response: 10 − s2. For s2 = 10 this shows that any s1 is a best response. Similarly,
the dash-dot line is Player 2’s best response correspondence. For any s1, moving
up to the dash-dot line and thenmoving to the left to the vertical axis tells you
the s2 (or set of s2’s) that is a best response by Player 2 to that s1. For any s1 < 10,
this identifies a unique best response: 10 − s1. For s1 = 10 this shows that any s2
is a best response.
Nash equilibria are points where these two best response correspondences
intersect—along the diagonal line that identifies pairs s1 + s2 = 10 and at the
point (10, 10).
A.7 Takeaways
• A best response by Player i to the strategies of all other players is a
strategy for Player i that gives her at least as good a payoff as any
of her other strategies, given the strategies being played by all other
players.
• Player i’s best response correspondence tells you Player i’s best responses to
all possible profiles of strategies by other players.
• A Nash equilibrium is a profile of strategies (i.e., one strategy for each
player) with the property that each player’s strategy is a best response
to what all the other players are doing.
• Nash equilibrium is the primary tool we use to generate predictions
from games. It can be justified on a variety of grounds including
no regrets, self-enforcing agreements, social learning, and analyst
humility.
A.8 Exercises
1. Consider a person deciding whether to go back to graduate school next year.
The person is making this decision facing uncertainty about what next
year’s jobmarket is likely to look like. Her most preferred outcome is not to
go to school and have a good jobmarket. Her next most preferred outcome
is to go to school and have a good jobmarket. Her next most preferred
outcome is to go to school and have a bad jobmarket. And, from her
perspective, the worst possible outcome is to not go to school and have a bad
jobmarket. Suppose she has a vnm expected utility function over the four
Strategic-Form Games 359
possible outcomes given by
u(No School, Good JobMarket) = 10
u(School, Good JobMarket) = 8
u(School, Bad JobMarket) = 7
u(No School, Bad JobMarket) = 1.
Suppose, finally, that she believes the probability of a good jobmarket is a
number p between 0 and 1.
(a) Calculate her expected utility from going to school.
(b) Calculate her expected utility from not going to school.
(c) For what values of p is going back to school a best response?
2. Consider the game in Figure A.9, in which each player can either act
collaboratively or selfishly. If the players both collaborate, then they get a very
good outcome. But if one player acts selfishly, the other wants to act
selfishly.
(a) Write down each player’s best response correspondence.
(b) Identify all the (pure strategy) Nash equilibria of the game.
S
0, 2
C
Player 2
C
S
Player 1
3, 3
1, 12, 0
Figure A.9. Collaboration game.
3. Consider the game of chicken in Figure A.10. A player can continue or swerve.
The goal is to continue and have your opponent swerve. But if you both
continue, you crash, which is bad.
(a) Write down each player’s best response correspondence.
(b) Identify all the (pure strategy) Nash equilibria of the game.
S
3, 1
C
Player 2
C
S
Player 1
0, 0
2, 21, 3
Figure A.10. Chicken.
4. Consider the military escalation game in Figure A.11:
(a) Write down each player’s best response correspondence.
(b) Identify all the (pure strategy) Nash equilibria of the game.
360 Appendix A
Arm
0, 3
Don’t arm
Country 2
Don’t arm
Arm
Country 1
4, 4
1, 13, 0
Figure A.11. Military escalation.
5. Consider a game in which there are 3 people. Each player can either
participate or not participate in a revolution. If at least 2 people participate,
the revolution succeeds.
If the revolution succeeds, each player gets a benefit of B. If the revolution
fails, each player gets a benefit of 0. Each player who participates bears a cost
c < B, whether or not the revolution succeeds.
(a) Write down each player’s best response correspondence.
(b) Is it a Nash equilibrium for no players to participate?Why or why not?
(c) Is there a Nash equilibrium in which only one player participates?Why
or why not?
(d) Is there a Nash equilibrium in which only two players participate?Why
or why not?
(e) Is it a Nash equilibrium for all three players to participate?Why or why
not?
6. Two firms each decide howmany widgets to produce. Firm 1 produces s1
widgets and Firm 2 produces s2 widgets. The price per widget is 100 − s1 − s2.
The cost of producing swidgets is s2. Hence, Firm 1’s profits are
(100 − s1 − s2) × s1 − s21
and Firm 2’s profits are
(100 − s1 − s2) × s2 − s22.
Firms’ utilities are equal to their profits.
(a) What is Firm 1’s best response if Firm 2 produces 100 or more widgets?
(b) Use calculus to derive each firm’s best response correspondence,
assuming the other firm produces fewer than 100 widgets.
(c) Draw the best response correspondences and identify the Nash
equilibrium graphically.
(d) Now solve for the Nash equilibrium. Do this in three steps:
• Substitute Firm 2’s best response correspondence (assuming
Firm 1 produces fewer than 100 widgets) into Firm 1’s best
Strategic-Form Games 361
response correspondence to find out Firm 1’s equilibrium
number of widgets.
• Substitute this back into Firm 2’s best response correspondence
to find Firm 2’s equilibrium number of widgets.
• Confirm that these are in fact less than 100.
(e) Argue that there is not an equilibriumwhere either firm produces 100 or
more widgets.
7. Four students—let’s call them 1, 2, 3, and 4—are in a study group together.
Eachmust simultaneously and independently decide whether or not to
study before their study session. Studying will help them pass their
midterm. The value to a student of passing themidterm is 8. The value of
failing is 0.
A student who does not study passes with probability 1/8. A student who
studies passes with probability n/4, where n is the number of students
(including himself) who studied. By way of example, if only students 1, 2,
and 3 studied, they would each pass with probability 3/4 and student 4
would pass with probability 1/8.
Different students face different costs from studying. In particular, the cost
to student 1 is 1, the cost to student 2 is 2, the cost to student 3 is 6, and the
cost to student 4 is 8.
Suppose each student aims tomaximize her expected payoff. Expected
payoffs are found as follows. Suppose only students 1, 2, and 3 study. Then
student 1’s expected payoff is 34 × 8 − 1 = 5, student 2’s expected payoff is
3
4 × 8 − 2 = 4, student 3’s expected payoff is 34 × 8 − 6 = 0, and student 4’s
expected payoff is 18 × 8 = 1.
(a) Is it a Nash equilibrium for all students to study?
(b) Is it a Nash equilibrium for students 1, 2, and 3 to study, but not student
4?
(c) Is it a Nash equilibrium for students 1 and 2 to study, but not students 3
and 4?
(d) Is it a Nash equilibrium for just student 1 to study?
(e) Is it a Nash equilibrium for no one to study?
B
Extensive-Form Games
Thus far, we have studied games in strategic form, which can be fully repre-
sented in terms of players, strategies, and payoffs. The strategic form can be
understood to represent complex games with multiple moves over time. The
way to do so is to think about a player’s strategy in such a game as a complete con-
tingent plan which states what a player would do in every possible contingency
that could arise. If all players submitted such a complete contingent plan to a
computer, the computer could play the game for the players and tell them the
outcome. Hence, all that we need to describe such a game is the players, all their
possible strategies (this could get very complicated, since a complete contingent
plan in a long game is a very big object), and payoffs for the outcome associated
with every possible profile of strategies.
To see what I’m talking about, think about the game tic-tac-toe. This game
is played dynamically—first the X player moves, then the O player moves, then
the X player moves again, and so on. We can think of a tic-tac-toe strategy as a
complete contingent plan for the game and then represent the game in strategic
form.
What would a strategy look like for the X player? It would say what X does as
a first move. Then it would say what X does for a second move for every possible
combination of firstmoves byX and secondmoves byO. Then itwould saywhat
X does as a thirdmove for every possible combination of first moves byX andO
and secondmoves byX andO. And so on.
You can imagine, even in a simple game like tic-tac-toe, a complete con-
tingent plan for a player will get very complicated. Nonetheless, in theory, we
could write such a strategy down. Indeed, we could write down all the possible
complete contingent plans for each player, so that we knew the full set of
strategies, Si, for each Player i. And once we’d done so, we could analyze the
game for its Nash equilibria.
All that said, sometimes it is useful to explicitlymodel the dynamic nature of
a game. In this appendix, we will learn how to do so.
B.1 Games in Extensive Form
Wemodel the dynamics of a game using the extensive form. A game in extensive
form is described by four things:
Extensive-Form Games 363
Figure B.1. A terminal history of tic tac toe in which Xwins.
1. A list of players.
2. A player functionwhich tells us whose turn it is tomove at every possible
point in the game.
3. A list of possible paths through the game, called terminal histories.
4. Player preferences over terminal histories (i.e., over things that can
happen in the game).
These four pieces of information fully describe the game.
Figures B.1 and B.2 show two terminal histories of tic-tac-toe. In Figure B.1,
the X player wins. In Figure B.2, there is a tie. Of course, there are many other
terminal histories of this game.
You can also see from this example why preferences are defined over ter-
minal histories in games like this. In the case of tic-tac-toe, players care about
winning—which is determined by a terminal history. For instance, presumably
the X player likes the terminal history in Figure B.1 better than the terminal
history in Figure B.2.
Fascinating as tic-tac-toe is, let’s move on to an example with a little more
substantive motivation.
B.1.1 A Model of International Crisis
Consider two countries—call them A and B—engaged in a dispute over a
piece of landwhichB currently controls. At the beginning of the game,Country
A decides whether or not to demand the land from Country B. If A makes
no demand, the game ends peacefully. If A makes a demand, Country B must
decide whether to acquiesce toA’s demand or start a war. If B acquiesces, thenA
gets the land and the game ends. If B starts a war, then the game ends with the
two countries fighting.
A’s most preferred outcome is to get the land. A’s least preferred outcome is
to fight a war. B’s most preferred outcome is to keep the land peacefully. B’s least
364 Appendix B
Figure B.2. A terminal history of tic tac toe in which there is a tie.
preferred outcome is to fight awar. This story constitutes a complete description
of an extensive-form game.
• Players: A and B
• Player Function:
– At the beginning of the game Amoves.
– If Amakes a demand, Bmoves.
• Terminal Histories:
– NoDemand
– (Demand, Acquiesce)
– (Demand,War)
• Preferences:
– uA(Demand, Acquiesce) = 3, uA(No Demand) = 2,
uA(Demand,War) = 1
– uB(No Demand) = 3, uB(Demand, Acquiesce) = 2,
uB(Demand,War) = 1
Beforewe learn to analyze such games, let’s find an easierway to represent them.
