Open Access Senior Thesis
Bachelor of Science
J.Alongi (Pomona College)
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.
Daugherty, Zajj, "An Algebraic Approach to Voting Theory" (2005). HMC Senior Theses. 169.