Physics Theory Seminar with Daryl DeFord on Political Geometries: MCMC Sampling and Legislative Redistricting
The problem of constructing "fair" political districts and the related problem of detecting intentional gerrymandering has received a significant amount of attention in recent years. Analyzing these issues from a scientific perspective leads to a wide variety of research problems in geometry, graph theory, and probability. Given a partition of a state into a set of geographic units, such as census blocks or voting precincts, a districting plan becomes a labelled partition of the associated dual graph formed by connecting vertices representing adjacent units with the property that each induced subgraph is connected. This is abstractly similar to many spin glass problems and techniques from statistical physics have motivated much of the recent progress in this domain. In this talk, I will discuss recent work centered around Markov chain sampling of districting plans, including designing proposal distributions, evaluating the computational complexity of sampling, and measuring the geometric and partisan properties of districts. This work has also helped inform legislative reform efforts and appeared in court challenges, including cases in the Supreme Court this year, and I will discuss what it is like to translate theoretical research to these applied settings and some of the related data, computational, and communication challenges.
This lecture was made possible by the William C. Ferguson fund.