Election Dissection
Imagine that you and a number of friends—two dozen in all—are planning dinner together at a restaurant to be chosen by a vote. Fifteen diet-conscious people request a light cuisine with lots of veggies. Eight of them vote for Terry’s Thai and seven for Lucy’s Sushi. The nine remaining members want thick, marbled steaks with huge helpings of fries. They vote for Steve’s Steakhouse.
So where will you eat?
If you choose the method that Americans usually employ to select candidates for public office, you’ll end up at Steve’s. Although nearly two-thirds of your group would prefer the healthier fare, the high cholesterol hangout got more votes than either of the other two eateries.
Most single-office political contests in America are decided by a plurality-takes-all rule that often does not reflect the true preferences of the majority of those voting. Take, for example, Louisiana’s 1991 gubernatorial election, in which 12 candidates crowded a general-election ballot. Two candidates—one of them twice indicted on federal racketeering charges and the other a former Klan grand wizard—each received about a third of the votes. A third candidate, the incumbent governor, won almost all the rest, but not quite enough to get his name on a run-off ballot. Yet all opinion polls indicated that he would have won a head-to-head contest against either of the other two finalists.
He may have wished that Louisiana used voting rules suggested some 200 years earlier by the Marquis de Condorcet, a French mathematician. Condorcet proposed that elections be decided by presenting voters with multiple one-to-one match-ups. That sounds fair, sure, but the necessary ballot would be absurdly cumbersome and confusing. Moreover, Condorcet’s method can yield paradoxical results of the rock-paper-scissors variety—for example, differently composed majorities may vote for Thai over sushi, for sushi over steak, and for steak over Thai.
A number of very bright people have devoted an impressive amount of intellectual energy to designing and evaluating voting alternatives. They disagree about which plan is best, but most say that any of several methods would be better than the familiar plurality-wins system. The methods they favor are widely used in national elections around the world, in a few state and local elections in this country, and for many kinds of nonpolitical choices.
For example, each week during college football season the Associated Press and other news organizations ask leading sportswriters and coaches to rank the top 25 teams. A first-place vote earns a team 25 points, a second-place vote 24 points, and so on down to one point. Final rankings are based on the sum of points for the top 25 vote-getters among all the teams mentioned. This way of voting is known as a “Borda count,” so named for Jean-Charles de Borda, an 18th-century French physicist (and contemporary of Condorcet) who, when he wasn’t solving problems in astronomy and fluid mechanics, applied his talents to designing a “fair” voting system.
In our hypothetical restaurant example, Borda voting would greatly improve the odds that either Terry’s Thai or Lucy’s Sushi would win. Terry’s could probably count on at least 47 votes (24 points from first-place votes of eight loyal fans, 14 points from second-place votes from seven sushi-lovers, and a minimum of 9 points from the meat-and-potatoes crowd). Lucy’s minimum score would probably be 46 (21 first-place points from seven sushi fans, 16 points from eight Thai fans, and at least 9 points from those who’d prefer steak). Steve’s fans could expect to be the swing votes between Thai and sushi, but they couldn’t count on more than 42 points for steak (27 first-place points from 9 red-meat loyalists and 15 points from their friends’ third-place votes).
Alas, those “probablys” are necessary because somebody might decide to “game” the system. If a few people who really wanted sushi voted as if they preferred steak to Thai, they might sink Terry’s score below Lucy’s. Indeed, if enough voters for the two front-running restaurants dishonestly ranked their closest competitor third, Steve’s might win-again contrary to the true preferences of the majority. Borda once wrote, “My system is intended for use by honest men,” an acknowledgement that might seem to disqualify it for use in politics and maybe even for menu choices.
In 1972, American economist Kenneth Arrow won a Nobel Prize for “Arrow’s Impossibility Theorem,” proving with mathematical rigor that, for more than two ballot choices, any voting system will sometimes produce “paradoxes”—outcomes that violate the true wishes of the majority. “There is no consistent method,” Arrow wrote, “by which a democratic society can make a choice (when voting) that is always fair when that choice must be made from among three or more alternatives.”
