Making Multicandidate Elections More Democratic

by Samuel Merrill

Overview

This book addresses a significant area of applied social-choice theory—the evaluation of voting procedures designed to select a single winner from a field of three or more candidates. Such procedures can differ strikingly in the election outcomes they produce, the opportunities for manipulation that they create, and the nature of the candidates—centrist or extremist—whom they advantage. The author uses computer simulations based on models of voting behavior and reconstructions of historical elections to assess the likelihood that each multicandidate voting system meets political objectives.

Alternative procedures abound: the single-vote plurality method, ubiquitous in the United States, Canada, and Britain; runoff, used in certain primaries; the Borda count, based on rank scores submitted by each voter; approval voting, which permits each voter to support several candidates equally; and the Hare system of successive eliminations, to name a few. This work concludes that single-vote plurality is most often at odds with the majoritarian principle of Condorcet. Those methods most likely to choose the Condorcet candidate under sincere voting are generally the most vulnerable to manipulation. Approval voting and the Hare and runoff methods emerge from the analyses as the most reliable.

Originally published in 1988.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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ISBN-13:	9780691633671
Publisher:	Princeton University Press
Publication date:	04/19/2016
Series:	Princeton Legacy Library , #912
Pages:	172
Product dimensions:	7.10(w) x 10.20(h) x 1.00(d)

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Making Multicandidate Elections More Democratic

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By Samuel Merrill III

PRINCETON UNIVERSITY PRESS

Copyright © 1988 Princeton University Press
All rights reserved.
ISBN: 978-0-691-07770-3

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CHAPTER 1

MULTICANDIDATE ELECTIONS: CHOOSING A WINNER

1.1. Introduction

The votes for U.S. House majority leader by the 1976 Democratic caucus had been counted. Representative Jim Wright — to the surprise of many, perhaps to Wright himself — had cleared the last hurdle by the barest of margins to become, as it turned out, the new majority leader for the next decade and eventually the speaker of the House of Representatives.

The electoral process by which Wright wound his way to leadership says much about the effect of rules on the outcome of elections. In the United States, the top congressional leaders are chosen by a procedure almost unique in U.S. politics — although it is a variant of the method in general use in Ireland and Australia. When faced with more than two candidates, a congressional caucus conducts a series of ballots, eliminating on each ballot the candidate receiving the fewest votes.

In 1976 four Democrats — Philip Burton, Richard Boiling, John McFall, and Jim Wright — contended for majority leader. Most observers place them ideologically from left to right in that order. McFall, plagued by possible scandal, withdrew after the first ballot (see table 1.1). Wright, although initially third, moved into second place on the next ballot, just in time to save himself from elimination. In the final showdown, he faced Burton, who had easily led the first two ballots. This third ballot, between the most conservative and the most liberal of the four, was the closest contest of all — Wright won by a single vote.

The outcome of the election — and the ideological stance it signalled — was highly dependent on the electoral procedure. If, as in most American elections, a single ballot had been used instead of a succession of ballots, the plurality leader, Burton, would have been elected. Had a traditional runoff been stipulated, both McFall and Wright would have been eliminated on the first ballot, pitting the popular, moderate Boiling against the strongly liberal and acerbic Burton — a race most observers believe Boiling would have won (see Oppenheimer and Peabody 1977).

In fact it appears that Boiling would likely have won under all of the other alternative electoral procedures that will be introduced later in this chapter. Furthermore, he probably could have defeated each of the others in two-way races. The sensitivity, in general, of multicandidate electoral outcomes to the rules of balloting and to the decision rules that determine the winner suggests the need for a careful study of alternative procedures.

Since the late eighteenth century, a variety of procedures have been proposed to select a winner in a multicandidate election, that is, one in which there are more than two candidates. Many of these methods are known today by the names of their proposers: Borda (1781), Hare (1859), Coombs (1954), and Black (1958). Some are old and commonly used (such as the ordinary plurality and Hare systems), whereas others (such as approval voting) have only recently come to the attention of political scientists and politicians.

I will be concerned here with the design of such procedures in order to meet the political objectives of legitimacy and mandate, resistance to manipulation, simplicity, and stability. These criteria will be discussed in detail in the remainder of this chapter. The treatment in this book will be limited to elections in which a single winner is to be chosen.

