A Primer in Social Choice Theory Revised Edition

by Gaertner, Wulf

• ISBN13: 9780199565306
• ISBN10: 0199565309
• Edition: Revised
• Format: Paperback
• Copyright: 2009-06-26
• Publisher: Oxford University Press

Summary

This revised edition includes new exercise sections designed for students to put theory into practice as well as a hints section that provides useful pointers and help on solving the exercises.

Author Biography

Wulf Gaertner is Professor of Economics at the University of Osnabruck in Germany and Fellow of Wissenschaftskolleg, Berlin. He has held several visiting posts at Tulane University, Harvard University, and the London School of Economics and Political Science, and was the recipient of the Ludwig Lachmann Research Fellowship from the LSE for the period 2006-2008. Professor Gaertner is also one of the managing editors of the journal, Social Choice and Welfare.

Table of Contents

Preface to the Revised Edition	p. vii
Preface and Acknowledgements to the First Edition	p. viii
About the Author	p. xiii
Introduction	p. 1
Basic questions	p. 1
Catching a glimpse of the past	p. 3
Basic formalism	p. 6
Aggregation of preferences - how can this be done?	p. 9
The informational aspect	p. 12
A path through haze, or how to read this book	p. 14
Some exercises	p. 16
Arrow's impossibility result	p. 19
The axiom system and the theorem	p. 19
The original proof	p. 21
A second proof	p. 25
A third diagrammatic proof	p. 28
A short summary	p. 34
Some exercises	p. 34
Majority decision under restricted domains	p. 37
The simple majority rule	p. 37
Single-peaked preferences	p. 43
Other domain conditions: qualitative and quantitative	p. 49
A short summary	p. 53
Some exercises	p. 53
Individual rights	p. 57
Sen's impossibility of a Paretian liberal	p. 57
Gibbard's theory of alienable rights	p. 59
Conditional and unconditional preferences	p. 62
Conditional and unconditional preferences again: matching pennies and the prisoners' dilemma	p. 64
The game form approach to rights	p. 66
A short summary	p. 70
Some exercises	p. 71
Manipulability	p. 75
The underlying problem	p. 75
The Gibbard-Satterthwaite theorem	p. 80
Strategy-proofness and restricted domains	p. 85
A short summary	p. 92
Some exercises	p. 93
Escaping impossibilities: social choice rules	p. 97
The Pareto-extension rule and veto power	p. 97
Scoring functions and the Borda rule	p. 102
Other social choice rules	p. 109
A parliamentary vote: Berlin vs. Bonn	p. 114
A short summary	p. 117
Some exercises	p. 117
Distributive justice: Rawlsian and utilitarian rules	p. 121
The philosophical background	p. 121
The informational structure	p. 122
Axioms and characterizations	p. 124
Diagrammatic proofs again	p. 129
Harsanyi's utilitarianism	p. 134
A short summary	p. 136
Some exercises	p. 137
Cooperative bargaining	p. 139
The bargaining problem	p. 139
Nash's bargaining solution	p. 140
Zeuthen's principle of alternating concessions	p. 148
The Kalai-Smorodinsky bargaining solution	p. 151
A philosopher's view	p. 155
Kalai's egalitarian solution	p. 157
A short summary	p. 159
Some exercises	p. 160
Empirical social choice	p. 163
Theory and opinions of the general public	p. 163
Needs vs. tastes - the approach by Yaari and Bar-Hillel	p. 164
Rawls's equity axiom - how does it fare?	p. 171
From here to where?	p. 177
A short summary	p. 179
Some exercises	p. 179
A few steps beyond	p. 181
Social choice rules in continuous space	p. 181
The uniform rule	p. 187
Freedom of choice	p. 192
An epilogue instead of a summary	p. 199
References	p. 201
Hints to the Exercises	p. 209
Author Index	p. 213
Subject Index	p. 215
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