Social Choice: A Framework for Collective Decisions and Individual Judgements Book

	Preface
1	Introduction	1
1.1	Social choice theory	1
1.2	Elections	3
1.3	Committees	5
1.4	Economic contexts	6
1.5	Moral judgements	8
1.6	Further reading	10
2	Preference and choice	13
2.1	Individuals and alternatives	13
2.2	Preferences: notation and basic assumptions	15
2.3	Choice	18
2.4	Preferences about sets of alternatives	24
2.5	Utility	26
3	Arrow's theorem	29
3.1	Social choice rules	29
3.2	The domain of social choice	30
3.3	Independence	31
3.4	Unanimity and the Pareto condition	34
3.5	Dictatorship	35
3.6	Arrow's theorem	36
3.7	Proof of Arrow's theorem: the epidemic	36
3.8	Proof of Arrow's theorem: the collective	41
3.9	Proof of Arrow's theorem: the dictator	43
3.10	Alternative versions	44
3.11	Strong Pareto and a hierarchy of dictators	45
3.12	Fixed preferences	46
3.13	Possible resolutions	47
4	Collective rationality	51
4.1	Limited path independence	51
4.2	Path independence	55
4.3	Quasitransitivity and oligarchy	57
4.4	Acyclic preferences and extended majority voting	61
	Appendix to chapter 4: Conventional rationality conditions	63
5	Strategic manipulation of choice rules	67
5.1	Non-manipulable social choice rules	67
5.2	Non-manipulability and the proof of Arrow's theorem	69
5.3	Maximin criterion for preferences	74
5.4	Replacing weak Pareto	76
5.5	Resolute social choice rules	76
5.6	Further considerations	80
6	Rescuing majority voting	85
6.1	Value restriction without indifference	85
6.2	Preference restrictions with individual indifference	91
6.3	Manipulability with restricted preferences	96
6.4	Support for majority voting	98
6.5	Limited agendas	100
	Appendix to chapter 6: Counting single-peaked preferences	104
7	Rights	107
7.1	Imposed social choices	107
7.2	Rights to choose	109
7.3	Rights and Arrow's theorem	111
7.4	Sacrificing the Pareto condition	115
7.5	Limiting rights	116
8	Justice	123
8.1	Impersonal principles of justice	123
8.2	Status rankings	124
8.3	Maximin and leximin	127
8.4	Less demanding principles of justice	130
8.5	Personal principles of justice	131
9	Utilitarian judgements	133
9.1	Utility functions	134
9.2	von Neumann-Morgenstern utility	135
9.3	Measurability without comparability	137
9.4	Utilitarianism and justice	139
9.5	Utilitarianism and Arrow's theorem	142
	Bibliography	145
	Index	149