Revisiting Compactness for District Plans

TL;DR

This paper introduces population-weighted compactness scores and modifies the ReCom sampling method to generate district maps with improved shape-based compactness, enhancing fairness and litigability.

Contribution

It presents novel population-weighted compactness scores and a modified ReCom sampling method for better shape-based compactness in district maps.

Findings

Population-weighted scores interpolate between shape and discrete scores.

Modified ReCom improves shape-based compactness scores.

Enhanced tools for fair districting and litigation.

Abstract

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.