B.2 Game Trees
It is often convenient to represent an extensive-form game with a game tree. A
game tree is a full description of the game. It shows the players, player function,
preferences, and terminal histories.
Extensive-Form Games 365
B.2.1 International Crisis Game
Figure B.3 represents the international crisis game on a tree. The A at the
top of the figure indicates that Country Amoves at the beginning of the game.
The two branches are labeled with each of A’s possible actions—D for demand
and ND for no demand. If A makes no demand, the game ends (i.e., ND is a
terminal history). At the end of that branch, the two numbers indicate the
players’ payoffs (2 for A and 3 for B). If A makes a demand, then it is B’s turn
to move (as indicated on the tree). B can do one of two things: declare war (the
left branch) or acquiesce (the right branch). Either move by B takes us to the
end of a terminal history and payoffs are indicated, with Country A’s payoffs
first because Country Amoved first in the game.
ND
War Acq
D
A
1
1
2
3
3
2
B
Figure B.3. International crisis game on a tree.
B.2.2 A Budget Game
Figure B.4 represents a game between the Congress and the president.
Congress starts the game by passing a large budget or a small budget. The pres-
ident then decides whether to sign or veto the budget. Let’s assume Congress
wants a small budget and the president wants a large budget. Moreover, the
president dislikes the small budget enough that she is willing to veto it. Payoffs
are represented after each terminal history, with Congress’s listed first.
Sign Veto
Small
Congress
Large
Pres.Pres.
Sign Veto
5
2
0
3
3
5
1
0
Figure B.4. The budget game in extensive form.
366 Appendix B
Figure B.5. The centipede game.
1
Out
2
3
3
1
2
Out
0
2
1 In In In
Out
1
0
B.2.3 The Centipede Game
Figure B.5 represents another classic game—the centipede game (named for
the shape of the tree that represents it). In this game, there are two players. The
game starts with Player 1 choosing In orOut. If he goesOut, the game ends. If he
goes In the game continues and Player 2 chooses In or Out. If she goes Out, the
game ends. If she goes In the game continues and Player 1 again chooses In or
Out, at which point the game ends regardless of what Player 1 did.
At each terminal history, payoffs are shown. Player 1’s payoffs are always
listed first. The key feature of the centipede game is that, if a player goes In,
he or she raises the future payoffs for the other player. So this is a game that
captures some interesting dynamics about players trying to establish trust with
one another. We will discuss it in greater detail later.
B.3 Strategies as Complete Contingent Plans
Now that we’ve seen what a game in extensive form is, we need to be a little
more precise about strategies. As I said at the outset, a strategy for a player is a
complete contingent plan. That is, it is a statement of what that player would do at
every point in the game where it is that player’s turn to play. The definition of a
strategy in an extensive-form game is often a major source of confusion, so we
are going to go through each of our examples in detail.
B.3.1 International Crisis Game
Strategies are easy in the international crisis game in Figure B.3. Each player
moves only once. Country A has two strategies: Demand or No Demand.
Similarly, Country B has two strategies: War or Acquiesce. Notice, given the
dynamic structure of this game, Country B only gets to move if Country A
chooses Demand. Thus, one should understand Country B’s strategy “War” as
being a contingent plan of the form: “If Country Amakes a demand, I will go to
war,” and similarly with the strategy Acquiesce.
B.3.2 Budget Game
Strategies are only a little more complicated in the budget game represented
in Figure B.4. Congress moves in only one place and has only two actions
available. So, Congress has two strategies: Small and Large.
Extensive-Form Games 367
The president, however, has the potential tomove in two different places: fol-
lowing a large budget proposal and following a small budget proposal. A strategy
for the president must specify what she would do in either circumstance.
I will write a strategy for the president as a pair, where the first element of the
pair represents what she would do following Large and the second element of
the pair represents what she would do following Small. The president has four
possible strategies:
• (Sign, Sign)
• (Sign, Veto)
• (Veto, Sign)
• (Veto, Veto)
Remember, a strategy for the president is a complete contingent plan. So, for
instance, the strategy (Sign, Veto) should be understood to mean: “If Congress
passes a large budget, I will sign. If Congress passes a small budget, I will veto.”
B.3.3 The Centipede Game
Things are even a little more complicated in the centipede game represented
in Figure B.5. Here, Player 1 has two potential opportunities to move—at the
beginning of the game and after both players play In. Hence, a strategy for
Player 1 must say what Player 1 will do at each of the points where he might
be called on to play. I will write a strategy for Player 1 as a pair, where the first
element in the pair says what Player 1 does at the beginning of the game and
the second element in the pair says what Player 1 would do if called on to play
at the end of the game. Player 1 has four strategies:
• (In, In)
• (In, Out)
• (Out, In)
• (Out, Out)
It is at this point that things tend to get confusing for people. I suspect you
are wondering to yourself what the strategies (Out, In) and (Out, Out) could
possibly mean. If Player 1 knows he is going to play Out at the beginning of the
game, there is no way he could possibly be called on to act later in the game. So
it is weird that his strategy has a plan for later in the game. To see what I mean,
notice that the strategy (Out, In)means “PlayOut atmy firstmove. If I played In
at my first move and Player 2 played In, then play In at my secondmove.” Why
must Player 1’s strategy say what he will do in his second move following In by
both himself and Player 2, when he knows he will actually play Out at his first
move?
368 Appendix B
Acquiesce
3, 2
War
Country B
Demand
No demand
Country A
1, 1
2, 32, 3
Figure B.6. International crisis game.
The answer is this. Player 1’s strategy must be a complete contingent plan. It
says what he would do were he to reach any point in the game where he might
be called on to play—even if he knows he will not reach that point. That may
seem strange. It will become clear why we define strategies this way. For now, I
simply ask that you accept that strategies are so defined and play along.
A strategy for Player 2 in this game is more straightforward. Player 2 only
has one spot where she can move. Hence, she has only 2 possible strategies:
In or Out.
B.4 Representing an Extensive-Form Game as a Strategic-Form Game
Now that we understand that a strategy is a complete contingent plan, it is
straightforward to move back and forth between extensive-form and strategic-
form representations of games. Let’s do so for each of our examples.
B.4.1 The International Crisis Game
In the international crisis game represented in Figure B.3, each player has two
strategies. Country A can make a demand or no demand. Country B can start a
war or acquiesce. Thus, there are four possible strategy profiles: (Demand,War),
(Demand, Acquiesce), (No Demand,War), and (No Demand, Acquiesce).
While the game has four strategy profiles, it only has three terminal histories
(and, so, three sets of payoffs). The reason for the discrepancy is that the strategy
profiles (No Demand, War) and (No Demand, Acquiesce) lead to the same
terminal history: No Demand. When we move from representing this game on
a tree, to representing it in a matrix, this will mean that the cells representing
these two strategy profiles will have the same payoffs in them. Figure B.6 is a
matrix representation of the international crisis game.
B.4.2 The Budget Game
In the budget game from Figure B.4, Congress has only two strategies: Large
or Small. The president, however, has four strategies: (Sign, Sign), (Sign, Veto),
(Veto, Sign), and (Veto, Veto). As a result, when we put this game in amatrix, as
in Figure B.7, there are four columns (one for each strategy of the president) and
two rows (one for each strategy of the Congress).
Extensive-Form Games 369
3, 5
(Sign, Sign) (Sign, Veto)
President
Large
Small
Congress
3, 5
0, 35, 2
1, 0
(Veto, Sign)
5, 2
1, 0
(Veto, Veto)
0, 3
Figure B.7. Budget game.
Out
0, 2
In
Player 2
(In, In)
(In, Out)
(Out, In)
(Out, Out)
Player 1
2, 3
0, 23, 1
1, 01, 0
1, 01, 0
Figure B.8. Centipede game.
Although the matrix has eight cells, there are only four terminal histories of
the game. For instance, the strategy profile (Large, (Sign, Sign)) and the strategy
profile (Large, (Sign, Veto)) lead to the same terminal history (and, so, the same
payoffs): the Congress proposes a large budget and the president signs it. The
reason the two profiles lead to the same payoffs is that, once the Congress
has proposed a large budget, it is irrelevant for the outcome of the game what
the president would have done had the Congress proposed a small budget.
Nonetheless, since the president’s strategy is a complete contingent plan, her
strategy has to say what she would have done in that eventuality.
B.4.3 The Centipede Game
Finally, in the centipede game, Player 1 has four strategies while Player 2 has
only two. Again there are eight strategy profiles and four terminal histories.
Figure B.8 shows the game in amatrix.
B.5 Nash Equilibria of Extensive-Form Games
ANash equilibrium in an extensive-form game is no different than a Nash equi-
librium in a strategic-form game. It is a strategy profile—that is, one complete
contingent plan for each player—inwhich each player is playing a best response
to what the other players are doing.
Let’s solve for the Nash equilibria in each of our examples.
370 Appendix B
B.5.1 International Crisis Game
It is straightforward to calculate best responses for the international crisis
game represented in Figures B.3 and B.6. Country A’s best response correspon-
dence is
BRA(War) = NoDemand
BRA(Acquiesce) = Demand.
This says that if Country A believes that Country Bwill go to war if challenged,
then Country A should back down, making no demand. However, if Country A
believes Country Bwill acquiesce, then Country A should make a demand.
Now consider Country B’s best response correspondence:
BRB(Demand) = Acquiesce
BRB(NoDemand) = {War,Acquiesce}.
B’s best response correspondence is slightly more subtle. If Country B believes
Country A will make a demand, then she is best off playing the strategy
Acquiesce, since
u2(Demand,Acquiesce) = 2 > 1 = u2(Demand,War).
However, if Country B believes Country A will make no demand, then she
is indifferent between her two strategies. This is because, in the event that
Country A makes no demand, what Country B would have done had Country
Amade a demand is irrelevant in terms of payoffs.
Given these best response correspondences, the international crisis gamehas
exactly two Nash equilibria:
1. (Demand, Acquiesce)
2. (No Demand,War)
To see that the first is a Nash equilibrium, note that Demand is a best response
to Acquiesce and that Acquiesce is a best response to Demand. To see that the
second is a Nash equilibrium, note that No Demand is a best response to War
and that War is a best response to No Demand. I leave it to you to convince
yourself that the other two possible strategy profiles are not Nash equilibria.
