A metric to identify gerrymandering

Abstract

Because the US judicial system relies upon subjective evaluations, we set aside the notion of establishing an objectively-determined metric to identify gerrymandering and identify a metric that well represents human judgment. We consider several metrics for political district shapes to measure the presence of the undesirable geometric characteristics of puncturedness, elongation, indentation, and separation, each of which is a hallmark of gerrymandering as per Taylor (1973). Considering a set of 16 shapes that represent the possible combinations of these characteristics, we compare 80 different combinations of characteristic metrics and selected techniques to combine them into a single measurement, as they relate to the results of a survey-based subjective weighting. We show that several are highly correlated, with our superlative metric exhibiting a correlation coefficient of 0.804. Finally, we propose a method to calibrate this metric using recently adjudicated redistricting plans to identify whether litigation is appropriate to contest suspected gerrymandering.