Social choice

Cover......Page 1
Title page......Page 5
Contents......Page 7
Preface......Page 11
1.1 Social choice theory......Page 13
1.2 Elections......Page 15
1.3 Committees......Page 17
1.4 Economic contexts......Page 18
1.5 Moral judgements......Page 20
1.6 Further reading......Page 22
2.1 Individuals and alternatives......Page 25
2.2 Preferences: notation and basic assumptions......Page 27
2.3 Choice......Page 30
2.4 Preferences about sets of alternatives......Page 36
2.5 Utility......Page 38
3.1 Social choice rules......Page 41
3.2 The domain of social choice......Page 42
3.3 Independence......Page 43
3.4 Unanimity and the Pareto condition......Page 46
3.5 Dictatorship......Page 47
3.7 Proof of Arrow's theorem: the epidemic......Page 48
3.8 Proof of Arrow's theorem: the collective......Page 53
3.9 Proof of Arrow's theorem: the dictator......Page 55
3.10 Alternative versions......Page 56
3.11 Strong Pareto and a hierarchy of dictators......Page 57
3.12 Fixed preferences......Page 58
3.13 Possible resolutions......Page 59
4.1 Limited path independence......Page 63
4.2 Path independence......Page 67
4.3 Quasitransitivity and oligarchy......Page 69
4.4 Acyclic preferences and extended majority voting......Page 73
Appendix: Conventional rationality conditions......Page 75
5.1 Non-manipulable social choice rules......Page 79
5.2 Non-manipulability and the proof of Arrow's theorem......Page 81
5.3 Maximin criterion for preferences......Page 86
5.5 Resolute social choice rules......Page 88
5.6 Further considerations......Page 92
6.1 Value restriction without indifference......Page 97
6.2 Preference restrictions with individual indifference......Page 103
6.3 Manipulability with restricted preferences......Page 108
6.4 Support for majority voting......Page 110
6.5 Limited agendas......Page 112
Appendix: Counting single-peaked preferences......Page 116
7.1 Imposed social choices......Page 119
7.2 Rights to choose......Page 121
7.3 Rights and Arrow's theorem......Page 123
7.4 Sacrificing the Pareto condition......Page 127
7.5 Limiting rights......Page 128
8.1 Impersonal principles of justice......Page 135
8.2 Status rankings......Page 136
8.3 Maximin and leximin......Page 139
8.4 Less demanding principles of justice......Page 142
8.5 Personal principles of justice......Page 143
9 Utilitarian judgements......Page 145
9.1 Utility functions......Page 146
9.2 von Neumann-Morgenstern utility......Page 147
9.3 Measurability without comparability......Page 149
9.4 Utilitarianism and justice......Page 151
9.5 Utilitarianism and Arrow's theorem......Page 154
Bibliography......Page 157
Index......Page 161