Northwestern mathematician to discuss voting paradoxes at AAAS meeting

February 13, 2000

Northwestern mathematician Donald G. Saari will present his research on voting paradoxes Friday, Feb. 18, at 4:35 p.m. at the 2000 American Association for the Advancement of Science (AAAS) Annual Meeting in Washington. His presentation is part of the session titled "The Mathematics of Politics: Census, Representation and Voting."

In elections with three or more candidates, like the New Hampshire Republican primary earlier this month, "winning doesn't mean you are the favorite of the voters" says Saari, Pancoe Professor of Mathematics at Northwestern.

He contends that the outcomes of such races may not accurately reflect voters' true wishes -- a paradox that can result from elections decided on a simple plurality where one person casts one vote.

Using principles adopted from geometry, Saari has demonstrated that in most decision-making processes, including political elections, a weighted vote of two for first place, one for second and none for third is the most effective means of making choices among three candidates. Such weighted voting was first proposed by the French mathematician Jean-Charles Borda in 1770.

Saari uses the 1996 New Hampshire Republican primary as an example of where election results can be misleading. In that contest, social conservative Patrick J. Buchanan won with 27 percent of the vote, followed by Bob Dole with 26 percent, Lamar Alexander with 23 percent and Steve Forbes with 12 percent. There also were three other candidates.

"With the results in, the Republican establishment was wondering what went wrong," Saari said. "But the real problem was a lousy election procedure. The 1996 polls suggested that for the majority of voters, Buchanan would have been a last choice. With a more accurate voting procedure, the election results would have better reflected the voters' beliefs."

Saari's research, published in the January 2000 issue of the journal Economic Theory, has shown that the "Borda count" of weighted choices is far more reflective of an electorate's wishes than simple plurality voting or other procedures.

"My research shows that different voting procedures -- plurality voting and weighted voting -- produce dramatically different results when using the same data," Saari said. "On the other hand, it appears that the outcome of this year's New Hampshire primary would have remained essentially the same no matter what weighted voting procedure had been used."

"Allowing voters to name only their top choice is akin to ranking students based only on the number of As they receive," Saari said. "A student with three As and two Fs would be ranked above one with two As and three Bs. When elections are decided by a simple plurality, the same inequity can occur."

His research goal, he said, is to understand which ranking procedures can unintentionally lead to inferior choices. The research relates not only to elections, but also to engineering and business decisions, such as weighing factors in deciding where to locate a new plant.
The AAAS annual meeting will be held Feb. 17-22 at Washington's Marriott Wardman Park and Omni Shoreham hotels.

(Source contact: Donald Saari at 847-491-5580 or

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