This analysis may seem a bit fishy to you. In particular, you may be worried
that the (No Demand, War) equilibrium doesn’t make any sense. In this equi-
librium, Country B plays the strategy “go towar if CountryAmakes a demand.”
Country A makes no demand. The reason it is a best response for Country A
to make no demand in this equilibrium is as follows: if Country A made a
demand, then according to Country B’s strategy, Country B would go to war,
Extensive-Form Games 371
which Country Awants to avoid. Thus, Country A is deterred. But it is deterred
in a weird way. After all, going to war is bad for Country B. She would prefer
to acquiesce. The strategy War is only a best response for Country B because
Country A makes no demand, which implies that Country B’s planned action
ends up having no effect on her payoffs, since she is not called on to act. But
we’ve already seen that if Country A were to make a demand, surely Country B
would want to acquiesce, making a payoff of 2 instead of 1. Why, then, should
Country A believe and be deterred by Country B’s strategy of playing war?
I agree, the strategy profile (No Demand, War) doesn’t make any sense as a
predicted outcome of this game. For now, however, it is important to see that
(No Demand, War) is a Nash equilibrium. It is just that Nash equilibrium, as
a prediction for what happens in the game, is failing to capture some of our
strategic intuitions.Wewill come back to this shortly and propose a refinement
of the Nash equilibrium solution concept that will do a better job. Be patient.
B.5.2 The Budget Game
Now consider Nash equilibria of the budget game represented in Figures
B.4 and B.7. If the president believes Congress will propose a large budget,
she wants to sign it and is indifferent as to what she would have done had
Congress passed a small budget. If the president believes Congress will propose
a small budget, she wants to veto it and is indifferent as to what she would have
done had Congress passed a large budget. Hence, the president’s best response
correspondence is
BRP(Large) = {(Sign, Sign), (Sign,Veto)}
BRP(Small) = {(Sign,Veto), (Veto,Veto)}.
Congress’s most preferred outcome is a small, signed budget. But it prefers a
large signed budget to a veto. If its proposal must be vetoed, then it prefers to
have a large budget vetoed. Here, then, is Congress’s best response correspon-
dence:
BRC(Sign, Sign) = Small
BRC(Sign,Veto) = Large
BRC(Veto, Sign) = Small
BRC(Veto,Veto) = Large.
Given these best responses, this game has a unique Nash equilibrium: (Large,
(Sign, Veto)). To see that this strategy profile is a Nash equilibrium, it suffices
372 Appendix B
to see that no player would be better off by unilaterally changing behavior. If
Congress were to switch to proposing a small budget, the president’s strategy
calls on her to veto, leaving Congress worse off. If the president were to change
her strategy, either nothing would change (if she were to switch to (Sign, Sign))
or she would end up vetoing a large budget, making herself worse off.
Let’s now look at one non-Nash profile to see why it isn’t an equilibrium.
Consider the profile (Large, (Sign, Sign)), whichmight seem like it should be an
equilibrium, since it leads to the same terminal history as (Large, (Sign, Veto)).
But, notice, if the president is using the strategy (Sign, Sign), then it is not a
best response by Congress to choose Large. Instead, if Congress anticipates that
the president will sign any budget (i.e., play (Sign, Sign)), then Congress’s best
response is to propose a small budget. Hence, (Large, (Sign, Sign)) is not a Nash
equilibrium.
I leave it to you to check that no other profile is a Nash equilibrium.
B.5.3 The Centipede Game
Consider Nash equilibria of the centipede game represented in Figures B.5
and B.8. First let’s find Player 1’s best responses. If Player 1 believes Player 2 will
play In, then Player 1’s best response is (In, Out). If Player 1 believes Player 2
will play Out, then Player 1 has two best responses—(Out, In) and (Out, Out)—
both ofwhich lead to the same terminal history: Out. So Player 1’s best response
correspondence is
BR1(In) = (In,Out)
BR1(Out) = {(Out, In), (Out,Out)}.
Player 2’s best response correspondence is found similarly and given by
BR2(In, In) = In
BR2(In,Out) = Out
BR2(Out, In) = {In,Out}
BR2(Out,Out) = {In,Out}.
Clearly, from these best responses, there is no Nash equilibrium where
Player 2 plays In. To see this, note that if Player 2 plays In, then Player 1’s best
response is (In, Out). But if Player 1 plays (In, Out), then Player 2’s best response
is Out.
So the only possibility for a Nash equilibrium is a profile in which Player 2
plays Out. If Player 2 plays Out, both (Out, In) and (Out, Out) are best responses
Extensive-Form Games 373
by Player 1. And, since both of those strategies involve Player 1 playing Out
immediately, any strategy by Player 2 is a best response for her. Hence, there
are two Nash equilibria: ((Out, In), Out) and ((Out, Out), Out). Both equilibria
lead to the same terminal history—Player 1 goes Out immediately.
B.6 Subgame Perfect Nash Equilibrium
As we’ve already noted, sometimes the Nash equilibria of extensive-form games
don’t make a lot of sense as predictions. For instance, in the international crisis
game, there was an equilibrium in which Country A did not make a demand
because it believed Country B would start a war following a demand. That
equilibrium is strange because, once a demand is actually made, Country B
clearly prefers to acquiesce. So why should Country A believe that Country B
would really start a war following a demand? It seems as though Country Awas
being deterred by a non-credible threat.
If the threat was non-credible, why was Country B able to make it? The an-
swer comes from the logic of Nash equilibrium. In a world in which Country B
actually succeeds at deterring Country A, Country B is never called on to carry
through on the threat. The fact that Country Bwould have gone to war (against
its interests) in a part of the game that never actually got played has no effect on
Country B’s payoffs. As such, when considering a unilateral change in strategy
by Country B, we found that Country B’s planned action did not affect Country
B’s payoffs (because Country Bwas never actually forced to act). Thus, we had a
Nash equilibrium.
This equilibrium strains credulity for a couple of reasons. First, it seems hard
to believe that Country A couldn’t “look down the tree” and anticipate that
Country B would in fact choose to acquiesce if called on to act. If Country A
can do so, it should not believe that Country Bwill go to war. Instead, Country
A should say to itself, “Country B is rational. At the point where it is called on
to make a decision, after I make a demand, surely it will acquiesce, since doing
so will be in its best interest.” And if Country A believes its own thinking, it will
make a demand, counting on Country B’s rationality to lead to acquiescence.
Second, think of Country B. When playing the strategy War as part of a
Nash equilibrium, Country B is leaning quite strongly on its complete certainty
that A will not make a demand. If Country B thinks there is even a tiny
chance that Country A will make a demand, then Country B should play the
strategy Acquiesce. The strategy War is only a best response because, when
there is absolutely no chance Country A will make a demand, Country B is
exactly indifferent between its two strategies. If Country B assigns any positive
probability, however small, to actually having to act, then Country B strictly
prefers to acquiesce.
374 Appendix B
ND
War Acq
D
A
1
1
2
3
3
2
B
War Acq
1
1
3
2
B
Subgame of length 1 Subgame of length 2
Figure B.9. International crisis game subgames.
For both of these reasons, we want to think about a prediction for games like
this that refines Nash equilibrium to rule out non-credible threats of this sort.
The concept we use is called subgame perfection.
B.6.1 Subgame Perfection
The basic idea of subgame perfection is that players play best responses not
just in the full game, but at every possible point in the game where they might
be called upon to move. Defining subgame perfection formally requires a bit
more notation than I’d like to present, so I will be a little informal. But we do
need some terminology.
A subgame of an extensive-form game is another extensive-form game made
up of part of the original extensive-form game. You can find a subgame of an
extensive-formgameby cutting the tree at any decision point. Then, everything
from that decision down constitutes a subgame of the original game. Games are
also always considered subgames of themselves.
We also talk about the length of a subgame, which is the largest number
of actions that could be taken in a terminal history of a subgame. Looking
at our examples will help to fix ideas. Figures B.9–B.11 show the subgames
of the international crisis game, the budget game, and the centipede game,
respectively.
Now we can develop the refinement of Nash equilibrium that rules out non-
credible threats. A strategy profile is a subgame perfect Nash equilibrium if every
player is playing a best response to what the other players are doing, not only in
the game as a whole, but in every subgame.
To see how subgame perfection rules out non-credible threats, let’s revisit
the international crisis game. There we had two Nash equilibria: (Demand,
Acquiesce) and (NoDemand,War). Earlier, we argued that theNash equilibrium
(No Demand, War) depended on a non-credible threat. Consider the subgame
of length one shown in Figure B.9. Subgame perfection requires that, if we treat
Extensive-Form Games 375
Sign Veto
Small
Congress
Subgame of
length 2
Subgame of
length 1
Subgame of
length 1
Large
Pres.Pres.
Sign Veto
5
2
0
3
3
5
1
0
Sign Veto
Pres.Pres.
Sign Veto
5
2
0
3
3
5
1
0
Figure B.10. Budget game subgames.
this subgame as a game unto itself, the actions that are specified by the strategy
profile must be best responses. The strategy profile calls on Country B to play
War. But, clearly, in the simple one-player game created by considering just
this subgame, Country B’s best response (i.e., optimal action, since there are
no other players) is to choose Acquiesce. Hence, the profile (No Demand, War)
is not a subgame perfect Nash equilibrium, since it involves a player taking an
action that is not a best response in one of the subgames.
Now consider the other Nash equilibrium, (Demand, Acquiesce). In the
subgame of length one, shown in Figure B.9, Country B, by choosing Acquiesce,
is playing a best response. And, given this, Country A is playing a best response
by choosing Demand. Thus, this profile satisfies the requirements of subgame
perfection. Subgame perfection rules out the unreasonable Nash equilibrium
that depended on a non-credible threat, leaving only the reasonable Nash
equilibrium as a prediction for what will happen.
B.6.2 Backward Induction
Solving for a subgame perfect Nash equilibrium is quite easy. It can be done
by following a simple algorithm called backward induction. Here is the idea.
1
Out
2
3
3
1
2
Out
0
2
1
Out
2
3
3
1
1
Out
2
3
3
1
2
Out
Subgame of
length 1
Subgame of
length 2
Subgame of
length 3
0
2
1 In In InIn In In
Out
1
0
Figure B.11. Centipede game subgames.
376 Appendix B
ND
War Acq
D
A
1
1
2
3
3
2
B
War Acq
1
1
3
2
B
Figure B.12. Finding the subgame perfect Nash equilibrium of the international crisis
game through backward induction.
