Optimizing Districting Plans to Maximize Majority-Minority Districts via IPs and Local Search

TL;DR

This paper introduces an integer programming approach with local search and compactness enhancements to optimize districting plans for maximizing majority-minority districts, outperforming previous heuristic methods.

Contribution

It presents a novel integer programming method with column generation and local re-optimization to improve majority-minority district counts in statewide plans.

Findings

Outperforms heuristic methods in generating more majority-minority districts

Achieves higher district compactness without reducing minority representation

Demonstrates effectiveness across multiple data sets

Abstract

In redistricting litigation, effective enforcement of the Voting Rights Act has often involved providing the court with districting plans that display a larger number of majority-minority districts than the current proposal (as was true, for example, in what followed Allen v. Milligan concerning the congressional districting plan for Alabama in 2023). Recent work by Cannon et al. proposed a heuristic algorithm for generating plans to optimize majority-minority districts, which they called short bursts; that algorithm relies on a sophisticated random walk over the space of all plans, transitioning in bursts, where the initial plan for each burst is the most successful plan from the previous burst. We propose a method based on integer programming, where we build upon another previous work, the stochastic hierarchical partitioning algorithm, which heuristically generates a robust set of potential districts (viewed as columns in a standard set partitioning formulation); that approach was designed to optimize a different notion of fairness across a statewide plan. We design a new column generation algorithm to find plans via integer programming that outperforms short bursts on multiple data sets in generating statewide plans with significantly more majority-minority districts. These results also rely on a new local re-optimization algorithm to iteratively improve on any baseline solution, as well as an algorithm to increase the compactness of districts in plans generated (without impacting the number of majority-minority districts).