Algorithmic Fingerprints in Redistricting Ensembles

Abstract

Ensemble analysis is a leading statistical tool for evaluating redistricting plans and detecting partisan gerrymandering. Modern algorithms can efficiently generate thousands of alternative plans under neutral criteria, establishing a baseline against which proposed or enacted maps can be compared. We investigate whether three sampling algorithms—Flip, ReCom, and SMC—leave detectable fingerprints in their respective ensembles, and whether those fingerprints affect the partisan conclusions drawn from them. We generated 10,000-plan ensembles for each algorithm under identical constraints in Pennsylvania, North Carolina, and Maryland, then trained random forest classifiers to predict the sampling method from each plan's spatial and partisan features. The classifiers achieved accuracies well above chance, showing that algorithmic fingerprints do exist. But those fingerprints were primarily spatial rather than partisan: feature ablation and SHAP analysis showed that compactness measures and cut edges carried the signal, while partisan metrics contributed negligibly. ReCom and SMC were indistinguishable on partisan metrics, and even Flip, despite targeting a wholly different distribution, produced similar partisan outcomes. Furthermore, all three sampling methods agreed on the outlier verdicts for enacted plans in each state from the 2010s redistricting cycle. Taken together, these results imply that the choice of sampling algorithm affects district geometry more than partisan verdicts, supporting confidence in the robustness of ensemble analysis.