Start by finding all of the subgames of length 1. Figure out the best responses
of the relevant player in each of those subgames. Now find all the subgames
of length 2. Find the best responses of all the relevant players in those games,
taking as fixed the actions in the subgames of length 1 that you already
identified. Now take the actions you’ve found in subgames of length 1 and 2 as
given and do the same thing for subgames of length 3. Continue this procedure
until you get to the beginning of the game.
Any strategy profile you identify following this backward induction algo-
rithm is a subgame perfect Nash equilibrium. The reason should be clear—
by doing backward induction, you are making sure players are playing best
responses at every subgame. Any subgame perfect Nash equilibrium will be
found using backward induction.
Let’s go through our three examples. In the international crisis game, there is
one subgame of length 1. It is Country B’s choice. In that subgame, as we’ve
already discussed, Country B’s best response is Acquiesce. Now we take this
action as fixed and look at the one subgame of length 2. Taking B’s action
as fixed means that we assume Country A knows that if it makes a demand,
Country B will acquiesce. Hence, Country A’s best response, given Country B’s
behavior, is to make a demand. Thus, there is a unique subgame perfect Nash
equilibrium: (Demand, Acquiesce).
Figure B.12 shows the logic of the backward induction. The hash-marked
line in the first panel shows Country B’s best response in the subgame. The
hash-marked line in the second panel shows, given Country B’s behavior in the
subgame, that Country A’s best response is Demand.
In the budget game, there are two subgames of length 1. In each of them,
the president decides whether or not to veto. In the subgame following a large
budget proposal, the president’s best response is to sign the budget. In the
subgame following a small budget proposal, the president’s best response is to
veto the budget.
Extensive-Form Games 377
Sign Veto
Small
Congress
Large
Pres.Pres.
Sign Veto
5
2
0
3
3
5
1
0
Sign Veto
Pres.Pres.
Sign Veto
5
2
0
3
3
5
1
0
Figure B.13. Finding the subgame perfect Nash equilibrium of the budget game through
backward induction.
Taking these actions as fixed, now consider the single subgame of length 2—
in which Congress makes a choice of what type of budget to pass. Congress
anticipates that if it proposes a large budget, the budget will be signed and
Congress will make a payoff of 3. Congress also anticipates that if it passes a
small budget, the budget will be vetoed and Congress will make a payoff of 0.
Hence, Congress’s best response is to propose a large budget and the unique
subgame perfect Nash equilibrium is (Large, (Sign, Veto)). Figure B.13 illustrates
the backward induction for this game.
There are two things to point out here. First, notice how I’ve written the
equilibrium. I did not write (Large, Sign). That is what happens—that is, the
terminal history in this equilibrium—but it is not the equilibrium itself. An
equilibrium is a strategy profile. A strategy profile is made up of one strategy
for each player. And a strategy for a player is a complete contingent plan.
Hence,whendescribing the equilibrium, youmust report a full strategy for each
player—that is, what the player does in the places he is actually called on to play
and what he would have done everywhere else.
The budget game actually makes it clear why it is so important to write a
strategy as a complete contingent plan. Proposing a large budget is only a best
response for Congress because the president would veto a small budget. If the
president would sign a small budget, Congress would propose a small budget.
Hence, Congress’s incentives depend on what action the President would take
in the subgame that is never actually reached as part of equilibrium play.
It is worth noting that the subgame perfect Nash equilibrium of this game is
the same as the unique Nash equilibrium of the game. This is because subgame
perfection is a refinement of Nash. All subgame perfect Nash equilibria are Nash
equilibria. But not all Nash equilibria are subgame perfect (as we saw in the
International Crisis example).
In the centipede game, there is one subgame of length 1, one subgame of
length 2, and one subgame of length 3. In the subgame of length 1, Player 1 will
chooseOut. Anticipating this behavior, in the subgame of length 2, Player 2will
378 Appendix B
1
Out
2
3
3
1
2
Out
0
2
1
Out
2
3
3
1
1 In In In In In In
Out
2
3
3
1
2
Out
0
2
1
Out
1
0
Figure B.14. Finding the subgame perfect Nash equilibrium of the centipede game
through backward induction.
choose Out. And, anticipating both of these decisions, Player 1 will choose Out
in the subgameof length 3.Hence, the gamehas a unique subgameperfectNash
equilibrium: ((Out, Out), Out). This analysis is illustrated in Figure B.14.
B.6.3 Indifference and Multiple Equilibria
Subgame perfect Nash equilibria need not be unique. Sometimes a player has
more than one best response in a subgame.Which action the player is expected
to choose from amongst her best responses can affect what happens earlier
in the game. In such circumstances, to find all of the subgame perfect Nash
equilibria, you must go case-by-case, considering each possible best response
and its implications for behavior up the tree.
To see how this works, consider the example in Figure B.15. The key point
comes from studying the subgame that follows an action of A by Player 1 and
an action of C by Player 2. In this subgame of length 1, Player 1 is indifferent
between the actions G and H. Hence, when we do the backward induction, we
have to allow for the possibility of either action.
Let’s first do the backward induction in the case where Player 1 chooses G
in that subgame, as illustrated in the left-hand cell of Figure B.15. In the other
subgame of length 1, Player 1 has a clear best response, I. Now there are two
subgames of length 2. In the subgame on the left, Player 2 anticipates that
Player 1 will choose G down the tree. Hence, she plays D, making a payoff of 5
rather than 2. In the subgame of length 2 on the right, Player 2 anticipates that
Player 1 will choose I down the tree, so Player 2 chooses E, making a payoff of 4
rather than 3. Finally, hold all of this behavior fixed and consider the subgame
of length 3. Player 1 anticipates that if he chooses A, Player 2 will chooseD and
he’ll make a payoff of 5. If, instead, he chooses B, Player 2 will choose E and
then Player 1 will choose I, yielding a payoff of 4. Hence, Player 1 chooses A.
The subgame perfect Nash equilibriumwe’ve identified is ((A,G, I), (D,E)).
Now we must go back and redo our backward induction for the case
where Player 1 chooses H instead of G. As illustrated in the right-hand cell of
Figure B.15, doing so identifies a second subgame perfect Nash equilibrium:
((B,H, I), (C,E)).
Extensive-Form Games 379
E F
B
1
A
22
1 1
C D
6
3
I J
3
2
4
4
3
2
5
5
G H
3
6
E F
B
1
A
22
1 1
C D
6
3
I J
3
2
4
4
3
2
5
5
G H
3
6
Figure B.15. The backward induction when Player 1 chooses G.
RejectAccept
1
2
α
1 – α
0
0
α
Figure B.16. The ultimatum game.
B.6.4 Continuous Choices
Another issue that arises involves extensive-form games inwhich at least one
of the players makes a choice from a continuum. For instance, consider the
ultimatum game in Figure B.16. In the ultimatum game, Player 1 proposes a
division of a dollar, keeping a share α ∈ [0, 1] for herself. Player 2 then either
accepts or declines the offer. If Player 2 accepts, Player 1 gets a payoff of α and
Player 2 gets a payoff of 1 − α. If Player 2 declines, both players get nothing.
In Figure B.16, the fact that Player 1 has a continuous choice (any α between
0 and 1) is represented by the curve at her decision node. The dashed line
coming from this choice indicates that there are actually a continuum of
subgames after Player 1’s decision. Player 2’s strategy must specify an accept or
reject decision at each of these infinity of subgames.
Let’s analyze this game using backward induction. For any proposal
α �= 1, Player 2 strictly prefers to accept Player 1’s offer. But if α = 1, Player 2
is indifferent between accepting and rejecting. So, as we saw in the previous
section, wemust do the backward induction twice.
