The Traveling Mailman: Topological Optimization Methods for User-Centric Redistricting

TL;DR

This paper presents a novel topological and statistical approach to redistricting using USPS data, improving community integrity and compactness of districts, with implications for fairer political representation.

Contribution

It introduces a new redistricting method combining Topological Data Analysis and MCMC, applied to Iowa, outperforming official plans in community preservation.

Findings

Fewer cut edges in generated plans compared to official Iowa plan.

More compact district shapes achieved with the new method.

Identified three distinct districting landscape distributions.

Abstract

This study introduces a new districting approach using the US Postal Service network to measure community connectivity. We combine Topological Data Analysis with Markov Chain Monte Carlo methods to assess district boundaries' impact on community integrity. Using Iowa as a case study, we generate and refine districting plans using KMeans clustering and stochastic rebalancing. Our method produces plans with fewer cut edges and more compact shapes than the official Iowa plan under relaxed conditions. The low likelihood of finding plans as disruptive as the official one suggests potential inefficiencies in existing boundaries. Gaussian Mixture Model analysis reveals three distinct distributions in the districting landscape. This framework offers a more accurate reflection of community interactions for fairer political representation.