The legal standard set in Rucho v Common Cause puts the onus on the plaintiffs in a Voting Rights Act (VRA) case to demonstrate that a map is a racial rather than a partisan gerrymander in order for it to be struck down as unlawful. This means plaintiffs have to 'do the homework' of the defendants for them: they must produce a map that is at least as politically gerrymandered as the defendants drew, while achieving better racial representation outcomes. In this talk I will describe how Markov Chain Monte Carlo (MCMC) methods are typically used to solve these problems, and use this opportunity to describe the underlying mathematics.
The Mathematics of Redistricting