Voting Paradoxes and How to Deal With Them

by Nurmi, Hannu

• ISBN13: 9783540662365
• ISBN10: 3540662367
• Format: Hardcover
• Copyright: 1999-11-01
• Publisher: Springer Verlag

Summary

Voting paradoxes are unpleasant surprises encountered in elections. They pertain to such phenomena as additional support being detrimental for candidates and not voting leading to better outcomes than voting for some voters. No voting system is immune to all paradoxes and, therefore voting paradoxes are being dealt with by all voting systems currently in use. How they are and how they should be handled is the main subject of this book. The book outlines, explains and classifies a number of paradoxes: Borda's and Condorcet's classic ones, several monotonicity and compound majority paradoxes as well as some paradoxes of representation. Both theoretical and practical ways of avoiding them are discussed.

Table of Contents

Preface
Introduction	p. 1
Basic Concepts and Tools	p. 4
Alternatives and Opinions	p. 4
Preference Profile	p. 6
Pairwise Comparison and Tournament Matrix	p. 7
McGarvey's Theorem	p. 8
Paradoxes of the Enlightenment Era	p. 11
Borda's Paradox	p. 11
Condorcet's Paradox	p. 15
Borda and Condorect Compared	p. 22
How Frequent Are the Paradoxes?	p. 25
The Geometry of Voting	p. 31
The Saari Triangles	p. 31
The Conditions of Paradoxes	p. 34
The Paradoxical Act of Voting	p. 41
The Cost Calculus	p. 41
The No-Show Paradox	p. 49
Monotonicity Paradoxes	p. 55
Additional Support Paradox	p. 55
Preference Truncation Paradox	p. 62
How to Deal with Monotonicity Paradoxes?	p. 67
Compound Majority Paradoxes	p. 70
Ostrogorski's Paradox	p. 70
Anscombe's Paradox	p. 73
The Paradox of Multiple Elections	p. 74
The Referendum Paradox	p. 76
Simpson's Paradox	p. 78
How to Deal With Compound Majority Paradoxes	p. 81
Intra-Profile Paradoxes	p. 87
Pareto Violations	p. 87
Inconsistency Paradox	p. 89
Choice Set Variance Paradoxes	p. 94
The q-Rules and Pareto Violations	p. 98
Tournament Solutions to Voting Paradoxes	p. 101
Paradoxes of Representation	p. 109
The Alabama Paradox	p. 109
Other Paradoxes of Hamilton Apportionments	p. 112
Schwartz's Paradox of Representation	p. 115
How to Deal with Representation Paradoxes	p. 118
Classification of Paradoxes	p. 120
Hard and Soft Solutions	p. 125
List of Figures	p. 129
List of Tables	p. 131
Bibliography	p. 135
Index	p. 145
Table of Contents provided by Blackwell. All Rights Reserved.