| Description |
1 online resource |
| Contents |
Cover; Half-title page; Title page; Copyright page; Dedication; Contents; Acknowledgements; Introduction; 1 Condorcet's Two Discoveries; 1.1 The Rejection of Condorcet Winners; 1.2 The Paradox of Voting; 1.3 What the Paradox Means and Does Not; 1.4 Why Majorities: May's Theorem; 1.5 More than Cycles: McGarvey's Theorem; 1.6 Beyond Majority Rule: Ward's Theorem; 1.7 Individual Rights: Sen's Paradox; 1.8 A Word about Words; 2 Incidence of the Paradox; 2.1 Black's Median-Stability Theorem; 2.2 Generalizations of Single Peakedness |
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2.3 More Dimensions and 360 Degree Medianhood: Cox's Theorem2.4 Pairwise Symmetry: Plott's Theorem; 2.5 Default Stability and a Side Trip beyond Majority Rule; 2.6 Essential Packaging; 2.7 Contrasts and Limitations, or Purging Preposterous Premises; 2.8 Observable Evidence of Cycles; 3 Social Rationality; 3.1 Choice Functions and Rationality; 3.2 Rationality and the Classical Framework of Social Choice; 3.3 Arrow's Theorem; 3.4 On interpreting and Misinterpreting the Independence of Irrelevant Alternatives; 3.5 Proof of Arrow's Theorem; 3.6 On Not Overstating the Theorem |
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4 Arrovian Cycle Theorems4.1 First Relaxation: Transitive Social Preference; 4.2 From ยป-Transitivity to Acyclicity, Assuming n Alternatives; 4.3 Wrong Turn: Positive Responsiveness; 4.4 Three or More Alternatives and a Reasonable Limit on Ties: (2k -- 2)-Resoluteness; 4.5 A Side Trip to Interpersonally Comparable Cardinal Utilities; 4.6 Proof of Inconsistency; 5 Second Line of Cycle Theorems: Condorcet Generalizations; 5.1 Simple Latin-Square Constructions: The Theorems of Ward, Brown, and Nakamura; 5.2 A General Condition for Cycles; 5.3 Proof that Cycles are Allowed |
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5.4 How Earlier Results and Proofs Fit the Pattern5.5 Individual Indifference and the Most General Cycle-Sufficiency Condition of All; 5.6 The Necessity Theorem; 6 Top Cycles in a Fixed Feasible Set; 6.1 New Bottle, Old Wines; 6.2 Top Cycles; 6.3 Tricycles and All-Inclusive Tight Cycles; 6.4 Absorbing Old Assumptions; 7 Strategic Consequences of Cycles; 7.1 Vote Manipulation; 7.2 Proof that Cycles Ensure Manipulability, and a Slight Generalization; 7.3 Comparison with Other Theorems; 7.4 Consequences of Nonmanipulability proved: The Duggan-Schwartz Theorem; 7.5 Cycles and Game Solutions |
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7.6 Proof that Cycles Block Nash Implementation8 Structural Consequences of Cycles; 8.1 Agenda Control: Trees; 8.2 Dendriform Details; 8.3 Agenda Control: Sets; 8.4 Agenda Control: Joining and Dividing Questions; 8.5 Cycles and Paradoxical Power; 8.6 Cycles, External Costs, and Political Parties; 9 Questions about Prediction and Explanation; 9.1 What Majorities Would Choose; 9.2 Proof that (1)-(4) Characterize TEQ; 9.3 Examples and Comparisons of TEQ with Other Solutions; 9.4 A Different Approach to Cooperative Solutions; 9.5 Beyond Tournaments; 9.6 Methodological Asides: The Use of Axioms |
| Summary |
This book illuminates the sources and consequences of cycles and instability in the mathematical theory of voting and social choice |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (EBSCO, viewed March 5, 2018) |
| Subject |
Voting -- Mathematical models
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Social choice.
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POLITICAL SCIENCE -- Government -- General.
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POLITICAL SCIENCE -- Political Process -- Elections.
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POLITICAL SCIENCE -- Political Process -- General.
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Social choice
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Voting -- Mathematical models
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| Form |
Electronic book
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| ISBN |
9781316853238 |
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1316853233 |
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9781107180918 |
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1107180910 |
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9781316848371 |
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131684837X |
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1316632377 |
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9781316632376 |
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