Detecting Partisan Gerrymandering through Mathematical Analysis: A Case Study of South Carolina

Partisan gerrymandering, the process of drawing the district boundaries of election maps unfairly for a given party\u27s political gain, is a practice that originated in the early 1800s and persists today. As partisan gerrymandering cases have met varying degrees of success in state and federal courts, now more than ever is there a need to define rigorous methods of assessing the partisan bias of election maps. In practice, two primary mathematical tools are utilized to quantify gerrymandering: measures of partisan bias and outlier analysis methods. This thesis analyzes the 2011 and 2018 Congressional districting plans of Pennsylvania and uses the results to inform an analysis of the 2011 South Carolina Congressional and state legislative maps. The goals of this study are to (1) provide a state-specific analysis of South Carolina and (2) contribute to the current body of literature by increasing transparency in gerrymandering detection procedures, investigating how outlier analysis methods perform for gerrymandered versus fair maps and how various partisan bias measures available perform compared to one another. Results of this study indicate that, using the √ε test as defined by Chikina et al. in the 2017 case League of Women Voters v. Commonwealth of Pennsylvania, relatively unbiased maps indicate clear levels of non-significance compared to their biased counterparts. Certain measures of partisan bias, such as median-mean and the geometric bias measure defined under a variable partisan swing assumption, are also found to perform more consistently as indicators of gerrymandering than other metrics. In addition, this study finds that there is insufficient evidence of partisan gerrymandering in the Congressional, state Senate, and state House maps of South Carolina drawn during the 2011 redistricting cycle