Table Of ContentHANDBOOK OF SOCIAL CHOICE AND
VOTING
Handbook of Social Choice
and Voting
Edited by
Jac C. Heckelman
Professor of Economics, Wake Forest University, USA
Nicholas R. Miller
Research Professor of Political Science, University of
Maryland Baltimore County, USA
Cheltenham, UK • Northampton, MA, USA
© Jac C. Heckelman and Nicholas R. Miller 2015
All rights reserved. No part of this publication may be reproduced, stored
in a retrieval system or transmitted in any form or by any means, electronic,
mechanical or photocopying, recording, or otherwise without the prior
permission of the publisher.
Published by
Edward Elgar Publishing Limited
The Lypiatts
15 Lansdown Road
Cheltenham
Glos GL50 2JA
UK
Edward Elgar Publishing, Inc.
William Pratt House
9 Dewey Court
Northampton
Massachusetts 01060
USA
A catalogue record for this book
is available from the British Library
Library of Congress Control Number: 2015945454
This book is available electronically in the
Economics subject collection
DOI 10.4337/9781783470730
ISBN 978 1 78347 072 3 (cased)
ISBN 978 1 78347 073 0 (eBook)
Typeset by Servis Filmsetting Ltd, Stockport, Cheshire
Contents
List of contributors vii
1 Introduction: issues in social choice and voting 1
Jac C. Heckelman and Nicholas R. Miller
PART I PERSPECTIVES ON SOCIAL CHOICE
2 The strange history of social choice 15
Iain McLean
3 Unanimous consent and constitutional economics 35
Randall G. Holcombe
4 Rational choice and the calculus of voting 54
André Blais
5 Computational social choice 67
Robi Ragan
PART II PAIRWISE SOCIAL CHOICE
6 Majority rule and tournament solutions 83
Scott Moser
7 Supermajority rules 102
Keith L. Dougherty
8 The measurement of a priori voting power 117
Dan S. Felsenthal and Moshé Machover
9 Condorcet jury theorems 140
Bryan C. McCannon
PART III SPATIAL MODELS OF SOCIAL CHOICE
10 The spatial model of social choice and voting 163
Nicholas R. Miller
11 A unified spatial model of American political institutions 182
Thomas H. Hammond
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vi Handbook of social choice and voting
12 Competing for votes 201
James F. Adams
13 Probabilistic voting in models of electoral competition 218
Peter J. Coughlin
PART IV S OCIAL CHOICE FROM MULTIPLE
ALTERNATIVES
14 Arrow’s Theorem and its descendants 237
Elizabeth Maggie Penn
15 Properties and paradoxes of common voting rules 263
Jac C. Heckelman
16 Voting mysteries: a picture is worth a thousand words 284
Donald G. Saari
17 Multiple- winner voting rules 303
Nicolaus Tideman
PART V EMPIRICAL SOCIAL CHOICE
18 Measuring ideology in Congress 327
Christopher Hare and Keith T. Poole
19 The uncovered set and its applications 347
William T. Bianco, Christopher Kam, Itai Sened and
Regina A. Smyth
20 Empirical examples of voting paradoxes 367
Marek M. Kaminski
Glossary of terms pertaining to social choice and voting 388
Index 399
Contributors
James F. Adams, Professor of Political Science, University of California,
Davis, USA.
William T. Bianco, Professor of Political Science, Indiana University,
Bloomington, USA.
André Blais, Professor of Political Science, Université de Montréal,
Canada.
Peter J. Coughlin, Associate Professor of Economics, University of
Maryland, College Park, USA.
Keith L. Dougherty, Professor of Political Science, University of Georgia,
Athens, USA.
Dan S. Felsenthal, Co- director, Voting Power and Procedures Project,
London School of Economics, UK and Professor Emeritus of Political
Science, University of Haifa, Israel.
Thomas H. Hammond, Professor of Political Science, Michigan State
University, East Lansing, USA.
Christopher Hare, Assistant Professor of Political Science, University of
California, Davis, USA.
Jac C. Heckelman, Professor of Economics, Wake Forest University,
Winston-S alem, USA.
Randall G. Holcombe, DeVoe Moore Professor of Economics, Florida
State University, Tallahassee, USA.
Christopher Kam, Associate Professor Political Science, University of
British Columbia, Canada.
Marek M. Kaminski, Associate Professor of Political Science, University
of California, Irvine, USA.
Moshé Machover, Co-d irector, Voting Power and Procedures Project,
London School of Economics, UK and Professor Emeritus of Philosophy,
Kings College London, UK.
Bryan C. McCannon, Assistant Professor of Economics, West Virginia
University, Morgantown, USA.
vii
viii Handbook of social choice and voting
Iain McLean, Director, Gwilym Gibbon Centre for Public Policy at
Nuffield College, and Professor of Politics, Oxford University, Oxford,
UK.
Nicholas R. Miller, Research Professor of Political Science, University of
Maryland Baltimore County, Baltimore, USA.
Scott Moser, Assistant Professor of Government, University of Texas,
Austin, USA.
Elizabeth Maggie Penn, Professor of Political Science, University of
Chicago, USA.
Keith T. Poole, Philip H. Alston Jr. Distinguished Professor of Political
Science, University of Georgia, Athens, USA and Professor Emeritus,
University of California, San Diego, USA.
Robi Ragan, Assistant Professor of Economics, San Jose State University,
San Jose, USA.
Donald G. Saari, Director, Institute for Mathematical Behavioral Sciences,
and Distinguished Professor of Mathematics and Economics, University
of California, Irvine, USA.
Itai Sened, Professor of Political Science, Washington University, St Louis,
USA.
Regina A. Smyth, Associate Professor of Political Science, Indiana
University, Bloomington, USA.
Nicolaus Tideman, Professor of Economics, Virginia Polytechnic Institute
and State University, Blacksburg, USA.
1. Introduction: issues in social choice and
voting
Jac C. Heckelman and Nicholas R. Miller
1.1 THE FIELD OF SOCIAL CHOICE
Individuals often make decisions as part of a group. While an individual
acting alone can choose as he or she prefers, a collective decision must
aggregate the preferences of multiple individuals. Collective decisions
may involve as few as two people, such as a couple deciding where to eat
dinner, or several members voting in a committee, hundreds of members
voting in a legislature, or millions of people voting on a referendum or
electing a parliament or president. Any such decision – except perhaps
an informal decision in a small group – requires a clearly defined rule to
aggregate diverse individual preferences and identify the social choice; for
example, the proposal or candidate to be selected. Yet different rules have
different properties, and they may produce different social choices even
for the same individual preferences.
Broadly understood, social choice theory identifies, analyzes and evalu-
ates rules that may be used to make collective decisions. So understood,
social choice is a subfield within the social sciences (especially economics
and political science) that examines institutions that may be called ‘voting
rules’ of various sorts. More narrowly understood, social choice theory
is a specialized branch of applied logic and mathematics that analyzes
abstract objects called ‘preference aggregation functions’, ‘social welfare
functions’ and ‘social choice functions’. While this Handbook includes
several chapters that introduce the reader to social choice theory in its
narrower sense, we included the word ‘voting’ in the title to signal that it
covers the field in its broader sense.
The most familiar voting institutions are based on majority rule.
Majority rule is straightforward in the event that a choice is to be made
between just two alternatives, but it presents complications once the field
of choice expands beyond two. Even in the two-a lternative case, other
voting rules (for example, supermajority rule and weighted voting) are
available and sometimes used.
Discussion of voting rules dates back at least to classical times. But
elections then were conducted largely by lot, and voting was restricted
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