1.2. Legitimacy and Mandate

An electoral system should be designed, it would seem, to select a candidate who possesses broad support from the electorate. In the 1970 presidential election in Chile, Salvadore Allende, representing the political left, received 36 percent of the popular vote; conservative Jorge Alessandri, 35 percent; while the centrist candidate, Radomiro Tomic Romero, squeezed from both sides, obtained 28 percent. Although the Chilean constitution provided that the outcome be resolved by the vote of a joint session of the Chamber of Deputies and the Senate (which eventually elected Allende), the obvious indeterminacy of the popular vote may have helped undermine Allende's mandate to govern. At the same time, the capacity of the two more extreme candidates to squeeze the centrist raises the question: would other voting systems have had the same effect?

Reaching farther back into history, we note that Abraham Lincoln won the U.S. presidency in 1860 with only 40 percent of the popular vote among four serious candidates. The others were Stephen A. Douglas (29 percent), John C. Breckinridge (18 percent), and John Bell (13 percent). Yet at least one analyst (Riker 1982a, section 9.e) estimates that Bell — who received the fewest votes — may have been acceptable to as many or more voters as Lincoln and possibly may have been acceptable to as many as any of the other candidates. Riker also believes that a majority preferred Douglas to Lincoln. Regardless of Lincoln's eventual contributions to the nation, one may ask whether his election with less than a majority mandate hastened the polarization of the nation.

In the United States, many multicandidate races occur in primaries intended to choose a party nominee. Unified support from within one's party is often necessary for success in the general election. The fates of Barry Goldwater in 1964 and George McGovern in 1972 are well known. Each won his party's nomination for president based on the fervent support of a fraction of his party's adherents, but, lacking a broad base, met disaster in the general election in November.

Even if a party nominee is elected, a strong mandate grounded in wide support may be needed for the eventual winner to serve as an effective executive or legislator. The three-cornered 1983 Democratic party primary for mayor of Chicago, for example, nominated Harold Washington (with 36 percent of the vote) over Jane Byrne (34 percent) and Richard M. Daley (30 percent). Washington's subsequent close shave in the general election — in a city overwhelmingly Democratic — and his chaotic first administration beset with opposition at every turn cast serious doubt on his mandate to govern. These administrative difficulties stem in part, I would argue, from the electoral process by which Washington became mayor. Most black mayors, such as Tom Bradley in Los Angeles, Wilson Goode in Philadelphia, Andrew Young in Atlanta, and Coleman Young in Detroit, received significant support from both whites and blacks. Washington's votes in 1983, in contrast, were largely limited to a racial minority — sufficient to eke out a plurality in a multicandidate primary but apparently not representative of broad acceptance by the electorate. Running for a second term in 1987, Washington attained majority support, receiving 53 percent of the vote in both the Democratic primary and the general election.

These examples of minority winners and others to be considered later suggest that alternative voting systems should be sought that might be more likely to lead to majority choices when broad support and a legitimizing mandate are deemed desirable. This would appear particularly apropos for executive offices (president, governor, or mayor) in which a single individual is entrusted with the power to govern.

But how can one measure the tendency for an electoral system to choose a candidate with a broad support or mandate? Since the time of Condorcet (1785), perhaps the most widely accepted principle has been that if there is a candidate who can beat each of the others in a two-way race, that candidate should be selected. That such a candidate, called the Condorcet candidate, should be elected is but a natural extension of the concept of majority rule from a two-candidate to a multicandidate setting.

Before evaluating the tendency of multicandidate voting systems to choose the Condorcet candidate, one may ask the question: should all conceivable candidates who might be selected by society be considered or only those official candidates for whom actual voting takes place? How are such candidates preselected for formal voting?

The latter question is addressed in depth in Riker's (1982a) assessment of the populist and Madisonian (liberal) interpretations of the meaning of voting. Under the populist interpretation, the outcome of voting is the articulation of the collective will of the people. By contrast, the Madisonian interpretation requires only that elections permit the electorate to reject unpopular leaders. Riker argues that the disequilibrium that results from the lack of a Condorcet candidate — interpreted as one position preferred to all conceivable other alternatives — and the possibility of manipulation undercut the notion that the voting result could represent the will of the electorate (or even a majority thereof). The Madisonian ideal, however — by making no such specific demands — can still be met.

