Lepelley Voting Paradoxes and Group Coherence

The Condorcet Efficiency of Voting Rules
1. Auflage 2010
ISBN: 978-3-642-03107-6
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 385 Seiten

The likelihood of observing Condorcet's Paradox is known to be very low for elections with a small number of candidates if voters' preferences on candidates reflect any significant degree of a number of different measures of mutual coherence. This reinforces the intuitive notion that strange election outcomes should become less likely as voters' preferences become more mutually coherent. Similar analysis is used here to indicate that this notion is valid for most, but not all, other voting paradoxes. This study also focuses on the Condorcet Criterion, which states that the pairwise majority rule winner should be chosen as the election winner, if one exists. Representations for the Condorcet Efficiency of the most common voting rules are obtained here as a function of various measures of the degree of mutual coherence of voters' preferences. An analysis of the Condorcet Efficiency representations that are obtained yields strong support for using Borda Rule.

Autoren/Hrsg.

Lepelley, Dominique

Inhaltsverzeichnis

1;Preface;8
2;Contents;10
3;Chapter 1: Voting Paradoxes and Their Probabilities;14
3.1;1.1 Introduction;14
3.2;1.2 The Case of More than Two Candidates;16
3.3;1.3 Voting Paradoxes;18
3.4;1.4 Empirical Evidence of the Existence of Voting Paradoxes;25
3.5;1.5 Probability Representations for Voting Paradoxes;29
3.6;1.6 Relevance of DC, IC, IAC and MC Based Probabilities;53
3.7;1.7 Conclusion;60
4;Chapter 2: Condorcet´s Paradox and Group Coherence;61
4.1;2.1 Introduction;61
4.2;2.2 Population Specific Measures of Homogeneity;61
4.3;2.3 Situation Specific Measures of Homogeneity;62
4.4;2.4 Obtaining Probability Representations;69
4.5;2.5 Cumulative Probabilities that a PMRW Exists;80
4.6;2.6 Proportions of Profiles with Specified Parameters;83
4.7;2.7 Results with Strong Measures of Group Coherence;85
4.8;2.8 Conclusion;90
5;Chapter 3: Other Incompatibility Paradoxes;92
5.1;3.1 Introduction;92
5.2;3.2 Borda´s Paradox;92
5.3;3.3 Condorcet´s Other Paradox;125
5.4;3.4 Conclusion;131
6;Chapter 4: Other Voting Paradoxes;133
6.1;4.1 Choice Set Variance Paradoxes;133
6.2;4.2 Monotonicity Paradoxes;160
6.3;4.3 The Instability Paradox;163
6.4;4.4 Conclusion;164
7;Chapter 5: Condorcet Efficiency and Social Homogeneity;166
7.1;5.1 Introduction;166
7.2;5.2 The Desirability of Using Simple Voting Rules;168
7.3;5.3 Early Research on the Condorcet Efficiency of Voting Rules;170
7.4;5.4 The Impact of Social Homogeneity on Efficiency;199
8;Chapter 6: Coherence and the Efficiency Hypothesis;208
8.1;6.1 Introduction;208
8.2;6.2 Numerical Evidence;208
8.3;6.3 Condorcet Efficiency with Single Peaked Preferences;210
8.4;6.4 Efficiency with Weak Measures of Group Coherence;212
8.5;6.5 Efficiency with Strong Measures of Group Coherence;235
8.6;6.6 Conclusion;255
9;Chapter 7: Other Characteristics of Voting Rules;257
9.1;7.1 Introduction;257
9.2;7.2 Empirical Studies of Condorcet Efficiency;257
9.3;7.3 Practical Factors and Condorcet Efficiency;260
9.4;7.4 Voter Indifference and Condorcet Efficiency;267
9.5;7.5 Voter Abstention and Condorcet Efficiency;277
9.6;7.6 The Presence of a PMR Cycle and Condorcet Efficiency;284
9.7;7.7 The Impact of Removing Candidates;290
9.8;7.8 Results from Saaris Analysis of WSRs;292
9.9;7.9 Characterizations of BR;295
9.10;7.10 Potential for Manipulation;297
9.11;7.11 Conclusion;302
10;Chapter 8: The Significance of Voting Rule Selection;303
10.1;8.1 Introduction;303
10.2;8.2 Same Winner with Two Voting Rules;303
10.3;8.3 The Probability that All WSR´s Elect the Same Winner;307
10.4;8.4 Homogeneity and Voting Rule Selection Sensitivity;310
10.5;8.5 Measures of Coherence and Voting Rule Selection Sensitivity;311
10.6;8.6 Other Voting Rules;322
10.7;8.7 Conclusion;336
11;Chapter 9: Complete PMR Ranking Efficiencies;338
11.1;9.1 Introduction;338
11.2;9.2 Candidate Ranking Sensitivity to WSR Selection;338
11.3;9.3 Condorcet Ranking Efficiency;340
11.4;9.4 Condorcet Committees;364
12;References;374
13;Index;388