Nov 03, 2009 - Claremont, Calif. -

As voters around the country head to the polls on Nov. 3, many may be unaware that the voting procedure used to tally their votes may be more important than what they actually think about the candidates.

In the paper “Voting, the Symmetric Group, and Representation Theory,” HMC researchers revealed huge possible discrepancies in election results when voters are asked to vote in different ways (even though the voter’s opinion on the subject remained unchanged).

“For example, the results of an election can change drastically when a voter is asked to order a slate of candidates from 'most preferred to least preferred' versus asking them to simply identify their 'favorite' candidate," said Michael E. Orrison, associate professor of mathematics and a co-author of the paper.

That election results can be altered by even slight changes to a voting procedure can create very complex problems. Orrison is hopeful that his team’s algebraic approach to analyzing voting structure and data will help. He collaborated on the voting research with his students, now alumni, Zajj Daugherty ’05, Alex Eustis ’06 and Greg Minton ’08. Their paper appeared in the October issue of the American Mathematical Monthly, a highly selective and high-profile mathematics journal.

Much of their research is built atop a geometric approach created by Don Saari, distinguished professor of mathematics and economics at UC Irvine. Saari’s work allows researchers to study certain questions regarding voting in a very systematic way. Orrison and the students took that geometric framework and augmented it with an algebraic framework. “We can create a common arena in which these seemingly different types of information can coincide and be studied simultaneously. In that sense, the algebraic (versus the geometric) framework is liberating because it allows us to ask practical questions and still harness a great deal of mathematical insights, tools and machinery to extend what was done before," said Orrison.

The vast scope of the issue is thrilling to Orrison. “I feel like I’m able to impress upon the student researchers that the joy of tackling this problem is sometimes bound up in the fact that it really is bigger than any of us and the contributions that a student can make in a given year or a given summer will undoubtedly contribute to our understanding of this big problem.”

“One of the things I admire most about Orrison’s research is that he has a knack for showing how very abstract ideas can be used to yield concrete insights into real-world problems. His passion for the field is enormous and he demonstrates once again that our undergraduates can produce first-rate research,” says mathematics department chair Andrew Bernoff.

The alumni who contributed to the paper are now working on research of their own. Daugherty is at the University of Wisconsin (Madison), where she is working on combinatorial representation theory; Eustis is at UC San Diego studying combinatorics; and Minton is working toward a Ph.D. at MIT.

Voting, the Symmetric Group, and Representation Theory pdf.