The topology of redistricting

Topological data analysis is a great tool for extracting insights from datasets with complicated structure (i.e. ones that are more than just a list of vectors). In this talk, we’ll show we can use TDA to analyze an ensemble of potential redistricting maps for a U.S. state, from both a geographic and political perspective. Ensembles of this kind have recently become the gold standard for detecting when individual maps are gerrymanders (unfair maps), both in the academic literature and in court cases. These ensembles can also tell us what a “typical map” looks like under various conditions, if analyzed correctly. We demonstrate how persistent homology can help us describe the effects of district size, electoral swing, and deliberate bias on political representation. This is joint work with Moon Duchin and Tom Needham.