Physics Colloquium - Computational Challenges in Quantifying Gerrymandering

The US political system is built on representatives chosen by geographically localized regions. This presents the government with the problem of designing these districts. Every ten years, the US census counts the population, and new political districts must be drawn. The practice of harnessing this administrative process for partisan political gain is often referred to as gerrymandering. How does one identify and understand gerrymandering? Can we really recognize gerrymandering when we see it? If one party wins over 50% of the vote, is it fair that it wins less than 50% of the seats? What do we mean by fair? Should we expect proportional representation? How can math help illuminate these questions? How does the geopolitical geometry of the state (where which groups live and the shape of the state) inform these answers? Our ability to answer these questions is still a work in progress and presents many interesting mathematical research questions. Topics include ideas from computation, statistic/statistical physics, combinatorics, high-dimensional probability, Markov Chain theory, and modern data science. The story thus far has been an interaction between lawyers, mathematicians, computational scientists, and policy advocates. The legal discussion has been increasingly informed by the mathematical framework. And the mathematics has been pushed to be better included in the policy considerations. This back and forth has been important to finding ways to effectively inform the policymakers and courts. The problem of understanding gerrymandering has also prompted the development of a number of new computational algorithms that come with new mathematical questions. There are strong connections to statistical mechanics, computational statistics, and ideas from Markov Chain Monte Carlo such as Parallel Tempering and the Swendsen-Wang/Wolff algorithm. The next round of redistricting analysis will necessarily need to be more refined and nuanced. There is also the opportunity to be less reactive. There are opportunities to try to influence the process by which new maps are drawn before turning to the courts. There is also the possibility to direct the conversation by showing the effect more fully, considering factors such as communities of interest, incumbency, or proposed procedural elements of laws. For me, these questions began with an undergraduate research program project in 2013 and have led me to testify in a number of cases that went to supreme court.