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To audit political district maps for partisan gerrymandering, one maydetermine a baseline for the expected distribution of partisan outcomes bysampling an ensemble of maps. One approach to sampling is to use redistrictingpolicy as a guide to precisely codify preferences between maps. Suchpreferences give rise to a probability distribution on the space ofredistricting plans, and Metropolis-Hastings methods allow one to sampleensembles of maps from the specified distribution. Although these approacheshave nice theoretical properties and have successfully detected gerrymanderingin legal settings, sampling from commonly-used policy-driven distributions isoften computationally difficult. As of yet, there is no algorithm that can beused off-the-shelf for checking maps under generic redistricting criteria. Inthis work, we mitigate the computational challenges in a Metropolized-samplingtechnique through a parallel tempering method combined with ReCom[12] and, forthe first time, validate that such techniques are effective on these problemsat the scale of statewide precinct graphs for more policy informed measures. Wedevelop these improvements through the first case study of district plans inGeorgia. Our analysis projects that any election in Georgia will reliably elect9 Republicans and 5 Democrats under the enacted plan. This result is largelyfixed even as public opinion shifts toward either party and the partisanoutcome of the enacted plan does not respond to the will of the people. Only0.12% of the $\sim$160K plans in our ensemble were similarly non-responsive.

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