Revisiting Compactness for District Plans
This addresses the need for fair district maps in political redistricting, though it appears incremental as it builds on existing methods.
The paper tackles the problem of district map compactness by introducing population-weighted versions of shape-based scores and modifying the ReCom sampling method, resulting in ensembles of maps with improved shape-based compactness scores.
Modern sampling methods create ensembles of district maps that score well on discrete compactness scores, whereas the Polsby-Popper and other shape-based scores remain highly relevant for building fair maps and litigating unfair ones. The aim of this paper is twofold. First, we introduce population-weighted versions of shape-based scores and show a precise sense in which this interpolates between shape-based and discrete scores. Second, we introduce a modification of the ReCom sampling method that produces ensembles of maps with improved shape-based compactness scores.