But here, in assessing the meaning and legitimacy of a voting outcome, I will restrict my attention to only those candidates who are formally recognized as such. I will discuss, however, the question of the effects of voting procedures on the opportunities for new candidates to enter a race effectively and whether each system favors the entry of candidates with centrist or extremist positions.

The Condorcet criterion ignores the question of intensity of support. If we interpret a voter's evaluation of a candidate as a utility we may assess the aggregate intensity of support by computing the social or average utility over all voters (see, e.g., Harsanyi 1977) and argue that the candidate who on the average is rated most highly by the voters should be elected. As we shall see, this criterion and that of Condorcet need not agree.

1.3. Resistance to Manipulation

Manipulation by insincere voting (i.e., voting in a way that does not reflect one's true preference order) or by other strategies, to be introduced later, can significantly alter the outcome. Such manipulation may perniciously undermine the selection of the candidate with the strongest support and call into question the legitimacy of the winner.

In other situations, however, this kind of manipulation may have just the opposite effect, permitting the selection of a Condorcet candidate who would otherwise have been defeated. As we will see in chapter 6, not only the opportunities for manipulation but also its likely consequences vary greatly from one voting procedure to another.

The best-known form of insincere voting occurs under ordinary plurality voting when a voter deserts a first choice who is perceived as unlikely to win and supports instead one of the front-runners who is less preferred.

Many voters may be torn between supporting their favorite and making their vote count by voting for a front-runner, being unable to register both feelings. One may therefore seek a voting system that only infrequently presents voters with such dilemmas. Such strategic voting, when it involves deserting minor party candidates to avoid "wasting votes," may, however, strengthen a two-party system at the same time that it poses dilemmas for the individual voter (see section 4 below).

In devising alternative procedures, one must be careful not to complicate unduly the job of the electorate. The simplicity of the balloting method helps ensure that voters are capable of voting as they intend with a minimum of mistakes. Relative freedom from opportunities to manipulate the outcome by misrepresenting preferences is one factor that helps in achieving simplicity and fairness to voters. Simplicity of the decision rule aids public understanding and acceptance of the outcome, and thus, the legitimacy of the process.

1.4. Political Stability

Each of the foregoing criteria impinges on the capacity of a voting system to promote political stability. Of signal importance is the acceptance of the winner as legitimate by the electorate — both in the sense of having achieved an adequate mandate and the relative freedom of the process from manipulation. The belief that a loser is preferred by a majority of the electorate to the winner or enjoys greater intensity of support can call into question that legitimacy. These two criteria may be at odds with one another. Lincoln, for example, enjoyed great intensity of support in the 1860 U.S. presidential election, while the broader, but less intense, support for Douglas and Bell suggests that one or both may have been preferred by majorities over Lincoln.

The differential impact of multicandidate voting systems on the electoral outcome, illustrated earlier in this chapter, is well known (see, e.g., Rae 1971, Straffin 1980, Riker 1982a, Bogdanor and Butler 1983). The influence of the electoral system in use on the number and nature of political parties, factions, or candidacies may also have a profound effect on political stability (see Duverger 1963,1984, Riker 1982b, Miller 1983).

Duverger formulated as a law a principle that had been discussed by numerous writers before him, namely, that ordinary plurality voting favors a two-party system. Although Canada and India are exceptions to this claim, there appears to be considerable empirical support (in the United States and Britain) for the argument that a plurality election without a runoff provides incentives for voters to focus on two candidates and for factions or parties to coalesce in an effort to receive a plurality of the votes on the single ballot. A runoff, by contrast, permits losing factions or parties a second chance in which they may bargain with one of the two leaders in return for their endorsement. The anticipation of this opportunity may encourage greater factionalism or proliferation of parties before the first ballot. In preparation for the second ballot, however, this opportunity promotes coalition building.

