Approval Voting, Second edition

211 Pages·2007·9.75 MB·English

by  Steven Brams

Approval Voting
Second Edition
Steven J. Brams
Peter C. Fishburn
Approval Voting
Second Edition
Springe]
Steven J. Brams Peter C. Fishbum
New York University P.O. Box 309
Department of Politics Basking Ridge, NJ 07920
New York, NY 10003
USA
s teven.brams @nyu.edu
Cover design by Joseph Sherman, Hamden, CT,
Library of Congress Control Number: 2006937105
ISBN-10: 0-387-49895-8 e-ISBN-10: 0-387-49896-6
ISBN-13: 978-387-49895-9 e-lSBN-13: 978-0-387-49896-6
Printed on acid-free paper.
© 1983 First Edition, Bell Telephone Laboratories, Inc., and Steven J. Brams
© 2007 Second Edition, Springer ScienceH-Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science-I-Business Media, LLC, 233 Spring Street, New York,
NY 10013, USA) and the author, except for brief excerpts in connection with reviews or scholarly
analysis. Use in connection with any form of information storage and retrieval, electronic adaptation,
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I am not an advocate for frequent changes in laws and constitutions,
but laws and institutions must go hand in hand with the progress of the
human mind. As that becomes more developed, more enlightened, as
new discoveries are made, new truths discovered and manners and
opinions change, with the change of circumstances, institutions must
advance also to keep pace with the times.
Thomas Jefferson, Letter to
Samuel Kerchaval, July 12, 1816
The method of choice . . . should be as scientifically framed and as
efficiently adapted to its purpose as experience and political wisdom
can make it. ... It is not sufficient for every citizen to have the vote; he
should also be assured of the greatest possible freedom and effec
tiveness in its use.
Enid Lakeman and James D. Lambert,
Voting in Democracies, 1955
The way we pick our presidents should not be fraught with danger and
uncertainty. It should be a clear, secure, sensible procedure in which
we can have confidence. . . .
Terry Sanford,
A Danger of Democracy, 1981
During lunch, a show of hands was taken, and the '47 [wine] received
more first-place votes than any other wine. Because of more numerous
second- and third-place votes, the '49 [wine] was judged the group's
favorite, although this method of scoring caused controversy.
Terry Robards, ''Wine Talk,"
New York Times, April 28, 1982
Contents
Preface to the Second Edition xi
Preface to the First Edition xiii
Acknowledgments xvii
List of Tables xix
List of Figures xxi
Chapter 1. Introduction: Overview of the Problem and Its
Solution 1
1.1. The Multicandidate Problem 1
1.2. A Solution: Approval Voting 3
1.3. What's Wrong with Approval Voting? 10
1.4. An Illustration of the Effects of Different Rules: The 1980 New
Hampshire Primaries under Approval Voting 11
1.5. Prospects for Adoption 12
Chapter 2. Sincerity and Strategy-Proofness: Which System Is
Most Honest? 15
2.1. Introduction 15
2.2. Voter Preferences and Dominance 16
2.3. Dominance between Strategies 19
2.4. Admissible Strategies 22
2.5. Sincere Voting and Strategy-Proofness 28
2.6. Conclusions 32
Chapter 3. The Condorcet Criterion: Which System Best
Finds The Majority Candidate? 35
3.1. Introduction 35
3.2. Dichotomous Preferences 37
vu
viii Contents
3.3. Runoff Systems 40
3.4. Dominance, Admissibility, Sincerity, and Strategy-Proofness
of Runoff Systems 42
3.5. Condorcet Possibility Theorems 47
3.6. Condorcet Election Guarantees 52
3.7. Conclusions 54
Chapter 4. The Reconstruction of an Election under
Alternative Rules 59
4.1. Introduction 59
4.2. Background on the 1976 House Majority Leader Election 60
4.3. Best/Worst Analysis: A Preliminary Appraisal 61
4.4. Single-Peaked Preferences 63
4.5. Different Voting Systems 66
4.6. Conclusions 69
Chapter 5. Power and Equity: Which System Is Fairest? 73
5.1. Introduction 73
5.2. Efficacy 74
5.3. Situation-Specific Effects and Power 78
5.4. Power and Equity for Dichotomous Voters 81
5.5. Optimal Voting Strategies 84
5.6. An Asymmetric Example 88
5.7. Conclusions 90
Chapter 6. Deducing Condorcet Candidates from Election
Data 93
6.1. Introduction 93
6.2. Deductions from Election Totals 94
6.3. Results for Three and Four Candidates 95
6.4. Modified Assumptions and Disaggregated Data 98
6.5. Analysis of Approval Voting Ballot Data 99
6.6. An Empirical Example and Probabilistic Analysis 103
6.7. Conclusions 106
Chapter 7. Polls and the Problem of Strategic Information in
Elections 109
7.1. Introduction 109
7.2. Concerns about Public Opinion Polling 110
7.3. Plurality Voting 112
7.4. Approval Voting 115
7.5. Runoff Systems and an Empirical Example 121
7.6. Conclusions 123
Contents IX
Chapter 8. Recent Empirical Examples and Theoretical
Extensions 127
8.1. Introduction 127
8.2. The 1980 New York Senate Race: A Reprise of 1970? 127
8.3. Approval Voting and Presidential Elections 129
8.4. The Sensitivity of Voting Systems to Numbers of Candidates 135
8.5. Approval Voting and Game Theory 138
8.6. The Monotonicity Paradox 141
8.7. Conclusions 145
Chapter 9. Deducing Preferences and Choices in the 1980
