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Cycles and Social Choice
The True and Unabridged Story of a Most Protean Paradox

$99.99 (C)

  • Date Published: March 2018
  • availability: In stock
  • format: Hardback
  • isbn: 9781107180918

$ 99.99 (C)

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About the Authors
  • 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.

    • Examines the sources and consequences of cycles and instability in the mathematical theory of voting and social choice with more numerous and varied sources and consequences of cycles and instability than those found in any other book
    • This book is more simple and succinct, and yet more rich and accurate, than other books on social choice
    • Includes many new and surprising results which should fascinate economists, philosophers, applied mathematicians, and especially political scientists
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    Reviews & endorsements

    ‘Thomas Schwartz reveals the mysteries of voting cycles, including their connections to famous results in social choice theory and game theory. Instead of bewailing cycles as incoherent, he casts them in a penetrating, positive light. Additionally, Cycles and Social Choice illuminates the philosophical implications of cycles for democratic rule, and their empirical ramifications for such political institutions as legislatures and political parties.' Steven J. Brams, New York University

    ‘Thomas Schwartz has been one of the handful of most important political science scholars in the formal study of properties of voting and social choice. He has made seminal contributions on topics such as logrolling, agenda manipulation, dimensionality of voting, and cycle sets. This book provides an integrated treatment of Schwartz's contributions over many decades. The ideas in it are relevant to anyone seriously interested in the study of democracy, regardless of whether their interests are primarily theoretical or primarily empirical.' Bernard Grofman, Jack W. Peltason Endowed Chair of Democracy Studies, University of California, Irvine

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    Product details

    • Date Published: March 2018
    • format: Hardback
    • isbn: 9781107180918
    • length: 170 pages
    • dimensions: 235 x 156 x 17 mm
    • weight: 0.37kg
    • contains: 37 b/w illus. 19 tables
    • availability: In stock
  • Table of Contents

    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.

  • Author

    Thomas Schwartz, University of California, Los Angeles
    Thomas Schwartz is Distinguished Professor of Political Science at University of California, Los Angeles. In the 1970s he migrated to political science from economics, previously having studied philosophy (Ph.D., University of Pittsburgh). With numerous journal publications and citations in all three disciplines and in mathematics, he is also the author of Freedom and Authority (1970), The Art of Logical Reasoning (1980), and The Logic of Collective Choice (1986). Many of his research results relate to the mathematical theory of voting and social choice, the subject of this book. His articles can be found in the American Political Science Review, the Journal of Economic Theory, the American Journal of Political Science, and Public Choice, among other places.

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