Marie Jameson

Harvey Mudd College Mathematics 2007

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Updated Thesis Proposal: Proposal: An Algebraic Study of Voting Theory
Thesis Report: Thesis Report:Voting Paradoxes Caused by Dropping Candidates in an Election
Thesis Advisor: Prof. Michael Orrison
Second Reader: Dr. Nathan Ryan

An Algebraic Study of Voting Theory

Voting theory is plagued by seemingly contradictory results, called voting paradoxes. For example, different methods of tallying votes can result in different election results; these voting paradoxes give contradictory answers to the question of what the voting population ''really'' wants. This paper studies voting paradoxes brought about by considering the effect of dropping one or more candidates in an election after the voting data has already been collected. Dropping a candidate may change the election results for the remaining candidates. This paper adopts an algebraic framework to approach this voting theoretic problem.