Disposing Dictators, Demystifying Voting Paradoxes

A description outlines how the material in a forthcoming book, with the same title, complements the material discussed in my article “Complexity and the Geometry of Voting” that appears in this issue. Book topics include explaining why several of the well-known “impossibility” results do not mean as...

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Tác giả chính:	G Saari, Donald
Định dạng:	Sách
Ngôn ngữ:	English
Được phát hành:	Cambridge University 2013
Những chủ đề:	Dictators Disposing
Truy cập trực tuyến:	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/34460
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institution	Thư viện Trường Đại học Đà Lạt
collection	Thư viện số
language	English
topic	Dictators Disposing
spellingShingle	Dictators Disposing G Saari, Donald Disposing Dictators, Demystifying Voting Paradoxes
description	A description outlines how the material in a forthcoming book, with the same title, complements the material discussed in my article “Complexity and the Geometry of Voting” that appears in this issue. Book topics include explaining why several of the well-known “impossibility” results do not mean as previously believed, a listing of all possible positional voting paradoxes, and how to understand voting paradoxes.
format	Book
author	G Saari, Donald
author_facet	G Saari, Donald
author_sort	G Saari, Donald
title	Disposing Dictators, Demystifying Voting Paradoxes
title_short	Disposing Dictators, Demystifying Voting Paradoxes
title_full	Disposing Dictators, Demystifying Voting Paradoxes
title_fullStr	Disposing Dictators, Demystifying Voting Paradoxes
title_full_unstemmed	Disposing Dictators, Demystifying Voting Paradoxes
title_sort	disposing dictators, demystifying voting paradoxes
publisher	Cambridge University
publishDate	2013
url	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/34460
_version_	1819839461107695616
spelling	oai:scholar.dlu.edu.vn:DLU123456789-344602014-01-20T03:39:30Z Disposing Dictators, Demystifying Voting Paradoxes G Saari, Donald Dictators Disposing A description outlines how the material in a forthcoming book, with the same title, complements the material discussed in my article “Complexity and the Geometry of Voting” that appears in this issue. Book topics include explaining why several of the well-known “impossibility” results do not mean as previously believed, a listing of all possible positional voting paradoxes, and how to understand voting paradoxes. Preface page xi 1 Subtle Complexity of Social Choice 1 1.1 Does Everything GoWrong? 1 1.2 And the Proud Father Is . . . 3 1.3 Enemies? 7 1.4 Curse of Dimensionality 13 1.5 Outline 15 1.5.1 Dethroning Dictators, and Then Paradoxes 16 1.5.2 The “Will of the Voters”:What Is It? 18 2 Dethroning Dictators 20 2.1 Major Negative Conclusions 21 2.1.1 Arrow’s Theorem 21 2.1.2 Sen’s Seminal Result 23 2.1.3 Topological Dictators 26 2.1.4 “Paradox of Voting” and Condorcet’s Triplets 28 2.1.5 List’s Lists 29 2.1.6 Anscombe 30 2.1.7 A Standard Requirement 31 2.2 Commonality 31 2.2.1 Condorcet’s Ideas Dominate 32 2.2.2 CanWe Trust the Majority Voting over Pairs? 40 2.2.3 A Common Explanation 422.3 WhyDo These Negative ResultsOccur? 43 2.3.1 Arrow’s Theorem 44 2.3.2 Sen’s Result 47 2.3.3 Topological Dictators and Beach Parties 51 2.4 Positive Replacements 58 2.4.1 Arrow’s Result 58 2.4.2 Sen’s Result 64 2.4.3 Topological Dictators and More Effective Agents 70 2.5 Final Thoughts 72 3 Voting Dictionaries 74 3.1 What GoesWrong? 76 3.1.1 Axiomatic Approach versus Paradoxes 77 3.1.2 Dictionaries 77 3.1.3 Aggregation Rules 80 3.2 Lassie and the Axiomatic Approach 81 3.3 Dictionaries 84 3.3.1 A Little Chaos 86 3.3.2 Chaos within Voting Theory 90 3.3.3 Dictionary Listings for Positional Rules 91 3.4 Using the Dictionaries 96 3.4.1 Variety Coming from Varieties 99 3.4.2 Other Dictionaries 104 3.5 Comparing Outcomes over a Set of Candidates 107 3.5.1 General Results 107 3.5.2 Let Elementary Geometry Do theWork 109 3.5.3 Procedure Lines 111 3.5.4 Other Rules, Such As Approval Voting 113 3.5.5 AWorking Tool for Actual Elections 116 3.5.6 Back to the Original Problem: Creating Examples 118 4 Explaining All Voting Paradoxes 123 4.1 Profile Coordinates 124 4.1.1 Coffee Reflections 124 4.1.2 The “Water” for Voting Rules 127 4.1.3 Nothing GoesWrong 1334.1.4 A Creamy Addition: Positional Differences 139 4.1.5 Anything Can Happen 144 4.1.6 Sugar and Spice, and All Those Nice Cycles 146 4.1.7 Differences between Borda and Condorcet 157 4.1.8 Kemeny, Dodgson, and Other Systems;Who Cares? 158 4.2 All Possible Three-Candidate Outcomes 160 4.2.1 Creating Examples 161 4.2.2 Converting Molecules into Coffee, Sugar, and Cream Coordinates 162 4.3 TheWill of the Voters 165 4.3.1 Selecting Conditions 166 4.3.2 Identifying the Voters’Wishes 168 4.3.3 Extensions and Questions 170 4.4 Teaser about More Candidates 170 4.4.1 Designing Profile Configurations 171 4.4.2 An Interesting Relationship 172 4.4.3 A New Approach 175 4.5 Finding and Proving New Theorems 178 4.5.1 Special Case; Three Candidates 180 4.5.2 CondorcetWinners and Losers 180 4.5.3 BordaWinners and Losers 181 4.5.4 Low-Hanging Fruit with n Candidates 182 4.5.5 Borda versus Pairwise Rankings 183 4.5.6 Borda versus Borda Rankings 187 5 Deliver Us from the Plurality Vote 190 5.1 Our Standard Voting Rule 190 5.1.1 The 2000 U.S. Presidential Election 191 5.1.2 The 2002 French Presidential Election 192 5.1.3 Reform, or Fighting Termites with Paint and Putty? 195 5.1.4 Resolutions, but Other Problems 197 5.2 Newton’s Third Law of Politics 198 5.2.1 Comparison with Pairwise Voting 200 5.2.2 Stability and the Core 202 5.2.3 McKelvey’s Chaos Theorem 206 5.3 Generic Stability of the Core 2085.4 More about Cycles and Chaos 211 5.4.1 Condorcet n-Cycles 212 5.4.2 Controlling Chaos 213 5.5 Final Comments 214 6 Appendix Extending the Upset Child Example 218 6.1 Source of the Problem 219 6.2 Generalizations 222 6.3 Level Sets 226 References 231 Index 237 2013-07-11T09:06:16Z 2013-07-11T09:06:16Z 2008 Book https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/34460 en application/pdf Cambridge University

Disposing Dictators, Demystifying Voting Paradoxes

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