Generalized Sequential Monte Carlo Sampling for Redistricting Simulation

TL;DR

This paper introduces a flexible generalized Sequential Monte Carlo (gSMC) algorithm for redistricting simulation, capable of handling multi-member districts and large-scale applications with improved efficiency and adaptability.

Contribution

The paper extends the SMC algorithm to support multi-member districts, various sampling spaces, and hybrid MCMC integration, enhancing redistricting analysis capabilities.

Findings

Effective sampling of multi-member districts demonstrated on Irish Parliament data.

Improved computational efficiency through optimal-variance incremental weights.

Successful application to large-scale redistricting with Pennsylvania data.

Abstract

Simulation methods have become important tools for quantifying partisan and racial bias in redistricting plans. We generalize the Sequential Monte Carlo (SMC) algorithm of McCartan and Imai (2023), one of the commonly used approaches. First, our generalized SMC (gSMC) algorithm can split off regions of arbitrary size, rather than a single district as in the original SMC framework, enabling the sampling of multi-member districts. Second, the gSMC algorithm can operate over various sampling spaces, providing additional computational flexibility. Third, we derive optimal-variance incremental weights and show how to compute them efficiently for each sampling space. Finally, we incorporate Markov chain Monte Carlo (MCMC) steps, creating a hybrid gSMC-MCMC algorithm that can be used for large-scale redistricting applications. We demonstrate the effectiveness of the proposed methodology through analyses of the Irish Parliament, which uses multi-member districts, and the Pennsylvania House of Representatives, which has more than 200 single-member districts.