"Ehrhart quasipolynomials and voting theory"

Matt Zeckner
University of Kentucky

Masters Exam Talk
Monday, October 6, 2008
4:00 pm, 845 Patterson Office Tower

Abstract:

Imagine a three candidate election with candidates A, B, and C in which candidate A is the plurality winner, i.e. candidate A receives the most votes. Does this result truly reflect the opinions of the voters or is it possible that candidate B is actually the most well-liked candidate? If instead the election used a Borda count to determine the winner, could a strategic method of voting allow the winner to be candidate C? We shall explore these possibilities and determine the probability of these events using Ehrhart's results in calculating the generating function of the number of lattice points within the integer dilates of a rational polytope. Topics such as quasipolynomials and unimodular cones shall be introduced as well as results by Brion and Barvinok.