# Revisiting Compactness for District Plans

arXiv: https://arxiv.org/abs/2501.02325 · HTML: https://mlsanity.com/paper/2501.02325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 8 references that are in the map.
- First posted on arXiv 4 Jan 2025.

## Builds on (most cited first, 5 of 5)

- [Recombination: A family of Markov chains for redistricting](https://mlsanity.com/paper/1911.05725/) (2019)
- [Sequential Monte Carlo for Sampling Balanced and Compact Redistricting Plans](https://mlsanity.com/paper/2008.06131/) (2020)
- [Metropolized Forest Recombination for Monte Carlo Sampling of Graph Partitions](https://mlsanity.com/paper/1911.01503/) (2019)
- [Compact Redistricting Plans Have Many Spanning Trees](https://mlsanity.com/paper/2109.13394/) (2021)
- [Spanning Trees and Redistricting: New Methods for Sampling and Validation](https://mlsanity.com/paper/2210.01401/) (2022)

## Abstract (arXiv)

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.