First, assume that Player 2 accepts any offer α < 1 and rejects if α = 1. Player 1’s best response is to propose the largest α that Player 2 will accept. So 380 Appendix B Player 1 wants to propose the largest α ∈ [0, 1). Now we run into a technical problem. There is no largest α ∈ [0, 1). For any α < 1, we can find an α′ such that α < α′ < 1. Hence, there is no equilibrium because, for technical reasons, Player 1 has no best response. That said, the basic incentives are clear. Player 1 wants to make a proposal that leaves Player 2 all but indifferent. Second, suppose Player 2 will accept any α, including α = 1. Then Player 1 wants to propose the largest α ∈ [0, 1]. This is straightforward to do; Player 1 keeps the whole dollar for herself. Thus, the unique subgame perfect Nash equilibrium of this game is that Player 1 proposes α = 1 and Player 2 accepts any α ∈ [0, 1]. B.7 Discounted Payoffs Another important type of extensive-form game is the infinitely repeated game. We define an infinitely repeated game by first specifying a strategic-form game. We then create an extensive-form game in which players play that strategic- form game over and over. In an infinitely repeated game, we think of players getting the payoff from the strategic-form game in each period. However, we can’t simply have them sum those payoffs. We need a way to model how players think about the value of future payoffs relative to current payoffs. A given payoff today is worth more than the same payoff tomorrow. (Think about whether you’d rather have a thousand dollars right now or in five years.) We model this by assuming that players discount future payoffs by a discount factor, δ ∈ (0, 1). The idea is that a unit of utility to be delivered a period from now is worth δ units of utility now. That further implies that a unit of utility to be delivered twoperiods fromnow isworth δ2 units of utility now.Hence, future payoffs are getting less and less valuable as they get further and further away from being realized. In an infinitely repeated game, a player’s payoff from some terminal history is the discounted sum of the payoffs she made throughout the game. The followingmathematical fact will prove useful: Fact B.7.1. If δ ∈ (0, 1), then the infinite series 1 + δ + δ2 + δ3 + . . . is equal to 11−δ . You can see this as follows. Assuming the series converges (i.e., the sum approaches some finite number), which it does, we can let that number be called Z: Z = 1 + δ + δ2 + δ3 + . . . Then we have δZ = δ + δ2 + δ3 + . . . . Extensive-Form Games 381 Subtracting the two left-hand sides from each other and the two right-hand sides from each other, we have Z − δZ = [1 + δ + δ2 + δ3 + . . .] − [δ + δ2 + δ3 + . . .] . Distributing the Z on the left-hand side and canceling things on the right-hand side, we have Z(1 − δ) = 1 ⇒ Z = 1 1 − δ . Using the definition of Z, we get Z = 1 + δ + δ2 + δ3 + . . . = 1 1 − δ . B.8 Takeaways • In some extensive-form games, some of the Nash equilibria involve players committing to non-credible threats “off the path of play” (i.e., in parts of the game tree that are never actually reached). • Subgame perfection refines the Nash equilibrium concept to rule out strategy profiles in which players make such non-credible threats. It does so by requiring that players play best responses in every subgame, whether or not that subgame is actually reached on the path of play. • You solve for a subgame perfect Nash equilibrium by backward induction. • A strategy in an extensive-form game is a complete contingent plan— that is, a statement of the action a player would take at every point in the game where she can be called on to play. B.9 Exercises 1. Consider the game in Figure B.17. (a) Howmany strategies does player 1 have? Howmany strategies does player 2 have?What are they? (b) Solve the game for all of its Nash equilibria. (c) Solve the game for all of its subgame perfect Nash equilibria. (d) Give an intuition for why the answers to (b) and (c) are different. 2. Consider a game between an administrative agency and a court. At the beginning of the game, the administrative agency can choose to regulate or 382 Appendix B Figure B.17. Exercise 1. E F B 1 A 22 C D 5 5 1 6 0 2 2 3 Figure B.18. A repeated game. B 5, 15 A Player 2 A B Player 1 10, 10 4, 415, 5 not. If the agency chooses not to regulate the game ends. If the agency chooses to regulate, the court can uphold the regulation or strike it down. The agency’s most preferred outcome is to successfully regulate and its least favorite outcome is to have its regulation struck down. The court’s most preferred outcome is no regulation and its least preferred outcome is to have to strike down regulation by the agency. (a) Represent this game in amatrix and on a tree. (b) What are all the Nash equilibria of this game? (c) What is the subgame perfect Nash equilibrium? Explain the intuition for why this equilibrium is the “right” prediction for the outcome of the game. (d) Explain how, intuitively, if the court could develop a reputation as enjoying conflict with the agency, it could make itself better off. 3. Suppose the game in Figure B.18 is repeated infinitely and that each player discounts the future according to discount factor δ (with δ between 0 and 1). (a) Consider the strategy: “Start playing A and continue to play A if all players have always played A. If any player (be it me or you) has ever played B, play B forever.” Give conditions on δ such that this strategy is a Nash equilibrium. 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Index of Referenced Authors Acemoglu, Daron, 232 33, 240, 315 18 Ahmed, Faisal Z., 321 Albouy, David Y., 317 Alchian, Armen A., 185 Alesina, Alberto, 241 Alt, James E., 294 95 Angrist, Joshua D., 13, 317n4 Ansolabehere, Stephen, 288 89 Appiah, Kwame Anthony, 169 Arrow, Kenneth J., 26, 60 69 Ashworth, Scott, 302 Austen Smith, David, 71 Azariadis, Costas, 169 Baker, George, 214 Banks, Jeffrey, 71 Barnett, Michael L., 100 Baron, David P., 276 Bartels, Daniel M., 27 Barlett, John G., 99n2 Beghin, John C., 194 Berry, Christopher R., 95, 120, 284, 286, 299 300 Besley, Timothy, 302 Besser, Richard E., 99n2 Black, Duncan, 67, 71 Bombardini, Matilde, 288 90 Broome, John, 17, 46 Bueno deMesquita, Bruce, 305 7, 322 24, 326 Bueno deMesquita, Ethan, 201n2, 294 95, 302 Burnside, Craig, 321 Butler, Christopher C., 99 100 Caliendo, Lorenzo, 74 Canes Wrone, Brandice, 301 2 Cherlow, Jay R., 194 Clarke, Edward H., 276 Coase, Ronald Harry, 133 35, 144 Cohen, Charles, 321 Cohen, Gerald Allan, 30 31, 33 34, 36, 46 Collier, Paul, 152, 319 Cooper, Richelle J., 99n2 Cooper, Russell, 169 Crawford, Robert G., 185 Crost, Benjamin, 321 Dal Bó, Ernesto, 276 Deaton, Angus, 239, 324 DeConcini, Dennis, 289 de Figueiredo, JohnM., 288 89 de Janvry, Alain, 293 94 Diamond, DouglasW., 169 Dixit, Avinash, 84n2, 284 Djankov, Simeon, 321 Dollar, David, 321 Downs, Anthony, 71 Dube, Oeindrila, 321 Dworkin, Ronald, 34 35, 46 Dybvig, Philip H., 169 Dynarski, SusanM., 13 Easterly, William, 319 22, 324 26 El Osta, Barbara, 194 Ely, Jeff, 246 Enders, Walter, 201 English, Richard, 175n2 Fearon, James D., 145, 169, 175, 178 79, 185 Felter, Joseph, 321 Feltham, Gerald A., 214 Ferraz, Claudio, 294 Fey, Mark, 175n1 Finan, Frederico, 293 94 Foot, Philippa, 23 Foucault, Michel, 91 Friedman, Milton, 169 Gagliarducci, Stefano, 293 Galiani, Sebastian, 321 Gans, Joshua S., 64 69, 71 Geanakoplos, John, 71 Gehlback, Scott, 302 Gersen, Jacob E., 286 Gibbons, Robert, 214 Giere, Ronald, 6, 9 Glaeser, Edward L., 169, 317 18 Gonzales, Ralph, 99n2 Gordon, Sanford C., 296 97, 301 Greenstone, Michael, 151, Groves, Theodore, 276 Hacking, Ian, 9 Hakobyan, Shushanik, 74 75 Hardin, Garrett, 144 Harrod, R. F., 26 Harsanyi, John, 19 21, 31 32, 47 Hart, Oliver D., 185 Herron, Michael C., 301 Hickner, JohnM., 99n2 Hoffman, Jerome R., 99n2 Holmström, Bengt, 214 394 Index of Referenced Authors Hornbeck, J. F., 80n1, 84n3 Hornbeck, Richard, 151 Howell, WilliamG., 299 300 Huber, Gregory A., 296 97, 301 Hutchings, Jeffrey A., 119 Jacob, Brian A., 211 Johnson, Simon, 315 18 Johnston, Patrick, 321 Kane, Thomas J., 13 Kant, Immanuel, 16, 31n9, 37 40 Kleiman, Mark, 204 Klein, Benjamin, 185 Kleiner, Morris M., 194 Kleppner, Daniel, 8 Kline, Patrick, 150 51 Knack, Stephen, 321 Kraay, Aart, 169 Krehbiel, Keith, 71 Krugman, Paul R., 9, 169 Kuziemko, Ilyana, 324 Kydland, Finn E., 241 La Porta, Rafael, 317 18 Lancaster, Kelvin, 125 Laffont, Jean Jacques, 276 Lafontaine, Francine, 181n4 Lane, Philip R., 225n8 Lapan, Harvey E., 226 Laitin, David D., 145 Linder, Jeffrey A., 100 Lipsey, Richard G., 125 Locke, John, 44 Londregan, John, 284 Lopez de Silanes, Florencio, 317 18 Mackie, Gerry, 159 60 Madison, James, 282, 290 91 Mankiw, N. Gregory, 2, 144 Marx, Karl, 31, 42 Mas Colell, Andreu, 62 63, 70 71 Maskin, Eric, 303 May, Kenneth O., 63 64, 69, 71 McKenzie, David, 169 McLaren, John, 74 75 Mickolus, Edward F., 202 Milgrom, Paul R., 145, 214, 248, 276 Mill, John Stuart, 22 Mohanty, Samarendu, 194 Mohl, Raymond A., 110 11 Montalvo, Jose G., 321 Moretti, Enrico, 150 51 Morgan, Mary S., 9 Morris, Stephen, 169 Morrow, James D., 305 7, 326 Morton, Fiona Scott, 181n4 Myerson, Roger B., 71, 133, 276 Naidu, Suresh, 151, 321 Nannicini, Tommaso, 293 Neal, Derek, 212 14 Norman, Victor, 84n2 North, Douglass C., 145, 326 Nozick, Robert, 22, 43 46, 48 Nunn, Nathan, 321 O’Hare, Michael, 48, 171 Olson, Mancur, 144 Osborne, Martin J., 8 Ostrom, Elinor, 135 39 Parro, Fernando, 74 Patashnik, Eric M., 