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Disposing Dictators, Demystifying Voting Paradoxes

Social Choice Analysis

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Paperback | 25 August 2008

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256 Pages

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22.6 x 15.5 x 1.4

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We decide by elections, but do we elect who the voters really want? The answer, as we have learned over the last two centuries, is ''not necessarily''. What a negative, frightening assertion about a principal tool of democracy! This negativism has been supported by two hundred years of published results showing how bad the situation can be. This expository, largely non-technical book is the first to find positive results showing that the situation is not anywhere as dire and negative as we have been led to believe. Instead there are surprisingly simple explanations for the negative assertions, and positive conclusions can be obtained.

Industry Reviews

Advance praise: 'The future generations of social choice theorists will certainly find much inspiration and profound insights in this book. For anyone working in the field of voting and social choice the book will provide a rich collection of results, methodological tools, and challenging open problems.' Hannu Nurmi, Academy of Finland Advance praise: 'Donald Saari provides not only an engaging and accessible explanation of the celebrated dictatorial theorems of Arrow, Sen, and Chichilnisky but also an intuitive argument for why we should not be surprised by the negative results of these seminal theorems.' Tommy Ratliff, Wheaton College Advance praise: 'Arrow's theorem is at the origin of the birth of modern social choice theory in the late 1940s and 1950s. Sen's theorem on liberalism and the Pareto principle (published in 1970) created an upsurge of fundamental studies in the so-called non-welfaristic issues in normative economics. Both results are essentially negative (impossibilities). Saari, in this book, demonstrates that we must not overestimate these negative aspects. Particularly noteworthy are the remarkable presentations of the topological approach to social choice and of the generic stability of the core of voting games (including a very short introduction to a new solution concept, the finesse point), where Saari, once again, shows his wonderful pedagogical talent.' Maurice Salles, University of Caen

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You Can Find This Book In

Non-Fiction Politics & Government Political Structure & Processes Political Structures & Democracy Elections & Referenda Economics Economic History Economic Theory & Philosophy Political Economy Mathematics Probability & Statistics Sociology & Anthropology

Sociology Social Research & Statistics

Preface	p. xi
Subtle Complexity of Social Choice	p. 1
Does Everything Go Wrong?	p. 1
And the Proud Father Is...	p. 3
Enemies?	p. 7
Curse of Dimensionality	p. 13
Outline	p. 15
Dethroning Dictators, and Then Paradoxes	p. 16
The "Will of the Voters": What Is It?	p. 18
Dethroning Dictators	p. 20
Major Negative Conclusions	p. 21
Arrow's Theorem	p. 21
Sen's Seminal Result	p. 23
Topological Dictators	p. 26
"Paradox of Voting" and Condorcet's Triplets	p. 28
List's Lists	p. 29
Anscombe	p. 30
A Standard Requirement	p. 31
Commonality	p. 31
Condorcet's Ideas Dominate	p. 32
Can We Trust the Majority Voting over Pairs?	p. 40
A Common Explanation	p. 42
Why Do These Negative Results Occur?	p. 43
Arrow's Theorem	p. 44
Sen's Result	p. 47
Topological Dictators and Beach Parties	p. 51
Positive Replacements	p. 58
Arrow's Result	p. 58
Sen's Result	p. 64
Topological Dictators and More Effective Agents	p. 70
Final Thoughts	p. 72
Voting Dictionaries	p. 74
What Goes Wrong?	p. 76
Axiomatic Approach versus Paradoxes	p. 77
Dictionaries	p. 77
Aggregation Rules	p. 80
Lassie and the Axiomatic Approach	p. 81
Dictionaries	p. 84
A Little Chaos	p. 86
Chaos within Voting Theory	p. 90
Dictionary Listings for Positional Rules	p. 91
Using the Dictionaries	p. 96
Variety Coming from Varieties	p. 99
Other Dictionaries	p. 104
Comparing Outcomes over a Set of Candidates	p. 107
General Results	p. 107
Let Elementary Geometry Do the Work	p. 109
Procedure Lines	p. 111
Other Rules, Such As Approval Voting	p. 113
A Working Tool for Actual Elections	p. 116
Back to the Original Problem: Creating Examples	p. 118
Explaining All Voting Paradoxes	p. 123
Profile Coordinates	p. 124
Coffee Reflections	p. 124
The "Water" for Voting Rules	p. 127
Nothing Goes Wrong	p. 133
A Creamy Addition: Positional Differences	p. 139
Anything Can Happen	p. 144
Sugar and Spice, and All Those Nice Cycles	p. 146
Differences between Borda and Condorcet	p. 157
Kemeny, Dodgson, and Other Systems; Who Cares?	p. 158
All Possible Three-Candidate Outcomes	p. 160
Creating Examples	p. 161
Converting Molecules into Coffee, Sugar, and Cream Coordinates	p. 162
The Will of the Voters	p. 165
Selecting Conditions	p. 166
Identifying the Voters' Wishes	p. 168
Extensions and Questions	p. 170
Teaser about More Candidates	p. 170
Designing Profile Configurations	p. 171
An Interesting Relationship	p. 172
A New Approach	p. 175
Finding and Proving New Theorems	p. 178
Special Case; Three Candidates	p. 180
Condorcet Winners and Losers	p. 180
Borda Winners and Losers	p. 181
Low-Hanging Fruit with n Candidates	p. 182
Borda versus Pairwise Rankings	p. 183
Borda versus Borda Rankings	p. 187
Deliver Us from the Plurality Vote	p. 190
Our Standard Voting Rule	p. 190
The 2000 U.S. Presidential Election	p. 191
The 2002 French Presidential Election	p. 192
Reform, or Fighting Termites with Paint and Putty?	p. 195
Resolutions, but Other Problems	p. 197
Newton's Third Law of Politics	p. 198
Comparison with Pairwise Voting	p. 200
Stability and the Core	p. 202
McKelvey's Chaos Theorem	p. 206
Generic Stability of the Core	p. 208
More about Cycles and Chaos	p. 211
Condorcet n-Cycles	p. 212
Controlling Chaos	p. 213
Final Comments	p. 214
Appendix: Extending the Upset Child Example	p. 218
Source of the Problem	p. 219
Generalizations	p. 222
Level Sets	p. 226
References	p. 231
Index	p. 237
Table of Contents provided by Ingram. All Rights Reserved.

Disposing Dictators, Demystifying Voting Paradoxes

Social Choice Analysis

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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