Generalized Sequential Monte Carlo Sampling for Redistricting Simulation
This work addresses computational challenges in redistricting simulation for political and legal analysis, but it is incremental as it builds on an existing method.
The authors tackled the problem of simulating redistricting plans for quantifying bias by generalizing a Sequential Monte Carlo algorithm to handle multi-member districts and various sampling spaces, resulting in a hybrid algorithm demonstrated on the Irish Parliament and Pennsylvania House of Representatives.
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.