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.
Recommended Citation
Daugherty, Zajj, "An Algebraic Approach to Voting Theory" (2005). HMC Senior Theses. 169.
https://scholarship.claremont.edu/hmc_theses/169
Thesis Proposal
Zajj Daugherty.jpg (88 kB)
Picture of Zajj Daugherty
expositorypaper.pdf (97 kB)
Expository Paper
zdaugherty-2005-thesis-poster.pdf (207 kB)
Thesis Poster
