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Positive Political Theory I
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MICHIGAN STUDIES IN POLITICAL ANALYSIS
Michigan Studies in Political Analysis promotes the development and dissemination of
innovative scholarship in the field of methodology in political science and the social
sciences in general. Methodology is defined to include statistical methods, mathematical
modeling, measurement, research design, and other topics related to the conduct
and development of analytical work. The series includes works that develop a new
model or method applicable to social sciences, as well as those that, through innovative
combination and presentation of current analytical tools, substantially extend the
use of these tools by other researchers.
General Editors: John E. Jackson (University of Michigan) and
Christopher H. Achen (Princeton University)
Keith Krehbiel
Information and Legislative Organization
Donald R. Kinder and Thomas R. Palfrey, Editors
Experimental Foundations of Political Science
William T. Bianco
Trust: Representatives and Constituents
Melvin 1. Hinich and Michael C. Munger
Ideology and the Theory of Political Choice
John Brehm and Scott Gates
Working, Shirking, and Sabotage: Bureaucratic Response to
a Democratic Public
R. Michael Alvarez
Information and Elections
David Austen-Smith and Jeffrey S. Banks
Positive Political Theory I: Collective Preference
Gregory Wawro
Legislative Entrepreneurship in the U.S. House of Representatives
David Austen-Smith and Jeffrey S. Banks
Positive Political Theory II: Strategy and Structure
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Positive Political Theory I
Collective Preference
David Austen-Smith and Jeffrey S. Banks
Ann Arbor
THE liNIVERSITY OF MICHIGAN PRESS
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First paperback edition 2000
Copyright © by the University of Michigan 1999
All rights reserved
Published in the United States of America by
The University of Michigan Press
Manufactured in the United States of America
@ Printed on acid-free paper
2010 2009 2008 2007 7 (, 5 4
No part of this publication may be reproduced,
stored in a retrieval svstem, or transmitted in any form
or by any means, electronic, mechanical, or otherwise,
without the written permission of the publisher.
A CIP cataloJ? recordfor this book is al'ailablefrom the British Library
Library of Congress Cataloging-in-Publication Data
Ansten-Smith, David.
Positive political theory I : collective preference 'David
Austen-Smith,Jetlrey S, Banks,
p, cm.-(Michigan studies in political analysis)
Includes bibliographical references and index.
ISBN 0-472-10480-2 (cloth: alk. paper)
1. Political science-Methodology. 2, Political science-Decision
making. 3. Rational choice theory. 4, Social choice. I. Banks,
Jeffrey S. II. Title. III. Series.
JA71.A76 1999.
320·.0l'l-dc21 98-42902
CIP
ISBN 0-472-08721-5 (pbk. : alk. paper)
ISBN 978-0-472-10480-2 (cloth: alk. paper)
ISBN 978-0-472-08721-1 (pbk, : alk. paper)
ISBN13 978-0-472-02246-5 (electronic)
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Dedicated to the merrwry of
William H. Riker
1921-1993
Teacher; Colleague, Friend
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Contents
Acknowledgments ix
Preface xi
1 Choice and Preference 1
1.1 Preference-driven choice .. 1
1.2 Rationalizable choice . .. 6
1.3 Application: The unitary actor assumption 12
1.4 Transitive rationalizability . .. 12
1.5 Application: Choice of coalitional partners. 18
1.6 Discussion . .. 19
1.7 Exercises 21
1.8 Further reading . 23
2 Power and Collective Rationality 25
2.1 Aggregation and Arrow's Theorem 26
2.2 Application: Choosing a representative. 38
2.3 Quasi-transitive and acyclic rules 39
2.4 Decisive sets and filters 46
2.5 Collective choice rules 49
2.6 Discussion . .. 52
2.7 Exercises 54
2.8 Further reading . 55
3 Restricting Outcomes 57
3.1 Decisive coalitions and simple rules. 58
3.2 Acyclic simple rules .. . .. 63
3.3 Application: A comparison of simple rules 70
3.4 Voting rules . 71
3.5 Counting rules 77
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viii CONTENTS
3.6 Discussion ... 88
3.7 Exercises 90
3.8 Further reading 91
4 Restricting Preferences 93
4.1 Single-peaked preferences 94
4.2 Core characterization. . . 99
4.3 One-dimensional outcome space . 102
4.4 Application: Public goods provision 104
4.5 Order-restricted preferences ..... 106
4.6 Application: Collective choice of tax-rates 113
4.7 Discussion... 115
4.8 Exercises 117
4.9 Further reading 118
5 The Spatial Model 119
5.1 Choosing from a continuum 122
5.2 Core existence ...... . 126
5.3 Application: Distributive politics 132
5.4 Characterizing core points 133
5.5 Discussion... 151
5.6 Exercises ... 152
5.7 Further reading 153
6 Instability and Chaos 155
6.1 Generic nonexistence of core points . 156
6.2 Application: Distributive politics revisited 167
6.3 Cycles ... 168
6.4 Discussion... 184
6.5 Exercises ... 185
6.6 Further reading 185
7 Summary and Conclusions 187
7.1 Social choice 190
7.2 Game theory . 192
Bibliography 195
Index 202
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Acknowledgments
The genesis of this book lies in graduate classes we taught at the University
of Rochester, roughly through the decade 1986-1996. Many people have
contributed to it in one way or another. We are very grateful to all of
the students who have suffered through our classes at Rochester, offering
constructive criticism, insight, and commentary on both the material itself
and on our presentation thereof. Among these students we are particularly
indebted to Daniel Diermeier, Tim Feddersen, Tarik Kara, Eichi Miyagawa,
Alastair Smith and Tayfun Sonmez. Special thanks are due to John Duggan
(who, among other things, proposed using the diagrams in Section 3.5),
David Epstein (who suggested Example 3.4) and Tim Groseclose, all of
whom were kind enough to use earlier drafts of the manuscript in classes
they taught and to offer valuable feedback for improving the text based
on their experiences. In addition, conversations over the years with Randy
Calvert, John Ferejohn, Richard McKelvey, Bill Riker, Norman Schofield,
and doubtless many others have influenced our appreciation of preference
aggregation theory and its role in understanding politics. We thank them
all.
We are also grateful to Bob Turring who drew the figures, deciphering
our handwritten scrawls and accomodating our changes with considerable
patience. Some of the material used in the Preface and Chapter 7 is taken
from our paper [4J and appears with permission from the Annual Review
of Political Science, Volume 1, copyright 1998, by Annual Reviews. The
final draft of the manuscript was completed while the second author was
a Fellow at the Center for Advanced Study in the Behavioral Sciences at
Stanford University. He gratefully acknowledges financial support from the
National Science Foundation under grant SBR-9601236. Both authors are
similarly grateful to the National Science Foundation for financial support
under grant SBR-9510877.
Finally, we should like to thank our wives, Maggie Weiss and Shannon
Banks, and children, Clare and Luke Austen-Smith, and Bryan and Danny
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