The shape of bias: Understanding the relationship between compactness and bias in U.S. elections

Gerrymandering is a central problem for many representative democracies. The manipulation of political boundaries for electoral advantage, gerrymandering is surprisingly difficult to detect in a systematic manner. In most past studies, gerrymandering analysis has focused on whether or not an entire state's districting plan is biased. Then, geometric measures of shape compactness are used to identify districts with egregiously odd shapes. However, it is not clear that the oddly-shaped districts are the real driver of bias in a given state. This lack of clarity is exacerbated because shape measures are computed for each individual district, whereas bias measures are used to summarize the bias of an entire state's districting plan. Through a new local form of contemporary measures of partisan bias, I demonstrate that a district's contribution to partisan bias is not systematically related to its shape regularity, at least for elections in the 2010 decade. This extends past work critical of compactness measures, and suggests new ways forward for the analysis of redistricting and partisan fairness.