Zajj Daugherty

Harvey Mudd College Mathematics 2005

Thesis Advisor: Prof. Michael Orrison
Second Reader: Prof. John M. Alongi

Thesis Documents: (all PDF)

      Thesis Proposal
      Expository paper
      Final Thesis
      Presentations Days Poster

An Algebraic Approach to Voting Theory

In classical voting theory, simple questions can lead to convoluted and sometimes paradoxical results. Many different voting schemes have been developed in an attempt to reach the best possible method for tallying votes for rankings. However, it is not always immediately clear which system gives rise to the most fair results. Donald Saari used geometric methods to study various voting schemes. He argues that a particular positional voting scheme (namely that proposed by Borda) gives rise to the fewest paradoxes. I wish to study voting schemes, but with an algebraic method. I intend to utilize Saari's ideas and his approaches, and expand upon these developments from an algebraic perspective. More specifically, I will use tools from representation theory to elicit some of the natural behaviors of voting profiles. I will also make generalizations to similar results for partially ranked data.