This talk presents LP and IP formulations that are used to answer a small open question in voting theory. In a much studied election scheme, every voter arranges a set of candidates in order of preference. The outcome of the election is determined by comparing the fraction of the total voters preferring u to v, for each pair of candidates u and v. By treating the candidates as vertices and including a directed edge uv whenever candidate u is preferred to candidate v by a prespecified fraction p of the voters, every election outcome can be represented as a directed graph. It is relatively easy to show that every directed graph represents a possible election outcome for some p>