A geometric measure for quantifying gerrymandering

Gerrymandering is the act of manipulating the boundaries of an electoral district so as to favor one party or group. There have been some attempts to explicitly quantify how much a district "meanders" or twists. By a mathematical structure called the medial axis which is essentially the skeleton of a given shape, we introduce a new measure to deal with quantification of district meandering. We performed analysis on the 18 districts in the state of Pennsylvania in the year 2015 as well as in the year 2018, after the district boundaries were redrawn in an attempt to reduce gerrymandering. By comparing our results with previous research in the field, we found that our proposed measure gives more reasonable and stable results and addresses some issues from the previous research such as partial gerrymandering and bias against larger districts.