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Approval Voting: A Better Way to Select a Winner

by Steven J. Brams '62

It may come as a surprise to many that there is a science of elections, whose provenance can be traced back to several important theorists, including: 1) the Marquis de Condorcet in 18th-century France; 2) Charles Dodgson (Lewis Carroll) in 19th-century England; and 3) Kenneth Arrow in 20th-century America. Since Arrow published his seminal book, Social Choice and Individual Values, 51 years ago -- for which in large part he received the Nobel Memorial Prize in Economics in 1972 -- there have been thousands of articles and hundreds of books published on everything from the mathematical properties of voting systems to empirical tests of the propensity of different systems to elect centrist candidates.

The 2000 U.S. presidential election highlighted, among other things, the frailties of voting machines and the seeming arbitrariness of such venerable U.S. institutions as the Electoral College and the Supreme Court. Political commentary has focused on these aspects but given little attention to alternative voting systems, about which the science of elections has much to say.

Several alternative systems for electing a single winner have been shown to be far superior to plurality voting (PV), our current system. PV, which allows citizens to vote for only one candidate, suffers from a dismaying flaw. In any race with more than two candidates, PV may elect the candidate least acceptable to the majority of voters. This frequently happens in a three-way contest, when the majority splits its votes between two centrist candidates, allowing a more extreme candidate to win. PV also forces minor-party candidates into the role of spoilers, as we saw in 2000, which can be decisive in a close contest between the major-party candidates.

Of the alternatives to PV, I recommend approval voting (AV) on both practical and theoretical grounds. Proposed independently by several analysts in the 1970s, AV is a voting procedure in which voters can vote for, or "approve of," as many candidates as they wish in multicandidate elections -- that is, elections with more than two candidates. Each candidate approved of receives one vote, and the candidate with the most votes wins.

In the United States, the case for AV seems particularly strong in primary and nonpartisan elections, which often draw large fields of candidates:

1. It gives voters more flexible options. They can do everything they can under PV -- vote for a single favorite -- but if they have no strong preference for one candidate, they can express this fact by voting for all candidates they find acceptable. In addition, if a voter's most preferred candidate has little chance of winning, that voter can vote for both a first choice and a more viable candidate without worrying about wasting his or her vote on the less popular candidate.

2. It helps elect the strongest candidate. Today the candidate supported by the largest minority often wins, or at least makes the runoff if there is one. Under AV, by contrast, the candidate with the greatest overall support will generally win. In particular, "Condorcet candidates," who can defeat every other candidate in separate pairwise contests, almost always win under AV, whereas under PV they often lose because they split the vote with one or more other centrist candidates. [Editor's note: "almost always" was too strong: three of the five 2001-2005 Debian leader elections featured different Approval and Condorcet winners. But certainly Condorcet winners are more common with AV than PV.]

3. It will reduce negative campaigning. AV induces candidates to try to mirror the views of a majority of voters, not just cater to minorities whose voters could give them a slight edge in a crowded plurality contest. It is thus likely to cut down on negative campaigning, because candidates will have an incentive to try to broaden their appeals by reaching out for approval to voters who might have a different first choice. Lambasting such a choice would risk alienating this candidate's supporters and losing their approval. [Editor's note: This claim may have validity but is not supported by any evidence I know of. And indeed there is some evidence against it. Specifically, J.H.Nagel has complained about a flaw in AV he calls Burr's Dilemma which involves exactly this kind of quandary.]

4. It will increase voter turnout. By being better able to express their preferences, voters are more likely to vote in the first place. Voters who think they might be wasting their votes under PV, or who cannot decide which of several candidates best represents their views, will not have to despair about making a choice. By not being forced to make a single--perhaps arbitrary--choice, they will feel that the election system allows them to be more honest, which will make voting more meaningful and encourage greater participation in elections. [Editor's note: This claim probably is true but is not supported by direct evidence.]

5. It will give minority candidates their proper due. Minority candidates will not suffer under AV: their supporters will not be torn away simply because there is another candidate who, though less appealing to them, is generally considered a stronger contender. Because AV allows these supporters to vote for both candidates, they will not be tempted to desert the one who is weak in the polls, as under PV. Hence, minority candidates will receive their true level of support under AV, even if they cannot win. This will make election returns a better reflection of the overall acceptability of candidates, relatively undistorted by strategic voting, which is important information often denied to voters today. [Editor's note: AV is more friendly to minority candidates than PV, but still "fails to give them their proper due," i.e. still distorts the vote totals heavily against them, in the sense that range voting experimentally gives such candidates far higher vote counts.]

6. It is eminently practicable. Unlike more complicated ranking systems, which suffer from a variety of theoretical as well as practical defects, AV is simple for voters to understand and use. Although more votes must be tallied under AV than under PV, AV can readily be implemented on existing voting machines. Because AV does not violate any state constitutions in the United States (or, for that matter, the constitutions of most countries in the world), it requires only an ordinary statute to enact.