Presidential Election 151
9.1. Introduction 151
9.2. Preferences and Voter Behavior 153
9.3. Analysis of Anderson Supporters (but Not Voters) 157
9.4. Inferences from Voter Percentages 163
9.5. Conclusions 167
Chapter 10. Epilogue 171
Appendix: Bill to Enact Approval Voting in New York State .. 173
Glossary 175
Bibliography 179
Index 189
Preface to the
Second Edition
It has been 25 years since the publication of Approval Voting. We find it
gratifying that our arguments in favor of a practically unknown election reform
in 1983 have stood the test of time. Perhaps the proof of the pudding lies in the
adoption of approval voting by about a dozen professional societies—several
with tens of thousands of members—and their generally favorable experience
with it.
To be sure, we would have liked to have seen our bold prediction that ap
proval voting would become the election reform of the twentieth century borne
out. But this was not to be, despite our efforts to promulgate approval voting's
virtues and to promote its use in public elections.
On the other hand, we were quite successful in inducing scholars to do re
search on approval voting that went beyond the standard paradigm for ana
lyzing ranking systems. This resulted in a better understanding of approval
voting's theoretical properties that distinguish it from virtually all other vot
ing systems. Empirical findings on approval voting's effects have been repeat
edly tested by the societies that adopted this reform as well as in controlled
approval-voting experiments in the laboratory.
We have decided not to revise Approval Voting, except to make minor correc
tions in the original text, because one of us (Brams) discusses recent research
on approval voting in Mathematics and Democracy: Designing Better Voting
and Fair-Division Procedures (forthcoming). Although only two of this book's
fifteen chapters are devoted to approval voting, several chapters analyze alter
native ways of aggregating approval ballots to accomplish different ends, such
as electing committees rather than single winners. Moreover, the two chapters
on approval voting are available in somewhat different form as journal articles:
(1) Brams and Fishbum, "Going from Theory to Practice: The Mixed Success
of Approval Voting," Social Choice and Welfare 25, 2 (2005), 457-474; (2)
Brams and M. Remzi Sanver, "Critical Strategies under Approval Voting: Who
XI
xii Preface to the Second Edition
Gets Ruled In and Ruled Out" Electoral Studies 25, 2 (2006), 287-305. The
first article summarizes the varied experiences, beginning in the late 1980s, of
several of the professional societies that adopted approval voting, whereas the
second article reports on recent theoretical research on approval voting, which
has become much more game-theoretic in its orientation since the first edition
of Approval Voting appeared.
Research on approval voting does not stand in isolation; it has been ac
companied by research on a variety of voting systems, of which we offer an
overview in a lengthy review article: (3) Brams and Fishbum, "Voting Pro
cedures," in Handbook of Social Choice and Welfare, Vol. 1, edited by K.J.
Arrow, A.K. Sen, and K. Suzumura (Amsterdam: Elsevier Science, 2002), pp.
175-236. In recent years, advocates of two prominent ranking systems—the
Borda count and the Hare system of single transferable vote (STV), which
in simplified form has been called instant runoff voting (IRV) in the United
States—have appeared on the scene. We have had spirited debates with these
people, both in person and in print, on the relative merits of the different voting
systems.
We will not rehearse here the pro and con arguments each side offers. Suf
fice it to say that the three aforementioned articles include references to these
debates as well as controversies over the significance of the properties that the
different systems satisfy.
What voting system one favors will presumably depend not only on the im
portance one attaches to the different properties but also the purposes that a
voting system is designed to serve. Approval voting, we have argued, is best
suited to elect single winners, such as a mayor, a governor, or a president.
In contrast, choosing a committee, or electing a legislature to mirror the di
versity of factions or interests in the electorate, is not what approval voting was
designed to do. Such multiwinner elections require very different voting sys
tems, some of which are discussed and compared in Mathematics and Democ
racy.
Choosing the one person who runs the show in most countries—whether he
or she be the president, the prime minister, or somebody else—is often the most
important decision citizens in a democracy make. In multicandidate races, we
contend that approval voting is the simplest and most effective way to make
this choice.
A generation of discussion and debate has not altered our view on this sub
ject. This is why we think Approval Voting is as relevant today as when rigorous
analysis and systematic empirical research on this election reform began more
than 30 years ago.