Voting Paradoxes and Group Coherence (eBook)

Preface 8
Contents 10
Chapter 1: Voting Paradoxes and Their Probabilities 14
1.1 Introduction 14
1.2 The Case of More than Two Candidates 16
1.3 Voting Paradoxes 18
1.4 Empirical Evidence of the Existence of Voting Paradoxes 25
1.5 Probability Representations for Voting Paradoxes 29
1.6 Relevance of DC, IC, IAC and MC Based Probabilities 53
1.7 Conclusion 60
Chapter 2: Condorcet´s Paradox and Group Coherence 61
2.1 Introduction 61
2.2 Population Specific Measures of Homogeneity 61
2.3 Situation Specific Measures of Homogeneity 62
2.4 Obtaining Probability Representations 69
2.5 Cumulative Probabilities that a PMRW Exists 80
2.6 Proportions of Profiles with Specified Parameters 83
2.7 Results with Strong Measures of Group Coherence 85
2.8 Conclusion 90
Chapter 3: Other Incompatibility Paradoxes 92
3.1 Introduction 92
3.2 Borda´s Paradox 92
3.3 Condorcet´s Other Paradox 125
3.4 Conclusion 131
Chapter 4: Other Voting Paradoxes 133
4.1 Choice Set Variance Paradoxes 133
4.2 Monotonicity Paradoxes 160
4.3 The Instability Paradox 163
4.4 Conclusion 164
Chapter 5: Condorcet Efficiency and Social Homogeneity 166
5.1 Introduction 166
5.2 The Desirability of Using Simple Voting Rules 168
5.3 Early Research on the Condorcet Efficiency of Voting Rules 170
5.4 The Impact of Social Homogeneity on Efficiency 199
Chapter 6: Coherence and the Efficiency Hypothesis 208
6.1 Introduction 208
6.2 Numerical Evidence 208
6.3 Condorcet Efficiency with Single Peaked Preferences 210
6.4 Efficiency with Weak Measures of Group Coherence 212
6.5 Efficiency with Strong Measures of Group Coherence 235
6.6 Conclusion 255
Chapter 7: Other Characteristics of Voting Rules 257
7.1 Introduction 257
7.2 Empirical Studies of Condorcet Efficiency 257
7.3 Practical Factors and Condorcet Efficiency 260
7.4 Voter Indifference and Condorcet Efficiency 267
7.5 Voter Abstention and Condorcet Efficiency 277
7.6 The Presence of a PMR Cycle and Condorcet Efficiency 284
7.7 The Impact of Removing Candidates 290
7.8 Results from Saaris Analysis of WSRs 292
7.9 Characterizations of BR 295
7.10 Potential for Manipulation 297
7.11 Conclusion 302
Chapter 8: The Significance of Voting Rule Selection 303
8.1 Introduction 303
8.2 Same Winner with Two Voting Rules 303
8.3 The Probability that All WSR´s Elect the Same Winner 307
8.4 Homogeneity and Voting Rule Selection Sensitivity 310
8.5 Measures of Coherence and Voting Rule Selection Sensitivity 311
8.6 Other Voting Rules 322
8.7 Conclusion 336
Chapter 9: Complete PMR Ranking Efficiencies 338
9.1 Introduction 338
9.2 Candidate Ranking Sensitivity to WSR Selection 338
9.3 Condorcet Ranking Efficiency 340
9.4 Condorcet Committees 364
References 374
Index 388