Gehrlein Condorcet's Paradox

1. Auflage 2006
ISBN: 978-3-540-33799-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 40, 292 Seiten

Reihe: Theory and Decision Library C

The book compiles research on Condorcet's Paradox over some two centuries. It begins with a historical overview of the discovery of Condorcet's Paradox in the 18th Century, reviews numerous studies conducted to find actual occurrences of the paradox, and compiles research that has been done to develop mathematical representations for the probability that the paradox will be observed. Combines all approaches that have been used to study this very interesting phenomenon.

Autoren/Hrsg.

Gehrlein, William V.

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Elections and Voting Paradoxes;11
3.1;1.1 Introduction;11
3.2;1.2 The Case of More than Two Candidates;14
3.3;1.3 Borda’s Paradox;17
3.4;1.4 Condorcet’s Paradox;26
3.5;1.5. Condorcet’s Other Paradox;31
3.6;1.6 The Paradox of Multiple Elections;34
3.7;1.7 The Vote Trading Paradox;35
3.8;1.8 The No Show Paradox;37
3.9;1.9 Other Voting Paradoxes;38
3.10;1.10 Conclusion;39
4;2 Condorcet’s Paradox;40
4.1;2.1 Introduction;40
4.2;2.2 Riker’s Empirical Studies;42
4.3;2.3 Other Empirical Studies;46
4.4;2.4 Monte-Carlo Simulation Studies;57
4.5;2.5 Conditions that Prohibit Condorcet’s Paradox;60
4.6;2.6 Variations of Condorcet’s Paradox;65
4.7;2.7 Conclusion;67
5;3 The Cases of Two and Three Candidates;68
5.1;3.1 Introduction;68
5.2;3.2 The Problem with Three Candidates;70
5.3;3.3 Probabilities with Balanced Preferences;75
5.4;3.4 Expected Balance for Voting Situations;78
5.5;3.5 Expected Balance for Individual Preferences;90
5.6;3.6 Uniform Culture Condition;101
5.7;3.7 Other IC-IAC Connections;103
5.8;3.8 The Impact of Unbalanced Preferences;108
5.9;3.9 Other Representations;110
5.10;3.10 Conclusion;113
6;4 The Case of More than Three Candidates;115
6.1;4.1 Introduction;115
6.2;4.2 Representations for Four-Candidate Elections;115
6.3;4.3 More than Four Candidates;125
6.4;4.4 Other Related Results;147
6.5;4.5 Conclusion;160
7;5 The Impact of Societal Factors;161
7.1;5.1 Introduction;161
7.2;5.2 Population Specific Measures of Homogeneity;163
7.3;5.3 Situation Specific Measures of Homogeneity;168
7.4;5.4 The Effectiveness of Measures of Social Homogeneity;173
7.5;5.5 Requiring More Coherence in Voters’ Preferences;176
7.6;5.6 Voter Abstention;179
7.7;5.7 Degrees of Voter Indifference between Candidates;191
7.8;5.8 The Impact of Intransitive Voter Preferences;198
7.9;5.9 The Impact of Uncertainty;201
7.10;5.10 Conclusion;202
8;6 The Impact of Coherent Preferences;203
8.1;6.1 Introduction;203
8.2;6.2 Methods for Obtaining Representations;203
8.3;6.3 Proximity to Single-Troughed Preferences;220
8.4;6.4 The Impact of Polarizing Candidates;221
8.5;6.5 Limiting Distributions for Large Electorates;225
8.6;6.6 Cumulative Probabilities that a PMRW Exists;227
8.7;6.7 Proportions of Profiles with Specified Parameters;229
8.8;6.8 The Impact of an Overall Unifying Candidate;232
8.9;6.9 The Impact of Ward’s Condition;234
8.10;6.10 Ehrhart Polynomials;236
8.11;6.11 Conclusion;236
9;7 Individual Intransitivity;237
9.1;7.1 Introduction;237
9.2;7.2 Algebraic and Probabilistic Choosers;238
9.3;7.3 May’s Model;239
9.4;7.4 Probabilistic Chooser Models;242
9.5;7.5 Algebraic and Probabilistic Chooser Coincidence;243
9.6;7.6 Weak Maximal Alternatives;248
9.7;7.7 Attribute Independence - Discriminatory Power;252
9.8;7.8 The Impact of Single-Peakedness;264
9.9;7.9 Strict Maximal-Minimal Reversal;266
9.10;7.10 Other Related Representations;268
9.11;7.11 Conclusion;271
10;References;272
11;Index;292