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

2025-08-10

AI Summary

This study addresses the underrepresentation of minority groups in electoral districts under the Voting Rights Act. Method: We propose an integer programming–based column generation algorithm that integrates local re-optimization and a compactness-enhancement mechanism to maximize the number of minority-majority districts. Unlike conventional heuristics, our approach systematically combines randomized stratified district initialization, exact column generation, and geography-driven local search—ensuring both contiguity and compactness. Contribution/Results: Experiments on real statewide datasets demonstrate that our method increases the number of minority-majority districts by 12.6%–28.3% on average across full-state redistricting plans, while achieving superior compactness metrics compared to state-of-the-art baselines. The framework provides a verifiable, scalable optimization paradigm for equitable redistricting.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Humans and AI: Voting

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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).

Problem

• Optimizing districting plans to maximize majority-minority districts
• Improving fairness in redistricting via integer programming
• Enhancing compactness of districts without reducing minority representation

Innovation

• Integer programming for districting optimization
• New column generation algorithm
• Local re-optimization for solution improvement