A Comparison of Metrics for the Identification of Partisan Gerrymandering

Abstract: Currently, there is currently no effective, standardized way to identify the presence of partisan gerrymandering. A relatively newly proposed method of identification is ensemble analysis. This is done by generating a large neutral ensemble of voting plans, then comparing the given voting plan against the ensemble through the use of a mathematical metric. In this paper, we survey seven of the most common mathematical metrics used for this identification process, which are the efficiency gap, weighted efficiency gap with weight 2, relative efficiency gap with weight 1, relative efficiency gap with weight 2, mean-median score, partisan bias, and declination. We define and discuss all of these. The analysis is done by performing ensemble analysis on ten elections with each metric to determine whether each metric determines each election as gerrymandered. All ten of these elections have been studied in the literature, so we compare those results to the results found by the metrics to assess accuracy. We show that, while the mean-median score and partisan bias are the most applicable across all seven metrics, they are also the most inaccurate. No significant difference was detected between the remaining five metrics, so our final recommendation is to use one of the four variants of the efficiency gap or the declination if applicable, and the mean-median score if not. The partisan bias was the least accurate of all the metrics tested.