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.
Cite
@article{arxiv.2501.02325,
title = {Revisiting Compactness for District Plans},
author = {Kristopher Tapp},
journal= {arXiv preprint arXiv:2501.02325},
year = {2025}
}