# E. Grant Clifford

Harvey Mudd College Mathematics 2004

Thesis: | The Actual Thesis | The Thesis Source |
---|---|---|

Thesis Advisor: | Prof. Jon Jacobsen | |

Second Reader: | Prof. Michael Orrison | |

E-Mail: | eclifford@math.hmc.edu |

## A Decomposition of Voting Profile Spaces

In many candidate races, acquiring data of rankings of candidates is simple, but tallying those votes is a tricky issue. The question is: What constitutes a fair system of tallying votes? Of the many methods, Donald Saari provided geometric reasoning to conclude that a particular positional procedure causes the fewest paradoxes. I wish, however, to provide an algebraic proof of this fact, which I believe could strengthen the theory and add more intuition to the study of voting theory. Hopefully I can bring together the worlds of economics, algebra, and political science.

I plan to provide a concise and intuitive decomposition of the profile space for an n-candidate vote for any arbitrary n. This means examining the n!-dimensional C Sn-module with a voting theoretical perspective, and discerning what pieces are important to the maps which tally the votes. Moreover, I wish to verify Saari's work that the Borda Count is the most fair method of tallying votes, by using representation theory to prove that it causes the fewest potential voting paradoxes.