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

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.