Parameter Effects in ReCom Ensembles

TL;DR

The paper addresses how parameter choices in ReCom ensembles influence redistricting metrics by conducting a large-scale analysis across seven states and three chambers. It introduces convergence diagnostics based on effective sample-size estimates and ensemble redundancy to ensure robust statistics, then systematically varying population tolerance, county preservation strength, and algorithm variant. The main findings show that population tolerance has negligible impact, while the ReCom variant and county-preservation settings can significantly alter compactness, county splitting, partisan bias, minority opportunity, and competitiveness, with varying consistency across jurisdictions. The practical significance is that modeling choices can bias ensemble-based arguments in litigation and policy analysis, underscoring the need for careful parameter selection and robust convergence validation in redistricting studies.

Abstract

Ensemble analysis has become central to redistricting litigation, but parameter effects remain understudied. We analyze 315 ReCom ensembles across the three legislative chambers in 7 states, systematically varying the population tolerance, county preservation strength, and algorithm variant. To validate convergence, we introduce new methods to approximate effective sample size and measure redundancy. We find that varying the population tolerance has a negligible effect on all scores, whereas the algorithm and county-preservation parameters can significantly affect some metrics, inconsistently in some cases but surprisingly consistently in others across jurisdictions. These findings suggest parameter choices should be thoughtfully considered when using ReCom ensembles.

Figures (5)

• Figure 1: kde plots for multiple ReCom variants (to be described later) with respect to a compactness score (left) and a competitiveness score (right) in the lower legislative chamber of Wisconsin.
• Figure 2: Ordered seats plots for two ensembles of FL congressional plans.
• Figure 3: County splits vs cut edges for FL lower (with $k=120$ districts).
• Figure 4: Box and whisker plots for WI congress (with $k=8$ districts).
• Figure 5: Score orders: The position of an ensemble represents how many standard deviations is lies from ${\sf A}\xspace_0$ with respect to that score. Each cyan box shows the range $[-.033,.033]$; positions outside of the box are significantly different from ${\sf A}\xspace_0$ at $p$-value $\leq 0.001$.