That does not mean, however, that all methods are equally error-prone. Donald Saari, a mathematician at the University of California, Irvine, has modeled the attributes of voting systems using a branch of mathematics called, aptly, chaos theory. Saari says he was astonished to discover that Borda’s method actually produced the fewest paradoxes and in practice is the hardest to manipulate successfully. And the worst system, mathematically speaking? You guessed it. “The procedure,” Saari says, “which is most susceptible to electing the ‘wrong’ person is our plurality vote.”
Plurality voting encourages people to vote against their real preferences in order to avoid “wasting their vote” or risking what they consider a worse outcome. After the 2000 presidential campaign, analysts commented that Ralph Nader’s candidacy took votes away from AI Gore in crucial states, greatly helping George W. Bush. Robert Richie, executive director of The Center for Voting and Democracy, a nonprofit group, adds that the more common situation is that candidates representing minority views choose not to run at all, rather than be labeled “spoilers.”
Last fall, when the free-for-all California gubernatorial recall race was in full swing, some pundits predicted that the Golden State’s governor would be elected by as few as 15 percent of the votes. That didn’t happen, says Michael Barone, editor of The Almanac of American Politics, because most potentially serious competitors to Republican front-runner Arnold Schwarzenegger and Democratic front-runner Carlos Bustamante dropped out. “The political process,” Barone says, “worked toward creating a two-party system inside a procedure which is not designed for it.” You can argue either that a two-party system promotes stability by blurring sharp differences or, as Richie maintains, that it typically lowers the vitality of political debate and reduces voter turnout.
In some contexts, the potential perversity of plurality voting may be seen as desirable. For example, Oscar nominations are made through a Borda count: Members of the Academy of Motion Pictures award one to five points to their favorite films and actors, guaranteeing strong contenders. But the choice among finalists is made by the “plurality wins” system. Although they can’t prove it, students of voting theory are convinced that this method is deliberately used to maintain suspense by maximizing the odds of unexpected outcomes.
Other systems meet other needs. The United Nations elects its Secretary-General through approval voting, a process apt to select the least objectionable leader. Voters give one point to as many candidates as they consider acceptable. The candidate with the highest points wins. (By contrast, in 508 B.C., Athenians instituted what might be designated “disapproval voting,” an annual ballot to choose the politician they wished most to exile. They soon changed the rules to require at least 6,000 such votes, lest too many political leaders be sent packing.)
Then there’s cumulative voting, a system that allots every voter as many votes as there are candidates. A voter can distribute these votes among several candidates or cast all of them for one candidate. This method improves the chances that minority interests will get a seat at the table. About 10 percent of Standard and Poor’s 500 corporations select their boards of directors through cumulative voting.
Robert Richie’s organization favors a procedure sometimes called instant runoff voting. Voters rank candidates, and whichever candidate gets the fewest first-place votes is automatically eliminated. The first-place votes of those who voted for that candidate are awarded to those voters’ second-place choices, a process that continues until a candidate gains a majority. Since every voter's rank-ordered preferences are included in the initial ballot, an actual run-off election is not required. Many nations use a form of instant run-off voting, and at least two states, Alaska and Vermont, have seriously considered using it.
Saari says that if you tell him the criteria you want maximized or minimized, he can tell you which system is “fairest” by your standards. Just forget perfection. For a healthy democracy, what’s critical is that voters understand the rules and have confidence that the rules will be followed. And, after the votes are counted, the winning candidate must have at least enough popular support to do the job for which he or she was elected.Those tests sound modest, but can’t be taken for granted. When we vote this year, we can be grateful for elections that usually meet them, even if we wonder whether that’s because of our voting rules or in spite of them.
Fred Baldwin, despite earning a Ph.D. in American History from Princeton, admits that he learned more about how to count votes during his ten years on a local school board in Carlisle, Pennsylvania.