Creative chaos

“Voting is a basic tool of every democracy,” Donald Saari writes. “We vote to choose the name for a pet dog, to choose a text book, a department chair, a U.S. Senator, . . . the president of the United States. But does the election outcome capture what the voters want?”

Not necessarily. According to Saari, sometimes the wrong person gets elected.

In seeking to understand why voting patterns sometimes lead to results that don’t reflect the true wishes of the electorate and why people vote the way they do, he has become a leading critic of the American electoral process and an advocate for voting procedures that more accurately represent the will of the people by taking into consideration their second choices. His current research focuses on the political process, the economy, supply and demand and the emergence of chaotic behavior in those processes.

In his recent book, Chaotic Elections! which looks at the 2000 election and voting systems in general, Saari shows that the problems aren’t with courts and counts, but with the very way we vote. And according to Saari, an apparent anomaly such as the 1998 election of wrestler Jesse Ventura as governor of Minnesota can be explained more accurately by mathematics than social theory. [In a three-way race, Ventura won with only 37 percent of the popular vote. By weighting ballot choices according to preference (first choice, second, etc.), the outcome would have reflected that more than 60 percent of the voters wanted a candidate other than Ventura – probably Hubert Humphrey III, Saari says.)

“Donald’s innovative research merges mathematics and the social sciences,” Chancellor Ralph J. Cicerone says. “He is a creative thinker who energizes colleagues and students alike with his enthusiasm and ideas, which contribute to UCI’s overall academic and research excellence.”

Duncan Luce, Distinguished Professor of Cognitive Sciences, adds, “Saari’s contributions to both economics and voting schemes and his research successes are what led to his recent election to the National Academy of Sciences.”

Luce recruited Saari to UCI in January 2000 from Northwestern University, where his wide-ranging interests led to contributions in the fields of economics, chaos theory and celestial mechanics (which investigates the motions of planetary systems or systems of stars).

“I saw the wide variety of interdisciplinary work going on here and I found it fascinating,” Saari says. “To be honest, I went back to Northwestern with the intention of finding out whether I would be able to duplicate it there. I thought, ‘Why should I spend all that time working on that, when I could come here and begin research right away?’”

A university that embraces interdisciplinary work is years ahead of more traditional academic institutions, explains Saari, who earned his doctorate in mathematics from Purdue University in 1967.

“The ideas of tomorrow are being developed at these schools. Students at UCI are getting a decade-advanced notice of these new ideas, new thinking and new approaches. They’re contributing to these ideas.

“Research is exactly the same as teaching. We’re influencing the way people think.

“And when I’m teaching, the only way to influence how students think is to know what they think,” Saari continues. “I want to know their aspirations. Their interests. I want them to know that I’m concerned about each and every one of them. Once they understand that, then I can push them. I can really, really push them to levels they never knew they could attain.”

He believes the biggest problems in American classrooms today are teachers who lecture students. They hand down knowledge rather than stimulate creative thinking about solving problems. “If I walk into the classroom with the attitude that what I’m presenting was etched on the tablets that Moses brought down, I’m not going to get very far,” Saari says. “There has to be interaction. Learning is not a spectator activity.”

As a volunteer “Math Awareness Week” teacher in a fourth-grade class some years ago, Saari demonstrated the effectiveness of his theories about both voting behavior and teaching. He used the mathematics of decision-making—particularly voting—to introduce math concepts from algebra and geometry to “certain delicate mathematical symmetries.” As he posed problems in achieving a fair vote, the students came up with an election method that assigned points to first, second and third place choices in counting the vote. They didn’t realize they were following the Borda Method developed more than 200 years ago by a French mathematician and still studied and debated by scholars.

In a half-hour session, Saari recalls, “These fourth-graders cut through the conceptual difficulties to achieve critical understanding” of issues that have confused generations of mathematicians, economists and political scientists.