3.3 - A Geometric Approach to Voting Theory for Mathematics Majors

Summary

Introduction

In the Spring of 2002, I taught an upper level course in Game and Voting Theory at Wheaton College, a small liberal arts college, in Norton, Massachusetts. There were twelve students enrolled in the course. Most were majors in Mathematics, Mathematics/Computer Science, or Mathematics/Economics, although there was one History major and one Psychology major. All the students had taken our Discrete Mathematics course, which serves as our introduction to proofs class. We spent the first half the semester on game theory and the remaining seven weeks on voting theory. In this paper, I will focus on the voting theory part of the course and give a brief tour through some of the course content. I also will describe the structure of the assignments and directions that I would like to take the course in the future.

Approximately four years ago, I changed my research area to voting theory from algebraic topology, in part because the questions and answers often are accessible to undergraduates, even if the proofs are not. The course provided an opportunity to expose the students to an active area of research and to explain recent results. For many students, this was the first time they had seen theorems from the last half of the 20th century, and it was certainly the first time any of the students had seen results published in the 21st century. This made quite an impression on several of the students, who commented on this in their course evaluations.