Methods used to Analyze 2020 North Carolina State Legislative Redistricting Landscape

We place probability distributions on redistricting plans of the state of North Carolina. The distributions embody different policy choices. With each distribution, we produce representative ensembles of maps to serve as benchmarks against which to compare specific maps. The ensembles are generated by using the Metropolis-Hasting Markov Chain Monte Carlo Algoritm in a parallel tempering framework which employees proposal from the multiscale forest RECOM algorithm [1, 2] and the single-node flip algorithm [3]. In our analysis, we use historical elections to help situate the behavior of our ensemble under a number of political climates, we do not use any political data in developing our distribution; and hence, the ensemble generated from it. We produce collections of histograms, showing the typical seats awarded to each party under our distribution and a number of different political climates. We also produce rank ordered boxplots which show the typical partisan make up of the collection of districts, again under the variety of election climates embodied in different historical votes. These figures and analyses for the North Carolina State House and Senate are included in a companion document. Here we give an overview of the methods used. A more complete description of our methods will be provided in later reports.