4n2 Pathak, Parag A., 13 Peltzman, Sam, 276 Persson, Torsten, 241 Pfutze, Tobais, 319n5 Pischke, Jörn Steffen, 317n4 Pizarro, David A., 27 Powell, Robert, 185, 201n2 Prescott, Edward C., 241 Qian, Nancy, 321, 326 Rajan, RaghuramG., 321 Ramsay, KristopherW., 175n1 Ramsey, Frank, 26 Ramsey, Norman, 8 Rawls, John, 19, 22 23, 31 32, 38, 46, 70 Reynal Querol, Marta, 321 Ribicoff, Abraham, 158 Robinson, James A., 232 33, 240, 315 18 Robinson, Joan, 9 Rodrik, Dani, 331 32 Roemer, John E., 21n3, 46, 70 Roodman, David, 321 Rose, Mark H., 110 11 Rose, Shanna, 294 95 Ross, ThomasW., 169 Roth, Alvin E., 276 Rousseau, Jean Jacques, 51 Sachs, Jeffrey, 319, 326 Sadoulet, Elisabeth, 293 94 Sande, Merle A., 99n2 Sandler, Todd, 201, 226 Satterthwaite, Mark A., 133 Schanzenbach, DianeWhitmore, 212 14 Schelling, Thomas C., 169 Schwartz, Anna J., 169 Sen, Amartya, 28, 46, 71 Shepsle, Kenneth A., 71 Shin, Hyun Song, 169 Shleifer, Andrei, 317 18 Shotts, KennethW., 301 2 Simmons, Beth A., 154 Index of Referenced Authors 395 Singer, Peter, 46 Siverson, RandlophM., 305 7, 326 Smart, Michael, 64 69, 71 Smith, Adam, 194 Smith, Alastair, 305 7, 322 24, 326 Snyder, James M., 288 90, 297 99 Solow, Robert, 26 Sonnenschein, Hugo, 62 63, 70 71 Stigler, George J., 193, 276 Stokey, Edith, 91 Stokey, Nancy L., 241 Strömberg, David, 297 99 Subramanian, Arvind, 321 Summers, Lawrence, 49 Sunstein, Cass R., 47 48, 87, 91 Svensson, Jakob, 321 Svensson, Lars E. O., 241 Swift, Adam, 46 Tabellini, Guido, 241 Thaler, Richard H., 47 48, 248 Thomas, Robert Paul, 326 Thomson, Judith Jarvis, 23 Tirole, Jean, 276, 302 Trebbi, Francesco, 288 90 Tullock, Gordon, 288 89 Turner, Leslie J., 198 Vickrey, William, 276 Wallis, John Joseph, 326 Walters, Christopher R., 13 Weingast, Barry R., 145, 169, 326 Werker, Eric, 321, 324 Williamson, Oliver E., 185 Xie, Jim, 214 Xu, Lixin Colin, 321 Zame,William R., 25n4 Zeckhauser, Richard, 91 Zou, Ben, 321 General Index Italic pages refer to figures and tables accountability: collective action and, 101; coordination problems and, 160, 169; dynamic inconsistency and, 218, 227; electoral, 282, 290 302 adverse selection, 278 agglomeration economies, 151 52, 161, 165, 167, 169, 319 aggregation: Borda count and, 55, 59 60; collective goals and, 51 65, 69 71; evaluative criteria for, 55 60; independence of irrelevant alternatives and, 58 60; majority rule and, 54 55, 57 58; procedures of, 53 60; transitivity and, 56 58; unanimity and, 56 58; universal domain and, 56 57 airport security, 201 altruism, 8, 130 32 amendment procedure, 57 58 antibiotics, 90, 99 100 Arab Spring, 164 65 Arrow’s theorem, 60 64, 70 71 auctions: cap and trade and 3, 332; second price, 246 48, 276 77 autocracy, 239, 306 7, 314, 325, 328, 333 autonomy, 38 39, 41 43, 45 backward induction, 176, 199, 221, 375 78, 381 bailouts, 225 26 balanced budget: fiscal manipulation and, 228, 241; need for information and, 245, 257 58, 276; transfer schemes and, 78, 81 82, 86, 93 94 bank runs, 153, 160, 162 63, 165 69 best response, 349 58, 370 72 Borda count, 55, 59 60, 64 bourgeois equality of opportunity, 33 campaign donations, 286 90 carbon: cap and trade system and, 2 4, 332 33; climate change and, 1 3, 17, 24, 77, 101, 122, 124, 213, 332 33; price of, 2; taxes on, 2 3, 77, 101, 122, 213, 332 33 cartels, 203 4, 322 California Electoral Code, 286 Categorical Imperative, 38 41, 50 Chamberlain,Wilt, 43 44 charter schools, 13 14 Chicago Public Schools, 211 12 civil war, 175, 179, 184 Climate Action Plan (Obama administration), 1 2 climate change: cap and trade system and, 2 4, 332 33; carbon emissions and, 1 3, 17, 24, 77, 101, 122, 124, 213, 332 33; Climate Action Plan and, 1 2; dynamic inconsistency and, 231 32; fossil fuels and, 1, 101, 122; global warming and, 1, 24, 26, 108, 332; normative frameworks and, 17, 24; utilitarianism and, 17, 24 Coase Theorem, 132 35 coercion, 15 16, 41 45, 48 ColdWar, 178 79 collective action, 100 5 collective goals: aggregation and, 51 65, 69 71; agreement and, 70; Arrow’s theorem and, 60 64, 70 71; impossibility theorems and, 63 70; majority rule and, 54 55, 57 58, 63 64, 68 69, 71; public interest and, 51 57, 61 64, 70 72; rationality and, 52 53, 56, 71; transitivity and, 52, 56 58, 60 61; unanimity and, 56 58, 60 64, 74; universal domain and, 56 57, 60 64, 69 commitment problems: concept of, 173; conflict and, 173 85; enforceable contracts and, 183 85, 191; foreign investment and, 173 74; future power and 232 39; global financial crisis and, 225 27; hold up problem and, 180 85; Irish Troubles and, 174 78; limiting future discretion and, 184 85; new technology and, 173, 179 80, 183, 238; policy responses and, 183 85; time inconsistency and, 218 27 commons. See tragedy of the commons common pool resource. See tragedy of the commons communication: coordination and 165 67; externalities and 120 22, 139 communitarianism, 30 31 complete contingent plan, 362, 366 69, 377, 381 completeness, 52 concentrated interests, 3, 109 14, 284, 287, 332 33 concessions, 175, 177, 180, 184, 233, 287, 289, 322 25 Condorcet Paradox, 57 General Index 397 conflict: ColdWar and, 178 79; commitment problems and, 173 81, 183 85; Congo Free State and, 305 6; coordination problems and, 169; Croatia and, 179; Easter Rising and, 174; externalities and, 135; foreign aid and, 321; Good Friday Agreement and, 174; inefficient, 178; Irish Troubles and, 174 78; Congo Free State, 305 6 Congressional Record, 158 Congressional Research Service, 80, 84, 159n2 consequentialism, 17, 26 27, 31n9, 37 40, 43 44, 89 90, 331 consumer surplus: marginal, 260 69, 273 74; monopolists and, 260 70, 273 74; total, 261 62 coordination failure, 153 59 coordination problems: bank runs and, 153, 160, 162 63, 165 69; communication and, 161, 165 67, 169; distributional consequences and, 153 54, 166; economies of agglomeration and, 151 52, 167, 169; foreign investment and, 160 62; insurance and, 167 68; logic of revolutions and, 163 65; new technology and, 152, 165; policy responses and, 165 68; poverty traps and, 151 53, 160 61, 169; revolutions and, 160, 163 66, 184; short run interventions and 167; strategic complementarities and, 152, 162 63; strategic uncertainty and, 153, 155 58, 165, 168 coordination traps, 159 65 Corporate Average Fuel Economy (CAFE), 77, 197, 213 cost benefit analysis: fiscal manipulation and, 232; need for information and, 245; normative frameworks and, 25 26; Pareto concepts and, 87 88, 91; politics and, 331; utilitarianism and, 25 26; willingness to pay and, 87 88 debt, 225 26 democracy, 184, 240, 282, 306, 325, 328 deontology: autonomy and, 38 39; Categorical Imperative and, 38 41, 50; challenges for, 39 41; freedom and, 37, 41 42; libertarianism and, 41; morality and, 37 41; multiple duties and, 40; paradox of, 40; rationality and, 38 41; rights/duties and, 37 38; usefulness of, 40 41; utilitarianism and, 39, 41 deposit insurance, 167 8 dictators: foreign aid and, 321 26; impossibility theorems and, 60 64; institutions and, 321 26; public interest and, 60 64, 69, 71 difference principle, 32, 70 diffuse interests, 109 14, 135, 284, 287, 333 diminishingmarginal utility inmoney, 30, 85 86, 221 direct revelationmechanism, 252 53, 256 disability insurance, 197 98 discounting: cost benefit and, 25 26; dynamic inconsistency and, 231 32; extensive form games and, 380 81; fiscal manipulation and, 231 32; intergenerational equity and 25 26; normative frameworks and, 25 26; ongoing relationships and, 137; payoffs and, 380 81; utilitarianism and, 25 26 disease environment, 316 dynamic inconsistency: accountability and, 218, 227; climate change and, 231 32; discounting and, 231 32, 241; fiscal manipulation and, 227 32; future power and, 232 41; policy change and, 233, 239 41; political second best and, 239 41; rent seeking and, 232; terrorism and, 226 27; time inconsistency and, 219 27 Earned Income Tax Credit (EITC), 244 Easter Rising of 1916, 174 economic development, 150 53, 239, 314 22 egalitarianism: communitarianism and, 30 31; consequentialism and, 27; difference principle and, 32; diminishingmarginal utility and, 30; equality of opportunity and, 32 37; equality of outcomes and, 28 32; incentives and, 29 32; leveling down and, 29 30, 32; luck elimination and, 33 36; prioritization and, 28 30; Rawlsian, 31 32; utilitarianism and, 28 32, 36; wealth, 29 32 elections: campaign donations and, 286 90; challengers and, 296 97; dependence on the people and, 282; electoral accountability and, 290 301; fiscal manipulation and, 230 31; incumbents and, 194, 230 31, 238, 283, 291 96, 300 2, 307 14; median voter theorem and, 64 69, 71; off cycle, 296; pandering and, 300 1; particularistic interests and, 283 86; reelection and, 290 96, 301 4; rent seeking and, 282; special purpose governments and, 284; voter responsiveness and, 299 300 398 General Index electoral accountability: challengers and, 296 97; electoral selection and, 290 91, 294 95; incentives and, 294 95; media coverage and, 297 99; pandering and, 300 1; quality of politician and, 291; reelection and, 290 96; screening and, 294 95; term limits and, 293 95, 301 2; voter responsiveness and, 299 300 electoral selection, 290 91, 294 95 equality of opportunity, 13, 15, 28, 32 37, 63 equality of outcomes, 28 32, 36 37 equity across generations, 24 26, 70 ethnic conflict, 175 79 European Space Agency, 114 European Union (EU), 225 26 eurozone, 225 26 excludable. See non excludable expected utility, 20 21, 338 42 extensive form games: backward induction and, 375 78; complete contingent