Voting systems that involve ranking candidates may appear, at first blush, more appealing than AV. One, the Borda count, awards points to candidates according to their ranking. Another is the Hare system of single transferable vote (sometimes called "instant runoff"), in which candidates receiving the fewest first-choice votes are progressively eliminated and their votes transferred to second choices -- and lower choices if necessary -- until one candidate emerges with a majority.

Compared with AV, these systems have serious drawbacks. The Borda count fosters "insincere voting" (for example, ranking a second choice at the bottom if that candidate is considered the strongest threat to one's top choice) and is also vulnerable to "irrelevant candidates" who cannot win but can affect the outcome. The Hare system may eliminate a centrist candidate early on and thereby elect one less acceptable to the majority. It suffers also from "nonmonotonicity," in which voters, by raising the ranking of a candidate, may actually cause that candidate to lose -- just the opposite of what one would want to happen.

Probably the best-known official elected by AV today is the secretary-general of the United Nations. AV has been used in internal elections by the political parties in some states, such as Pennsylvania, where a presidential straw poll using AV was conducted by the Democratic State Committee in 1983. Bills to implement AV have been introduced in several state legislatures. In 1987, a bill to enact AV in certain statewide elections passed the Senate but not the House in North Dakota. In 1990, Oregon used AV in a statewide advisory referendum on school financing, which presented voters with five different options and allowed them to vote for as many as they wished.

In the late 1980s, AV was used in some competitive elections in countries in Eastern Europe and the Soviet Union, where it was effectively "disapproval voting" because voters were permitted to cross off names on ballots but not to vote for candidates. But this procedure is logically equivalent to AV: candidates not crossed off are, in effect, approved of, although psychologically there is almost surely a difference between approving and disapproving of candidates.

Beginning in 1987, several scientific and engineering societies adopted AV. It has worked well in finding consensus candidates; all these societies continue to use it today and include the following:

Smaller societies that use AV include the Society for Judgment and Decision Making, the Social Choice and Welfare Society, the International Joint Conference on Artificial Intelligence, and the European Association for Logic, Language and Information.

Additionally, the Econometric Society has used AV (with certain emendations) to elect fellows since 1980; likewise, since 1981 the selection of members of the National Academy of Sciences at the final stage of balloting has been based on AV. Coupled with many colleges and universities that now use AV -- from the departmental level to the school-wide level -- it is no exaggeration to say that several hundred thousand individuals have had direct experience with AV.

As cherished a principle as "one person, one vote" is in single-winner elections, such as for president, it is probably an anachronism today. In my opinion, democracies can more benefit from the alternative principle of "one candidate, one vote," whereby voters make judgments about whether each candidate on the ballot is acceptable or not.

The latter principle makes the tie-in of a vote not to the voter but rather to the candidates, which is arguably more egalitarian than artificially restricting voters to casting only one vote in multicandidate races. This principle also affords voters an opportunity to express their intensities of preference by approving of, for example, all candidates except the one they despise.

Although AV encourages sincere voting, it does not altogether eliminate strategic calculations. Because approval of a less-preferred candidate can hurt a more-preferred approved candidate, the voter is still faced with the decision of where to draw the line between acceptable and nonacceptable candidates. A rational voter will vote for a second choice if his or her first choice appears to be a long shot--as indicated, for example, by polls -- but the voter's calculus and its effects on outcomes is not yet well understood for either AV or other voting procedures.

While AV is a strikingly simple election reform for finding consensus choices in single-winner elections, in elections with more than one winner -- such as for a council or a legislature -- AV would not be desirable if the goal is to mirror a diversity of views, especially of minorities; for this purpose, other voting systems should be considered. On the other hand, minorities may derive indirect benefit from AV in single-winner elections, because mainstream candidates, in order to win, will be forced to reach out to minority voters for the approval they (the mainstream candidates) need to win. While promoting majoritarian candidates, therefore, AV induces them to be responsive to minority views.

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About the Author

Steven J. Brams '62 holds an SB in economics, politics, and science from MIT and a PhD in political science from Northwestern University. He is Professor of Politics at New York University and the author or co-author of fourteen books, including Approval Voting, that involve applications of game theory and social choice theory to voting and elections, bargaining and fairness, international relations, and the Bible and theology. He is a fellow of the American Association for the Advancement of Science, the Public Choice Society, a Guggenheim fellow, a past president of the Peace Science Society (International), and in 1998-99 was a visiting scholar at the Russell Sage Foundation in New York City. A revised edition of his book, Biblical Games: Game Theory and the Hebrew Bible, was just published by The MIT Press.

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