### Mathematics Awareness Week 1996

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## Lecture at Purdue: Do we, inadvertently, choose badly?

### Do we, inadvertently, choose badly?

Northwestern University mathematics professor Don Saari gave a lecture at Purdue on Thursday, April 11, in conjunction with Math Awareness Week.

Professor Saari spoke about the mathematics of voting theory. Does voting need a theory, and is mathematics needed to study it? The answer is yes, once we realize that our traditional majority voting system can lead to some conundrums. For example, in a three way race, if one of the candidates is favored by a plurality of the voters, but is ranked dead last by a majority, does that candidate deserve to win? Consider a presidential race with one left of center candidate, and two right of center, or a mayoral race with one white candidate, and two black; does this sound familiar? Voting theory allows for many different kinds of voting procedures (e.g., Borda count, approval voting, plurality voting), and these different procedures will, given the same voter preferences, determine different outcomes. (Those of you who followed the Lani Guinier nomination a couple of years ago may recall that one of the things that got her into trouble was her consideration in print of some of these alternate voting systems.) Professor Saari has used mathematics to analyze these different voting processes to try and determine which one leads to the fewest "paradoxes." His results are new, surprising, and provocative.

Professor Saari is a very good speaker, a natural story teller, and an award winning writer; he has received the two highest prizes given by the math community for expository writing, the L. R. Ford Award (1985) and the Chauvenet Prize (1995). The work described in this talk is interdisciplinary, and so it should appeal to students in many fields, for example, political science, sociology, management, economics, history. If you would like to read a bit more about Professor Saari's work, visit his home page at:

http://www.math.nwu.edu/~d_saari/
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