Voting, Arbitration & Fair Division: Mathematics of Social Choice

I Voting and Social Choice......Page 7
Simple Majority Voting: May's Theorem......Page 9
Weighted Majority Voting Systems......Page 12
Vector-Weighted Voting Systems......Page 17
Voting Power Indices......Page 19
Plurality voting & Borda's Paradox......Page 23
Pairwise elections......Page 26
The Condorcet Scheme......Page 27
Borda Count......Page 29
Approval voting......Page 33
Preferences and Profiles......Page 35
Voting procedures......Page 37
Desiderata......Page 41
Sen and (Minimal) Liberalism......Page 45
Arrow's Impossibility Theorem......Page 46
Strategic Voting: Gibbard & Satterthwaite......Page 52
II Social Welfare Functions......Page 59
Utility functions......Page 61
The problem of interpersonal comparisons......Page 66
The Groves-Clarke Pivotal Mechanism......Page 68
Further Reading......Page 72
III Bargaining and Arbitration......Page 75
The von Neumann-Morgenstern Model......Page 77
The Nash Solution......Page 84
Hausdorff Continuity......Page 92
Introduction......Page 95
Normal-form games and Nash equilibria......Page 99
The Nash demand game......Page 107
The Harsanyi-Zeuthen concession model......Page 109
Discount Factors......Page 111
The Rubinstein-Ståhl Alternating Offers model......Page 115
Proof of Rubinstein's Theorem......Page 122
The Utilitarian Solution......Page 137
The Proportional Solution......Page 143
Solution Syzygy......Page 152
Contractarian Political Philosophy......Page 155
Kalai & Smorodinsky's Relative Egalitarianism......Page 161
Relative Utilitarianism......Page 166
IV Fair Division......Page 167
Partitions, Procedures, and Games......Page 169
Utility Measures......Page 171
Partition Procedures......Page 172
Partition Games......Page 173
Banach and Knaster's `Last Diminisher' game......Page 177
The Latecomer Problem: Fink's `Lone Chooser' game......Page 181
Symmetry: Dubins and Spanier's `Moving Knife' game......Page 184
Connectivity: Hill and Beck's Fair Border Procedure......Page 186
Appendix on Topology......Page 191
Introduction......Page 195
Mutually Beneficial Trade......Page 196
Utility Ratio Threshold Partitions......Page 198
Bentham Optimality & `Highest Bidder'......Page 202
Envy-freedom......Page 205
Equitable Partitions & `Adjusted Winner'......Page 209
Entitlements......Page 214
Indivisible Value......Page 216
Chores......Page 217
Nonmanipulability......Page 218
Bibliography......Page 219