Methodology in brief. Each county is a single node on a national adjacency graph of ~3,300 nodes; counties whose population exceeds ~25% of their state's per-district target (with a 200K floor) are slab-subdivided into fragments small enough (each ≤ 0.12 × target) for the chain to balance against. Adjacency is derived from shared topojson arcs (real land borders) plus manual water-gap bridges (Mackinac, Verrazzano, the Eastern Shore VA bay-bridge-tunnel, RI Newport, San Juan Islands, Hawaii inter-island, NYC borough crossings). Vote totals are official county-level two-party presidential returns for 2000, 2004, 2008, 2012, 2016, 2020, and 2024, sourced from the MIT Election Data and Science Lab county- returns dataset via the stiles/presidential-elections compilation (2000–2012) and the tonmcg/US_County_Level_Election_Results_08-24 tabulation (2016/2020/2024). Populations come from the Census Bureau's 2021 vintage of county-level estimates (preserves pre-CT-planning- region county geography to match the topojson). For counties subdivided into fragments, each fragment inherits the parent county's per-capita partisan rate (uniform dispersion within a county is an approximation; precinct-level data would refine this). Midterm House years (2006/2010/2014/2018/2022) are not included — U.S. House results are tabulated by congressional district, not county, so no unified national county-level dataset exists.
The districting algorithm is ReCom — the recombination Markov chain over balanced k-partitions of the adjacency graph (DeFord, Duchin, Solomon 2021). Each state runs independently from a recursive-spanning-tree-bisection initial partition, with a dynamic burn-in (scaling with seat count, 120–400 ReCom moves) under graduated tolerance, followed by a greedy boundary-unit polish phase wrapped in a perturb-and-repolish loop, up to 10 retries from independent seeds (kept best-of), and a graph-isoperimetric compactness gate on every accepted cut. The compactness threshold relaxes deterministically on later retries to preserve Markov-chain ergodicity. After the county-level pass, every state still over ±5% is automatically upgraded to tract-level partitioning: the state's 2020-Decennial tracts (~3,500 people each) become the units, ReCom runs on that tract graph until ±1% balance is achieved, and the tract assignments are projected back to county fragments by bbox containment for rendering. The variance metric shown in the headline reflects the underlying tract-level balance, not the projection. As a result the dashboard consistently delivers 44/44 states inside ±5% on default settings.
Tract-level partisanship is modeled, not measured. No federal authority publishes precinct-to-tract election crosswalks, so tract D-shares cannot be directly observed. The dashboard's previous version disaggregated county votes uniformly across tracts — losing all within-county urban/rural variation. We now apply a population- density partisanship model: each tract's D-share is shifted from the county average by 0.45 × log(tract_density / county_median_density) in logit space, then rescaled per (county, year) so that the sum of tract D-votes and R-votes exactly matches the official county totals. This adds the strongest non-racial geographic predictor of partisanship — population density — to the within-county picture, while preserving the county-level truth. Empirically the coefficient 0.45 matches the lower end of national multilevel-model estimates from Rodden, Chen, and the post-2016 partisan-geography literature. Future extensions (race, ethnicity, education) require ACS table fetches via the Census API and a build-time pipeline; the framework is in place.
Calibration sources: stiles/presidential-elections (2000–2024 county-level, processed JSON of MIT EDSL data); tonmcg/US_County_Level_Election_Results_08-24 (2016/2020/2024 presidential by county); US Census Bureau co-est2021-alldata (county populations); 2020 Decennial Census P1 totals (tract populations); us-atlas v3 counties-albers-10m (TopoJSON, Albers USA projection from Census 2017 cartographic boundary files); MGGG redistricting lab on ReCom (DeFord, Duchin, Solomon 2021, "Recombination: A Family of Markov Chains for Redistricting").
