Gerrymandering and Compactness: Implementation Flexibility and Abuse

Richard Barnes, Justin Solomon

The shape of an electoral district may suggest whether it was drawn with political motivations, or gerrymandered. For this reason, quantifying the shape of districts, in particular their compactness, is a key task in politics and civil rights. A growing body of literature suggests and analyzes compactness measures mathematically, but little consideration has been given to how these scores should be calculated in practice. Here, we consider the effects of a number of decisions that must be made in interpreting and implementing a set of popular compactness scores. We show that the choices made in quantifying compactness may themselves become political tools, with seemingly innocuous decisions leading to disparate scores. We show that when the full range of implementation flexibility is used, it can be abused to make clearly gerrymandered districts appear quantitatively reasonable. This complicates using compactness as a legislative or judicial standard to counteract unfair redistricting practices. This paper accompanies the release of packages in C++, Python, and R which correctly, efficiently, and reproducibly calculate a variety of compactness scores.

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