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Photo by James Bunoan Donald Saari has delved deep into America's voting system and unearthed a frightening statistic: 70 percent of three-person political races result in mathematically questionable outcomes.
The U.S. employs the plurality voting procedure, in which every citizen votes for only one candidate. "One man, one vote" we're taught from the time we're kids is the simplest, fairest form of democracy. Yet during the 1992 presidential race, most American voters preferred either George Bush or Ross Perot, but because they could only choose one candidate, they split their vote and a majority of Americans were left with their last choice: Bill Clinton. The phenomenon occurred again in 2000 when most voters preferred either Al Gore or Ralph Nader but ended up with George W. Bush.
The upcoming 2004 election has some political pundits predicting a possible 2000 repeat, with Nader affecting the outcome of the election by splitting the liberal vote in the states where he's on the ballot. Saari has speculated on this question, but unlike the average political pundit, his meditations are apolitical; they focus on math.
Saari is a distinguished professor of mathematics and economics at UC Irvine. Even as a kid, elections fascinated him and led him to more than two decades worth of research. Although Dr. Saari began working with voting theory because he thought it would provide simple answers to questions he had about celestial mechanics, he found the subject infinitely more complicated and grim than he had anticipated, saying that America's plurality system is "in the select class of worst possible [voting] procedures in the sense that more things can go wrong."
But if the plurality procedure fails to work, how can the U.S. ensure fair elections? Saari says he discovered the answer in the mid-1990s and published his findings three years ago in the book Chaotic Elections, in which he used advanced mathematics, laws of symmetry, geometry and chaos theory to argue that the Borda Count—an 18th-century French voting procedure—is the tallying system that best represents voters' preference.
Here's how it works: if someone prefers Nader over Kerry over Bush, he would give Nader two points, Kerry one point and Bush zero. Because the Borda Count records every voting citizen's second choice, it helps prevent 1992- and 2000-type situations. The method also works for any number of candidates in a race. In a six-candidate race, for example, voters give five points to their first choice, four points to their second choice and so on.
To understand the relationship between the Borda Count and the plurality procedure—and to comprehend why the plurality procedure is so bad—think of your high school or college days. The academic administration ranked your class standing according to the Borda Count—you received 4 points for an A, 3 points for a B and so on. If the administration decided to switch to the plurality procedure, a student would be judged only by his A's, so a student who received one A and all F's, for example, would be ranked over a student with straight B's. This is exactly what happened during the 2000 election. Gore's B's—the presumed second-choice votes he would have received from Nader voters—were never taken into consideration.
"There are situations where we have to wonder if the voting procedure we have used has actually subverted democracy," said Saari, who, if he sounds dour, actually bears a strong resemblance to Santa Claus—white beard, ruddy complexion—and is almost always smiling and is very popular with students.
The Borda Count serves as the only procedure that has been mathematically proven to reflect the will of the people. Experts such as Dr. Maurice Salles of the University of Caen (France), coordinating editor of the journal Social Choice and Welfare, believes Saari's result will forever attach his name to voting theory. In layman's terms, Saari is a math-world superstar; witness the fact that Saari's Borda theory helped earn him a spot in the prestigious National Academy of Sciences.
Not impressed? Consider that the Associated Press, USA Todayand ESPN's Coaches Poll use the Borda to rank college football and basketball teams—weekly elections Americans actually care about. As for national elections, the only countries currently employing the Borda count are Slovenia and Nauru, which have never had to depend on Katherine Harris to select their ultimate leader.
And one unintended "consequence" of the Borda count is that it requires voters to be knowledgeable about all candidates in a race. One can't just say, "I'm a Kerry man" and leave it at that. Under the Borda, the conscientious voter must acquaint themselves with all candidates in the race, a possible boon to Third Partiers.
Saari acknowledges that there are some winkles to be smoothed, not the least of which is how to mesh the Borda Count into the Electoral College as well as having to "counter the cultural mistake of one-person-one vote," Saari said. "An even more serious problem is that the people who have to vote to change the rules are those who got elected with the current rules. Will they vote for change when the new rules might elect someone else?"
They may have to if 2004 turns out to be a 2000 repeat.
"Disaster," he said, "makes people more willing to consider reform."