Graduation Year

2005

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Michael Orrison

Reader 2

J.Alongi (Pomona College)

Abstract

In voting theory, simple questions can lead to convoluted and sometimes paradoxical results. Recently, mathematician Donald Saari used geometric insights to study various voting methods. He argued that a particular positional voting method (namely that proposed by Borda) minimizes the frequency of paradoxes. We present an approach to similar ideas which draw from group theory and algebra. In particular, we employ tools from representation theory on the symmetric group to elicit some of the natural behaviors of voting profiles. We also make generalizations to similar results for partially ranked data.

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