plan and, 362, 366 69, 377, 381; continuous choices and, 379 80; definition, 364; game trees and, 364 66; indifference and, 378; multiple equilibria and, 378; Nash equilibrium and, 369 81; player function and, 363 64; preferences and, 363 64; strategic form representation and, 368 69; subgame perfection and, 373 81; terminal histories and, 363 externalities: altruism and, 130 32; Coase theorem and, 132 35; collective action and, 101 5; first best and, 107 8, 123 32, 144; market in, 131 35; negative, 100 1, 115 16; ongoing relationships and, 135 39; Pigovian taxes and subsidies and, 122 24; policy responses and, 101, 120 43; positive, 100 2, 104 5; prisoner’s dilemma and, 136 42; property rights and, 131 35; public goods and, 105 14; second best and 124 26 first best: definition, 107; monopolists and, 263 75; policy interventions and, 121, 123 24; second best and, 125 32; utilitarianism and, 107 8 fiscal manipulation: balanced budgets and, 228; Chicago and, 227; discounting and, 231 32, 241; electoral risk and, 230 31; first best and, 229 30; inequality and, 230; model for, 228 29; pensions and, 227 Force Publique, 305 foreign aid: accountability and, 322; effectiveness of, 321 22; institutions and, 318 25; political economy of, 322 25; poverty traps and, 161, 318 23 foreign investment, 153, 173 74, 319 fossil fuels, 1, 101, 122 freedom: autonomy and, 38 39, 41 43, 45, 179; from coercion, 15; Kantian Deontology and, 37, 41 42; libertarianism and, 41 43; normative frameworks and, 15 16, 37, 41 43, 45 46 free trade: future power and, 238; need for information and, 238; Pareto concepts and, 74, 77 81, 84n2 future power: declining industry and, 233 38; dynamic inconsistency and, 232 41; rent seeking and, 232 33; second best and, 239 41; game trees, 364 66, 381 General Agreement on Tariffs and Trade (GATT), 80 global financial crisis, 168, 225 26, 248 global warming, 1, 24, 26, 108, 332 Good Friday Agreement, 174 governance, 333; constraints on, 193 206, 328 29; dynamic inconsistency and, 218, 225; incentives and, 5, 195, 328; institutions and, 305, 314 15, 320 21; monetary influence and, 282, 290, 294 95, 299, 301 2; technological constraints and, 4 5, 84, 195, 328, 331 32 Governing the Commons (Ostrom), 135 Great Depression, 168 Grim Trigger strategy, 137 38, 140 health care, 37, 80, 206, 218 19, 239, 277 78 HealthCare.gov, 218 19 high stakes testing, 205 7, 211 13, 299 hijacking, 201, 202 Hobbesian tradition, 19, 42 hold up problem, 180 85 hostages, 201 3, 226 27 human capital, 151 52, 161, 317 19 immigration, 179, 238 imperfect monitoring, 143 44 impossibility theorems, 63 70, 95 incentive constraints, 5, 195, 328 incremental benefit, 103 incumbents: fiscal manipulation and, 230 31; future power and, 238; institutions and, 307 14; monetary influence and, 283, 291 96, 300 2 independence of irrelevant alternatives (IIA), 58 62 inequality: educational, 13 14; egalitarianism and, 29 34; http://HealthCare.gov General Index 399 libertarianism and, 44; normative frameworks and, 13 14, 16 17, 29 34, 44 institutions: accountability and, 305, 322; development and, 314 18; dictators and, 321 26; foreign aid and, 318 25; governance and, 305, 314 15, 320 21; human capital and, 317 19; Leopold II and, 305 6, 315; monetary influence in, 284; selectorate model of, 306 14, 319, 322, 326; settler mortality and, 315 18 international accounting standards, 154 International Criminal Court, 184 International Monetary Fund (IMF), 226 Interstate Highway System, 110 11, 158 Irish Republican Army (IRA), 175 78 Irish Troubles, 174 78 justice, 22, 28, 32, 34 35, 43 44, 46 Kantian Deontology, See deontology left liberal equality of opportunity, 33 Lehman Brothers, 225 Leopold II, King of Belgium, 305 6, 315 leveling down, 29 30, 32 libertarianism: autonomy and, 41 43; coercion and, 41 45, 48; concept of, 41; freedom and, 41 43; inequality and, 44; morality and, 41 46; motivations for, 43 44; Nozick and, 43 46; ownership of property and, 44 45; problems for, 44 45; trade offs and, 42, 45 46; utilitarianism and, 41, 43 46 licenses, 180, 193 94, 232, 283 lobbying, 111 13, 195 luck elimination, 33 36 majority rule: aggregation and, 54 55, 57 58; collective goals and, 54 55, 57 58, 64, 68 69, 71; institutions and, 305; May’s Theorem and, 63 64; median voter theorem and, 64 69; normative frameworks and, 11; public interest and, 64, 68 70 marginal benefits, 106 8, 123, 263, 354 marginal costs: externalities and, 106 8, 125; monopolists and, 260 75; need for information and, 260 75; public goods and, 106 8; strategic adjustment and, 207 Mas Colell and Sonnenschein theorem, 62 63, 70 71 May’s theorem, 63 64, 69, 71 mechanism design, 246, 276 media, 101, 295, 297 99 median voter theorem, 64 69, 71 Ming Dynasty, 160 monetary policy, 219 20 monopolists: competition and, 259; consumer surplus and, 260 70, 273 74; equilibrium and, 261 62; first best and, 263 75; full information and, 263 64; inefficiency and, 125; informed regulator and, 271 75; marginal costs and, 260 75; market conditions for, 259; need for information and, 259 75; Pareto concepts and, 259; regulating, 259 75; second best and, 125, 266 71; uncertainty and, 264 71 moral hazard, 168 69, 259 morality: Bentham on, 22; egalitarianism and, 27 28; Kantian Deontology and, 37 41; libertarianism and, 41 46; normative frameworks and, 16 17, 22, 24, 27, 37 46; private vs. public, 16 17; utilitarianism and, 22, 24, 27 multitask, 205 13 Nash equilibrium: analyst’s humility and, 349; definition, 345 47; examples, 350 58; extensive form games and, 362, 369 81; game theory and, 345 58, 362, 369 81; no regrets criterion and, 347 48; self enforcing agreements and, 348 49; social learning and, 347 48; subgame perfection and, 373 81; unilateral incentive to deviate and, 345 47 National Rural Employment Guarantee Act (NREGA), 244 National Traffic andMotor Vehicle Safety Act, 158 No Child Left Behind Act, 211 12 non excludable, 105 non rival, 105 North American Free Trade Agreement (NAFTA), 74 75, 78, 80 Nozickian libertarianism, 43 44 off cycle elections, 296 Ongoing relationships, 135 44 Operation Swordfish, 203 5 overlapping jurisdictions. See special purpose governments pandering, 300 1 Pareto dominates, 75 Pareto efficient: cost benefit analysis and, 87 88; critique of, 89 90; definition, 76; Pareto improvements and, 76 84; quasi linearity and 77 87; utilitarianism and, 82 Pareto improvement: definition, 76; Pareto efficient and, 76 84; quasi linearity and 77 87 400 General Index particularistic interests: dynamic inconsistency and, 232; future power and, 232; money in politics and, 282 86; normative frameworks and, 19; subsidies and, 286; taxes and, 283, 286 pensions, 109, 227 28, 238 Pigovian subsidies: policy interventions and, 122 24; second best and, 125 29; taxes and, 122 26, 129, 144, 191, 193 player function, 363 64 policy responses: commitment problems and, 183 85; coordination problems and, 165 68; externalities and, 101; need for information and, 276; social dilemmas and, 101, 165 68, 183 85, 191 political economy, xx, 5 7, traditional policy analysis and, 1 4, 331 33 pollution, 1, 108, 112, 114, 119, 125, 132, 239, 245 poverty traps, 151 53, 160 61, 169, 318 23, 333 preferences: aggregation and, 53 60; completeness, 52; expected utility and, 338 42; quasi linear, 78 79; rationality and, 7 8, 52 53; transitivity and, 52; utility functions and, 75, 338 prioritization, 28 30 prisoner’s dilemma, 135 44 professional licensing, 194, 232, 283 property rights, 44 45, 131 35, 173, 318 public goods: defining characteristics of, 105; externalities and, 105 14; informational problems and, 248 59; Pigovian subsidies and, 122 29 quasi linearity 78 79 rationality, 7 8; preferences and, 52 53 regulation: capture and, 272 75; coordination and, 158, 166 67; externalities and, 124; information and, 272 75; monopolists and, 125, 259 75, strategic adjustment and, 197 regulatory capture, 272 75 rent seeking, 193, 232, 282 repeated prisoner’s dilemma, 135 44 revelation principle, 252 53 revolving door, 271 72 revolutions, 101 5, 160 66, 184 rival. See non rival rules vs. discretion, 184 85, 219 20, 224 25 satellites, 49, 114 15, 120 screening, 294 95 second best: definition, 124 26; information and, 257 59; Pigovian subsidy and, 126 9; politics and, 239 41 second price auction, 247 48 selectorate, 306 14, 319, 322, 326 self enforcing agreements, 348 49 settler mortality, 315 18 short run interventions, 161, 167 social contract, 18 19, 51 Social Contract, The (Rousseau), 51 social decisions, 61 63 social dilemmas, 12; collective action and, 104; commitment problems and, 174 (see also commitment problems); coordination problems and, 151, 157 (see also coordination problems); summation of, 191. See also externalities social insurance, 244 socialist equality of opportunity, 33 34 Soviet Union, 114, 178 79, 188, 306 special purpose governments, 119 20, 284. See also tragedy of the commons special interests: campaign donations and, 286 90; concentrated interests and, 111 14; electoral politics and, 282 90; lobbying and, 111 13, 195 Stability and Growth Pact, 225 26 standardized tests, 205 7, 211 13, 299 stock exchange, 153 54 strategic adversaries, 199 205 strategic adjustment, 197 strategic complementarities, 152, 162 63 strategic form games, 342 45 strategic uncertainty, 153, 155 58, 165, 168 subgame perfection, 373 81 subsidies, 2; agglomeration and, 150 51, 167; agricultural, 193 94, 288; dynamic inconsistency and, 232 33, 235, 240; externalities and, 101, 122 