Mathematically Quantifying Non-responsiveness of the 2021 Georgia Congressional Districting Plan

TL;DR

This paper introduces a computationally efficient method combining parallel tempering and ReCom to sample redistricting plans, demonstrating its effectiveness on Georgia's district maps and revealing significant non-responsiveness in the enacted plan.

Contribution

It develops and validates a novel parallel tempering algorithm for policy-informed redistricting sampling at statewide scale.

Findings

The Georgia district plan reliably elects 9 Republicans and 5 Democrats regardless of public opinion shifts.

Only 0.12% of sampled plans show similar non-responsiveness as the enacted plan.

The method effectively addresses computational challenges in sampling complex redistricting distributions.

Abstract

To audit political district maps for partisan gerrymandering, one may determine a baseline for the expected distribution of partisan outcomes by sampling an ensemble of maps. One approach to sampling is to use redistricting policy as a guide to precisely codify preferences between maps. Such preferences give rise to a probability distribution on the space of redistricting plans, and Metropolis-Hastings methods allow one to sample ensembles of maps from the specified distribution. Although these approaches have nice theoretical properties and have successfully detected gerrymandering in legal settings, sampling from commonly-used policy-driven distributions is often computationally difficult. As of yet, there is no algorithm that can be used off-the-shelf for checking maps under generic redistricting criteria. In this work, we mitigate the computational challenges in a Metropolized-sampling technique through a parallel tempering method combined with ReCom[12] and, for the first time, validate that such techniques are effective on these problems at the scale of statewide precinct graphs for more policy informed measures. We develop these improvements through the first case study of district plans in Georgia. Our analysis projects that any election in Georgia will reliably elect 9 Republicans and 5 Democrats under the enacted plan. This result is largely fixed even as public opinion shifts toward either party and the partisan outcome of the enacted plan does not respond to the will of the people. Only 0.12% of the $\sim$160K plans in our ensemble were similarly non-responsive.