Date of Award
Bachelor of Science
election, voting, ties, Borda
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.
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 and Student Projects. 702.