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Evaluating the degree of partisan districting (Gerrymandering) in astatistical framework typically requires an ensemble of districting plans whichare drawn from a prescribed probability distribution that adheres to arealistic and non-partisan criteria. In this article we introduce novelnon-reversible Markov chain Monte-Carlo (MCMC) methods for the sampling of suchdistricting plans which have improved mixing properties in comparison topreviously used (reversible) MCMC algorithms. In doing so we extend the currentframework for construction of non-reversible Markov chains on discrete samplingspaces by considering a generalization of skew detailed balance. We provide adetailed description of the proposed algorithms and evaluate their performancein numerical experiments.

Non-reversible Markov chain Monte Carlo for sampling of districting maps