Canon (1978) studied the relationship of voting procedures to factionalism in the Democratic gubernatorial primaries in sixteen southern and border states of the United States during 1932 to 1977. Using a reasonable index of factionalism, he found this value lower in all but one of the six states using ordinary plurality than in the ten states employing a runoff. Thus Canon's findings tend to support the Duverger hypothesis. As Riker (1983b) points out, the Canadian and Indian exceptions may be accounted for by restricting the hypothesis. For a decentralized government such as that of Canada, different pairs of parties may be prominent in different provinces, giving rise to a multiparty system nationally. In a nation in which one centrist party (like the Congress party in India) maintains a prolonged domination of the government over smaller parties to the left and right, these latter parties may be unable to coalesce for ideological reasons.

Much of Duverger's argument contrasts ordinary plurality voting with proportional representation in multimember districts. This part of his work is not directly relevant to the concerns of the present book, which focuses on single-winner elections. There appears to be little evidence, either theoretical or empirical, concerning the impact of single-winner voting systems, other than ordinary plurality or runoff, on the possible proliferation of factions or parties. One should be careful, however, not to infer that alternative single-winner voting procedures would promote factionalism simply because they are different from ordinary plurality or because their multiwinner counterparts may have been shown to have this effect.

1.5. Arrow's Impossibility Result and Its Implications

Were it possible to design a multicandidate voting system satisfying all desirable political objectives, the choice of such a system would be simple and there would be no reason for this book. Remarkably, even a seemingly modest list of criteria may be self-contradictory, that is the satisfaction of one criterion may be incompatible with the satisfaction of others.

Arrow (1951) showed that no multicandidate system based on transitive rankings by voters can simultaneously satisfy the following four conditions: monotonicity, independence of irrelevant alternatives, nonimposition, and nondictatorship. As Arrow's axioms have been extensively analyzed elsewhere (see, e.g., Kelly 1978), I will only describe each intuitively here.

Roughly speaking, a voting system violates monotonicity if a candidate can achieve a win because of loss of support (or fail to win because of a gain in support). A system is independent of irrelevant alternatives if the relative standings of the candidates cannot be altered by the entry of additional candidates into the race. Nonimposition means that the outcome cannot be imposed independently of the voters' preferences, that is no candidate loses to another for every possible voting outcome. Nondictatorship means that the result need not always coincide with the preferences of one particular voter.

Arrow's impossibility theorem shows that any multicandidate voting system based on transitive rankings will violate one or more of these basic expectations at least some of the time. Accordingly, we must evaluate the degree to which these and other desired criteria are met.

(Continues...)

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Table of Contents

• FrontMatter, pg. i
• CONTENTS, pg. vii
• LIST OF FIGURES, pg. xi
• LIST OF TABLES, pg. xiii
• PREFACE, pg. xv
• ACKNOWLEDGMENTS, pg. xix
• CHAPTER 1. Multicandidate Elections: Choosing a Winner, pg. 1
• CHAPTER 2. Condorcet Efficiency, pg. 15
• CHAPTER 3. Social-Utility Efficiency, pg. 30
• CHAPTER 4. The Effect of Alternative Spatial Models on Condorcet and Social-Utility Efficiency, pg. 38
• CHAPTER 5. Strategic Voting under Plurality Electoral Systems: Decisions under Uncertainty and under Risk, pg. 47
• CHAPTER 6. Strategic Voting and Its Effects on Condorcet Efficiency, pg. 64
• CHAPTER 7. Strategic Voting for Approval Balloting under Alternative Decision Rules, pg. 79
• CHAPTER 8. Empirical Estimates for Single-Vote Plurality and Approval Voting, pg. 89
• CHAPTER 9. Other Criteria for Assessing Voting Systems, pg. 96
• CHAPTER 10. Conclusions, pg. 104
• APPENDIX A. A Statistical Model for Condorcet Efficiency, pg. 109
• APPENDIX B. Justification of the Shepsle Utility Function, pg. 114
• APPENDIX C. Proofs of Theorems 5.1 and 5.2, pg. 117
• APPENDIX D. Simulation Results for Approval Balloting with Alternative Decision Rules, pg. 121
• APPENDIX E. Characterization of the Potentially Uniquely Optimal Strategies as Extreme Points of the Permissible Set of Strategies, pg. 125
• APPENDIX F. Derivation of the Standard-Score Voting System, pg. 130
• GLOSSARY, pg. 133
• BIBLIOGRAPHY, pg. 139
• INDEX, pg. 145