Nitzan S. Collective preference and choice (Cambridge; New York, 2010). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаNitzan S. Collective preference and choice. - Cambridge; New York: Cambridge university press, 2010. - XVII,255 p.: ill., tab. - Bibliogr.: p. 246-250. - Auth. ind.: p. 251-252. - Subject ind.: p. 253-255. - ISBN 978-0-521-89725-9
Шифр: (И/С55-N71) 02

 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
List of figures ............................................... xii
Preface ...................................................... xiii
Acknowledgments ............................................... xvi

Part I: Introduction ............................................ 1
1  The reason for the problems .................................. 3
   1.1  Exercises ............................................... 6
   1.2  Summary ................................................. 7
2  Brief overview of the problems ............................... 9
   2.1  Exercises .............................................. 15
   2.2  Summary ................................................ 16
3  The relationship between preferences and choice ............. 19
   3.1  Preference-driven choice ............................... 20
   3.2  Rationalizable choice .................................. 23
   3.3  Exercises .............................................. 26
   3.4  Summary ................................................ 30

Part II: Different Preferences ................................. 33
4  Do social preferences exist? Arrow's and Sen's
   impossibility theorems ...................................... 35
   4.1  The social choice model ................................ 36
   4.2  Arrow impossibility theorem ............................ 39
   4.3  The Paretian liberal paradox ........................... 50
   4.4  Exercises .............................................. 51
   4.5  Summary ................................................ 58
5  The desirable decision rule: axiomatization ................. 60
   5.1  Dichotomous choice and the simple majority rule ........ 60
   5.2  The Borda rule ......................................... 64
   5.3  Exercises .............................................. 68
   5.4  Summary ................................................ 74
6  Rule selection based on compromise with the unanimity
   criterion ................................................... 76
   6.1  The unanimity criterion ................................ 76
   6.2  Distance between preferences ........................... 78
   6.3  The metric compromise with the unanimity criterion ..... 80
        6.3.1  The example of the Borda rule ................... 83
        6.3.2  The example of the plurality rule ............... 84
   6.4  Extensions ............................................. 84
   6.5  Exercises .............................................. 85
   6.6  Summary ................................................ 91
7  Paradoxes of voting ......................................... 93
   7.1  Condorcet's voting paradox ............................. 94
   7.2  Condorcet's inconsistency .............................. 97
   7.3  Violation of the Pareto criterion ...................... 99
   7.4  Violation of consistency .............................. 100
   7.5  Violation of consistency in contraction and in
        expansion ............................................. 102
   7.6  Inverted order paradox ................................ 103
   7.7  The winner-turns-loser paradox ........................ 104
   7.8  The no-show paradox ................................... 105
   7.9  Exercises ............................................. 106
   7.10  Summary .............................................. 114
8  Majority tyranny ........................................... 117
   8.1  Scoring rules ......................................... 118
   8.2  Majority decisiveness ................................. 120
   8.3  Resolution of the problem of majority tyranny under
        sincere voting ........................................ 123
   8.4  Resolution of the problem of majority tyranny under
        insincere voting ...................................... 124
   8.5  Erosion in the majority principle vs. majority
        tyranny ............................................... 126
   8.6  The golden scoring rule ............................... 127

   8.7  Appendix .............................................. 131
   8.8  Exercises ............................................. 132
   8.9  Summary ............................................... 142
9  The problem of inefficient provision of public goods ....... 146
   9.1  The collective decision rule and inefficient
        provision of a public good ............................ 147
   9.2  Voting ................................................ 148
        9.2.1  The simple majority rule ....................... 151
        9.2.2  The dictatorial rule ........................... 154
        9.2.3  The Borda rule ................................. 154
        9.2.4  The unanimity rule ............................. 154
   9.3  Voluntary provision of the public good ................ 155
   9.4  Appendix .............................................. 158
   9.5  Exercises ............................................. 158
   9.6  Summary ............................................... 173
 10 Do individuals reveal their true preferences? ............. 176
   10.1 Non-truthful revelation of preferences ................ 177
   10.2 The impossibility theorem of Gibbard-Satterthwaite .... 180
   10.3 Revelation of preferences and the efficient
        provision of a public good - the dichotomous case ..... 186
   10.3.1 The Groves-Clarke revelation mechanism .............. 188
   10.4 Exercises ............................................. 193
   10.5 Summary ............................................... 197

Part III: Identical Preferences, Different Decisional Skills .. 199
11 Which rule is better: the expert rule or the simple
   majority rule? Decisional errors in dichotomous choice
   and Condorcet's jury theorem ............................... 201
   11.1 The expert rale vs. the simple majority rule: the
        case of three identical decision makers ............... 202
   11.2 The expert rule vs. the simple majority rule: the
        case of three decision makers with unknown
        decisional skills ..................................... 203
   11.3 Condorcet's jury theorem .............................. 205
   11.4 Extensions of Condorcet's jury theorem ................ 207
        11.4.1 The superiority of the simple majority rule
               when the decisional skills of the n voters
               are unknown .................................... 207
        11.4.2 The superiority of the simple majority rule
               when the decisional skills of the n voters
               are different .................................. 207
   11.5 Is Condorcet's theorem valid when decisional skills
        are determined endogenously? .......................... 208
        11.5.1 The extended model: identical endogenous
               decisional skills .............................. 209
        11.5.2 Centrally determined decisional skills ......... 209
   11.6 Is Condorcet's theorem valid when individual
        decisions are insincere? .............................. 211
        11.6.1 Strategic considerations and insincere voting .. 212
        11.6.2 Condorcet's theorem and strategic
               considerations ................................. 213
   11.7 Exercises ............................................. 218
   11.8 Summary ............................................... 224

12 The optimal decision rule under uncertain dichotomous
   choice ..................................................... 227
   12.1 Dichotomous decision making - the model ............... 227
   12.2 The optimal decision rale ............................. 230
        12.2.1 Qualified weighted majority rule ............... 232
        12.2.2 Qualified majority rule ........................ 233
   12.3 The optimal decision rule in the symmetric case ....... 235
        12.3.1 Weighted majority rule ......................... 235
        12.3.2 Simple majority rule ........................... 235
        12.3.3 The expert rule ................................ 235
   12.4 Extensions ............................................ 236
        12.4.1 Dependence of decisional skills on the state
               of nature ...................................... 236
        12.4.2 Dependent decisions ............................ 236
        12.4.3 The number of decision makers is not fixed ..... 236
        12.4.4 Decisional skills are not fixed ................ 237
        12.4.5 Partial information on decisional skills ....... 237
        12.4.6 Sequential decision ............................ 238
        12.4.7 More than two alternatives ..................... 238
   12.5 Exercises ............................................. 238
   12.6 Summary ............................................... 243

Bibliography .................................................. 246
Author index .................................................. 251
Subject index ................................................. 253


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