COMMITTEE SELECTION WITH APPROVAL VOTING IN A HYPERCUBE
Caleb Bugg1, Gabriel Elvin2, Francis Su3.
1Morehouse College, Atlanta, GA, 2University of California, Los Angeles, Los Angeles, CA, 3Harvey Mudd College, Claremont, CA.
In this paper we examine elections in which a committee of size k is to be elected, with 2 candidates running for each position. Each voter submits a ballot with his or her ideal preference for a committee, which generates their approval set. The approval sets of voters consist of committees that are close to their ideal preference. We define this notion of closeness with Hamming distance in a hypercube: the number of candidates by which a particular committee differs from a voter's ideal preference. We establish a tight lower bound for the popularity of the most approved committee, and consider restrictions on voter preferences that may increase that popularity. Our approach considers both the combinatorial and geometric aspects of these elections.