Generalized Sequential Monte Carlo Sampling for Redistricting Simulation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915883804262400 |
|---|---|
| author | O'Sullivan, Philip Imai, Kosuke McCartan, Cory |
| author_facet | O'Sullivan, Philip Imai, Kosuke McCartan, Cory |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Sequential Monte Carlo Sampling for Redistricting Simulation O'Sullivan, Philip Imai, Kosuke McCartan, Cory Applications Computers and Society Probability 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. |
| title | Generalized Sequential Monte Carlo Sampling for Redistricting Simulation |
| topic | Applications Computers and Society Probability |
| url | https://arxiv.org/abs/2603.22188 |