Cycles and Social Choice

The True and Unabridged Story of a Most Protean Paradox

Thomas Schwartz

• Publisher: Cambridge University Press
• Year: 2018
• Print ISBN:
  9781107180918
• eBook ISBN:
  9781316853238
• Topic: Politics & International Relations
• Subtopic: American Government
• Index: Politics & International Relations

The centuries-old paradox of voting is that majorities sometimes prefer x to y, y to z, and z to x - a cycle. The discovery of the sources and consequences of such cycles, under majority rule and countless other regimes, constitutes much of the mathematical theory of voting and social choice. This book explores the big questions posed by the paradox of voting: positive questions about how to predict outcomes and explain observed stability, and normative questions about how to hold elections, how to take account of preference intensities, the relevance of social welfare to social choice, and challenges to formal 'rationality', individual and social. The overall lesson is that cycles are facts, ubiquitous, and consequential in non-obvious ways, not puzzles to be solved, much less maladies or misfortunes to be avoided or regretted.

Table of contents

• Cover
• Half-title page
• Title page
• Copyright page
• Dedication
• Contents
• Acknowledgements
• Introduction
• 1 Condorcet’s Two Discoveries
• 2 Incidence of the Paradox
• 3 Social Rationality
• 4 Arrovian Cycle Theorems
• 5 Second Line of Cycle Theorems: Condorcet Generalizations
• 6 Top Cycles in a Fixed Feasible Set
• 7 Strategic Consequences of Cycles
• 8 Structural Consequences of Cycles
• 9 Questions about Prediction and Explanation
• 10 Questions about Prescription and Evaluation
• Concluding Caveats
• Underbook: Background and Sources by Chapter
• References
• Index