The (homological) persistence of gerrymandering

We apply persistent homology, the dominant tool from field of topological data analysis, to study electoral redistricting. begin by combining geographic and a districting plan produce persistence diagram. Then, see beyond particular understand possibilities afforded choices made in redistricting, we build methods visualize analyze large ensembles alternative plans. Our detailed case studies use zero-dimensional homology (persistent components) filtered graphs constructed voting redistricting Pennsylvania North Carolina. find that, across partitions, features cluster diagrams way that corresponds strongly location, so can construct an average diagram for ensemble, with each point identified geographical region. Using this localization lets us zonings state at Congressional, Senate, House scales, show regional non-uniformity election shifts, identify attributes partitions tend correspond partisan advantage.The here are set up be broadly applicable TDA on data. Many will benefit interpretable summaries sets samples or simulations, work zoning readily generalize other partition problems, which abundant scientific applications. For mathematically politically rich problem particular, provides powerful elegant summarization whose findings useful practitioners.