Estimating the Probability Distribution of Party Representation as a Result of Political Redistricting Using a Random Walk Monte Carlo Technique

Abstract

With each decennial census states create the boundaries that are to be used for their legislative districts for the next ten years. In this paper we present a Random Walk Monte Carlo technique that can be used to determine the probability that a set of districts has been drawn without partisan bias – gerrymandered. This is done through the creation of random spanning trees to form the representative districts. Historical election results will then be used to estimate the party representation of that random redistricting map. Through bootstrapping a probability distribution can estimated. This distribution will be used to test the hypothesis that a particular redistricting plan does not disenfranchise voters of that state.