All Politics is Local: Redistricting via Local Fairness

TL;DR

This paper introduces the concept of local fairness for evaluating redistricting plans, proposing algorithms to audit and rank plans based on the presence of population-balanced, interest-majority regions, and demonstrates their effectiveness on real data.

Contribution

It formulates local fairness as a new criterion for redistricting plan evaluation, develops algorithms for auditing and ranking plans, and validates their effectiveness on real-world data.

Findings

Locally fair plans are achievable with minimal loss of traditional fairness metrics.

Auditing for local fairness is NP-complete, but practical algorithms are proposed.

Real-world data shows the existence of nearly or exactly locally fair plans.

Abstract

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans. Given a redistricting plan, a deviating group is a population-balanced contiguous region in which a majority of individuals are of the same interest and in the minority of their respective districts; such a set of individuals have a justified complaint with how the redistricting plan was drawn. A redistricting plan with no deviating groups is called locally fair. We show that the problem of auditing a given plan for local fairness is NP-complete. We present an MCMC approach for auditing as well as ranking redistricting plans. We also present a dynamic programming based algorithm for the auditing problem that we use to demonstrate the efficacy of our MCMC approach. Using these tools, we test local fairness on real-world election data, showing that it is indeed possible to find plans that are almost or exactly locally fair. Further, we show that such plans can be generated while sacrificing very little in terms of compactness and existing fairness measures such as competitiveness of the districts or seat shares of the plans.