Fairmandering: A column generation heuristic for fairness-optimized political districting

TL;DR

This paper introduces a scalable, flexible two-stage heuristic for political districting that explicitly optimizes for fairness, moving beyond traditional compactness-focused methods, and demonstrates its application on large ensemble studies.

Contribution

A novel two-stage column generation heuristic that explicitly optimizes for fairness in districting, allowing for flexible, scalable, and constraint-supporting solutions.

Findings

Produced an extensive ensemble of district plans demonstrating fairness outcomes.

Showed the method's flexibility to incorporate various fairness definitions.

Enabled analysis of the range of possible electoral outcomes.

Abstract

The American winner-take-all congressional district system empowers politicians to engineer electoral outcomes by manipulating district boundaries. Existing computational solutions mostly focus on drawing unbiased maps by ignoring political and demographic input, and instead simply optimize for compactness. We claim that this is a flawed approach because compactness and fairness are orthogonal qualities, and introduce a scalable two-stage method to explicitly optimize for arbitrary piecewise-linear definitions of fairness. The first stage is a randomized divide-and-conquer column generation heuristic which produces an exponential number of distinct district plans by exploiting the compositional structure of graph partitioning problems. This district ensemble forms the input to a master selection problem to choose the districts to include in the final plan. Our decoupled design allows for unprecedented flexibility in defining fairness-aligned objective functions. The pipeline is arbitrarily parallelizable, is flexible to support additional redistricting constraints, and can be applied to a wide array of other regionalization problems. In the largest ever ensemble study of congressional districts, we use our method to understand the range of possible expected outcomes and the implications of this range on potential definitions of fairness.