29, 144; governance constraints and, 193 95, 198; Pigovian, 122 29; second best, 126 29, 130; workfare and, 244 45 sugar industry, 193 94, 286 89 tariffs, 74, 80, 193, 293 taxes: carbon, 2 3, 77, 101, 122, 213, 332 33; dynamic inconsistency and, 220 25, 234 36, 239 40; electoral accountability and, 293, 295; externalities and, 101, 120, 122 29, 144; Pigovian, 122 26, 129, 144, 191, 193; second best and, 124 29; strategic adjustment and, 198, 213; time inconsistency and, 220 25 technological constraints, 4 5, 195 Tennessee Valley Authority (TVA), 150 51, 161, 167, 319 terminal histories, 363 69, 372 74, 377, 380 term limits, 293 95, 301 2 General Index 401 terrorism: dynamic inconsistency and, 226 27; negotiations and, 226 27; public goods and, 108; strategic adjustment and, 199 203, 213, 216; time inconsistency and, 226 27 test scores, 205 7, 211 13, 299 300 time discounting. See discounting time inconsistency, 220 37 Tokyo Round, 80 toxic assets, 248 Trade Adjustment Assistance (TAA), 80, 84 Trade Expansion Act, 80 Trade Promotion Authority (TPA), 80 tragedy of the commons: common pool resource and, 115 16, 119 20; defined, 115 16; environmental contamination and, 119; fishing and, 116 20; overlapping jurisdictions and, 120; space regulation and, 114 16, 119 transfer schemes, 77 78, 84 85 transitivity, 52, 56 58, 60 61 transplant problem, 23 24, 39 trolley problem, 23 24, 39 Troubled Asset Relief Program, 248 Tullock Paradox, 288 89 unanimity, 56 58, 60 64, 74 Uniform Vehicle Code (UVC), 158 unions, 180, 184, 190, 240, 284, 305 United Nations, 101, 158 59, 203n3, 324 United States Office of Management and Budget, 25 universal domain, 56 57, 60 64, 69 Urban Land Institute (ULI), 110 urban revitalization, 110 14 U.S. Commerce Department, 194 U.S. Drug Enforcement Administration, 203 5 U.S. Environmental Protection Agency (EPA), 119 U.S. Generally Accepted Accounting Principles, 154 U.S. Government Accountability Office (GAO), 218 utilitarianism: Bentham and, 22; consequentialism and, 17 18; cost benefit analysis and, 25 26; definition, 17 18; egalitarianism and, 28 32, 36; equality of opportunity and, 36 37; equity across generations and, 24 26; expected utility and, 20 21, 342; first best and, 107 8; monsters and, 23; motivation for, 18 21; Pareto concepts and, 82; problems of, 21 27; quasi linearity and, 78 84; relationships and, 26 27; transplant problem and, 23 24; trolley problem and, 23 24; veil of ignorance and, 19 21 veil of ignorance, 19 21, 31, 38 von Neumann Morgenstern (vnm) utility function, 340 43 voter information, 295 300 War on Drugs, 203 5 Wealth of Nations, The (Smith), 194 weakly dominant strategy, 247 welfare to work, 197 98, 244 welfarism, 17 Whig Party, 283 willingness to pay, 87 88 winning coalition, 306 14, 323 24 workfare, 244 45 World Bank, 49 World Health Organization (WHO), 99 Yugoslav civil war, 179 Cover Title Copyright Dedication Summary of Contents Contents Policy Applications Preface For Whom Is This Book Written? A Word on Tone and Technicality Acknowledgments Introduction Three Goals The Role of Models Why Rationality? I NORMATIVE FOUNDATIONS 1 Normative Frameworks 1.1 What Is a Normative Framework? 1.1.1 Private vs. Public Morality 1.2 Utilitarianism 1.2.1 Why Be a Utilitarian? 1.2.2 Some Problems for Utilitarianism 1.3 Egalitarianism 1.3.1 Equality of Outcomes 1.3.2 Equality of Opportunity 1.4 Kantian Deontology 1.4.1 Deontology and the Challenges to Utilitarianism 1.4.2 Challenges for Deontological Thinking 1.5 Libertarianism 1.5.1 Why Be a Libertarian? 1.5.2 Some Problems for Libertarianism 1.6 Takeaways 1.7 Further Reading 1.8 Exercises 2 Collective Goals 2.1 Rational Individuals 2.2 Aggregation Procedures 2.3 Evaluative Criteria for Aggregation Procedures 2.3.1 Transitivity of Social Preferences 2.3.2 Unanimity 2.3.3 Independence of Irrelevant Alternatives 2.4 Arrow’s Theorem 2.5 Social Decisions Instead of Social Preferences 2.6 The Public Interest? 2.6.1 Only Two Alternatives: May’s Theorem 2.6.2 Ruling Out Some Collections of Preferences: The Median Voter Theorem 2.6.3 Intensity of Preferences 2.6.4 Agreement 2.7 Takeaways 2.8 Further Reading 2.9 Exercises 3 Pareto Concepts 3.1 Pareto Concepts 3.2 From Pareto Efficiency to Pareto Improvements 3.3 A Model of Policies and Preferences 3.3.1 Actions and Transfers 3.3.2 Quasi Linearity: A Bridge from Pareto Efficiency to Pareto Improvement 3.4 A Bridge Too Far? 3.4.1 Limited Transfers and Distributional Concerns 3.4.2 Non Quasi Linear Preferences 3.5 Relationship to Cost-Benefit Analysis 3.6 Are Pareto Improvements Unambiguously in the Public Interest? 3.7 Takeaways 3.8 Further Reading 3.9 Exercises 3.10 Appendix: Proof of Theorem 3.3.1 Summing Up Normative Foundations II SOCIAL DILEMMAS 4 Externalities 4.1 Collective Action 4.1.1 The Social Dilemma 4.1.2 Interpretations 4.2 Public Goods 4.2.1 Comparison to the First Best or Utilitarian Optimum 4.2.2 Interpretation 4.2.3 Concentrated vs. Diffuse Interests 4.3 The Tragedy of the Commons 4.3.1 A Pareto Improvement 4.3.2 The First Best 4.3.3 Interpretation 4.4 Policy Interventions 4.4.1 The Failure of Persuasion 4.4.2 Pigovian Subsidies and Taxes 4.4.3 Regulation 4.5 The Theory of the Second Best 4.5.1 The Second Best Pigovian Subsidy 4.6 Alternative Responses 4.6.1 Altruism 4.6.2 A Market in Externalities 4.6.3 Ongoing Relationships and Self Organization 4.7 Takeaways 4.8 Further Reading 4.9 Exercises 5 Coordination Problems 5.1 Coordination Failure 5.1.1 Interpretation 5.2 Coordination Traps 5.2.1 A Basic Model of Coordination Traps: Investment in Developing Countries 5.2.2 A Model of Bank Runs 5.2.3 A Model of Revolutions 5.2.4 Interpretation 5.3 Policy Responses 5.3.1 Communication 5.3.2 Short Run Intervention 5.3.3 Insurance and the Second Best 5.4 Takeaways 5.5 Further Reading 5.6 Exercises 6 Commitment Problems 6.1 A Model of Conflict 6.1.1 Inefficient Conflict 6.1.2 Interpretation 6.2 The Hold-Up Problem 6.2.1 Interpretation 6.3 Policy Responses 6.4 Takeaways 6.5 Further Reading 6.6 Exercises Summing Up Social Dilemmas III CONSTRAINTS ON GOOD GOVERNANCE 7 Strategic Adjustment 7.1 Strategic Adversaries 7.1.1 Do Terrorists Really Strategically Adjust? 7.1.2 TheWar onDrugs 7.2 Incentivizing Multiple Tasks 7.2.1 High Stakes Testing 7.3 Takeaways 7.4 Further Reading 7.5 Exercises 8 Dynamic Inconsistency 8.1 Time Inconsistency 8.1.1 The First Best 8.1.2 What Will the Government Do? 8.1.3 How Much Will a Consumer Consume? 8.1.4 Is the Government Time Consistent? 8.1.5 Time Inconsistency and Externalities 8.1.6 Rules vs. Discretion 8.1.7 Applications 8.2 Fiscal Manipulation 8.2.1 The First Best 8.2.2 Electoral Risk 8.2.3 Discounting the Future 8.3 When Policy Affects Future Power 8.3.1 The (Political) Second Best 8.4 Takeaways 8.5 Further Readings 8.6 Exercises 9 The Need for Information 9.1 Auctions 9.1.1 Second Price Auction 9.2 Providing a Public Good 9.2.1 Split the Costs 9.2.2 Veto and Split 9.2.3 General Mechanisms 9.2.4 The Second Best 9.3 Regulating a Monopolist 9.3.1 Monopolistic Equilibrium 9.3.2 Regulation with Full Information 9.3.3 Regulation with Uncertainty 9.3.4 An Informed Regulator 9.4 Takeaways 9.5 Further Reading 9.6 Exercises 10 Influence over Elected Officials 10.1 Particularistic Interests 10.2 Special Interests and Campaign Donations 10.3 Electoral Accountability 10.3.1 Rewards of Office 10.3.2 Term Limits 10.3.3 Incentives and Screening 10.3.4 Voter Information 10.3.5 The Risk of Electoral Pandering 10.4 Takeaways 10.5 Further Reading 10.6 Exercises 11 Institutions, Incentives, and Power 11.1 A Selectorate Model 11.1.1 Equilibrium 11.1.2 Outcomes and Institutions 11.2 Institutions and Development 11.2.1 Settler Mortality, Institutions, and the Economy 11.3 Foreign Aid 11.3.1 Poverty Traps and Foreign Aid 11.3.2 Does Foreign Aid Work through Poverty Traps? 11.3.3 Effective Aid? 11.3.4 A Political Economy of Foreign Aid 11.4 Takeaways 11.5 Further Reading 11.6 Exercises Summing Up Constraints on Good Governance Concluding Reflections on Politics and Policy IV APPENDICES ON GAME THEORY A Utility, Strategic-Form Games, and Nash Equilibrium A.1 Utility A.1.1 Expected Utility A.2 Games in Strategic Form A.2.1 Where to Eat? A.2.2 Matching Pennies A.2.3 Cleaning an Apartment A.2.4 Choosing a Number A.3 Nash Equilibrium A.4 Why Nash Equilibrium? A.4.1 No Regrets and Social Learning A.4.2 Self Enforcing Agreements A.4.3 Analyst’s Humility A.5 Solving for Nash Equilibrium A.6 Nash Equilibrium Examples A.6.1 Where to Eat? A.6.2 Matching Pennies A.6.3 Cleaning an Apartment A.6.4 Choosing a Number with Two Players A.7 Takeaways A.8 Exercises B Extensive-Form Games B.1 Games in Extensive Form B.1.1 A Model of International Crisis B.2 Game Trees B.2.1 International Crisis Game B.2.2 A Budget Game B.2.3 The Centipede Game B.3 Strategies as Complete Contingent Plans B.3.1 International Crisis Game B.3.2 Budget Game B.3.3 The Centipede Game B.4 Representing an Extensive-Form Game as a Strategic-Form Game B.4.1 The International Crisis Game B.4.2 The Budget Game B.4.3 The Centipede Game B.5 Nash Equilibria of Extensive-Form Games B.5.1 International Crisis Game B.5.2 The Budget Game B.5.3 The Centipede Game B.6 Subgame Perfect Nash Equilibrium B.6.1 Subgame Perfection B.6.2 Backward Induction B.6.3 Indifference and Multiple Equilibria B.6.4 Continuous Choices B.7 Discounted Payoffs B.8 Takeaways B.9 Exercises Bibliography Index of Referenced Authors General Index 2016-07-19T20:13:12+0000 Preflight Ticket Signature