{"ID":22952692,"CreatedAt":"2026-09-17T02:12:05.498442134Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18741","arxiv_id":"2609.18741","title":"Towards stratified sampling for redistricting plans","abstract":"Rapid algorithmic developments have accelerated the sampling of redistricting ensembles (balanced graph partitions), yet evaluating rare events and sampling complex target measures remains a core challenge due to the high-dimensional and combinatorial nature of the phase space. We address a prerequisite for stratified sampling on this space: constructing and diagnosing candidate strata with suitable coverage and overlap. We build a grammar on observed plans by clustering districts into representative ``letters'' and using them to form plan-level ``words.'' A partition of unity over these words gives a soft assignment of plans to strata and allows us to estimate stratum masses and an overlap-induced flux matrix. We demonstrate this computational pipeline using real-world congressional redistricting data from Connecticut and examine how strata learned from one target distribution behave under related distributions. The resulting construction provides a foundation for future stratified sampling on spaces of redistricting plans or balanced graph partitions. We do not implement a complete stratified sampler here; evaluating whether the proposed strata improve sampling efficiency or reduce estimator variance is left for future work.","short_abstract":"Rapid algorithmic developments have accelerated the sampling of redistricting ensembles (balanced graph partitions), yet evaluating rare events and sampling complex target measures remains a core challenge due to the high-dimensional and combinatorial nature of the phase space. We address a prerequisite for stratified...","url_abs":"https://arxiv.org/abs/2609.18741","url_pdf":"https://arxiv.org/pdf/2609.18741v1","authors":"[\"Zijian Wang\",\"Gregory J. Herschlag\",\"Joon-Hyeok Yim\",\"Jonathan C. Mattingly\",\"Anna C. Gilbert\"]","published":"2026-09-16T14:38:27Z","proceeding":"physics.soc-ph","tasks":"[\"physics.soc-ph\",\"cs.CY\",\"math.PR\"]","methods":"[]","has_code":false}