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Abstract:
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Random sampling of graph partitions under constraints has become a popular tool for evaluating redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed plan with an ensemble of sampled alternative plans. For successful application, sampling methods must scale to large maps with many districts, incorporate realistic legal constraints, and accurately sample from a selected target distribution. Unfortunately, most existing methods struggle in at least one of these three areas. We present a new Sequential Monte Carlo algorithm that draws representative redistricting plans from a realistic target distribution of choice. Because it yields nearly independent samples, the SMC algorithm can more efficiently explore the relevant space of redistricting plans than existing MCMC algorithms. Our algorithm can simultaneously incorporate several constraints commonly imposed in real-world redistricting problems, including equal population, compactness, and preservation of administrative boundaries. We apply the SMC algorithm to evaluate the partisan implications of several maps submitted by parties to a recent high-profile redistricting case in Pennsylvania.
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