Date of Award
6-2013
Document Type
Open Access
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
William Zwicker
Language
English
Keywords
election, voting, ties, Borda
Abstract
In voting theory, the Borda count’s tendency to produce a tie in an election varies as a function of n, the number of voters, and m, the number of candidates. To better understand this tendency, we embed all possible rankings of candidates in a hyperplane sitting in m-dimensional space, to form an (m - 1)-dimensional polytope: the m-permutahedron. The number of possible ties may then be determined computationally using a special class of polynomials with modular coefficients. However, due to the growing complexity of the system, this method has not yet been extended past the case of m = 3. We examine the properties of certain voting situations for m ≥ 4 to better understand an election’s tendency to produce a Borda tie between all candidates.
Recommended Citation
Margulies, Adam, "Elections with Three Candidates Four Candidates and Beyond: Counting Ties in the Borda Count with Permutahedra and Ehrhart Quasi-Polynomials" (2013). Honors Theses. 702.
https://digitalworks.union.edu/theses/702