Quantifying Gerrymandering: Advances in Sampling Graph Partitions (Gregory Herschlag -- Duke)

Gerrymandering is the process of manipulating political districts either to amplify the power of a political group or suppress the representation of certain demographic groups. Although we have seen increasingly precise and effective gerrymanders, a number of mathematicians, political scientists, and lawyers are developing effective methodologies at uncovering and understanding the intent and effects of gerrymandered districts. The basic idea behind these methods is to compare a given set of districts to a large collection of neutrally drawn plans. The process relies on three distinct components: First, we determine rules for compliant redistricting plans along with codifying preferences between these plans; next, we sample the space of compliant redistricting plans (according to our preferences) and generate a large collection of non-partisan alternatives; finally, we compare the collection of plans to a particular plan of interest. The first step, though largely a legal question of compliance, provides interesting grounds for mathematical translation between policies and probability measures; the second and third points create rich problems in the fields of applied mathematics (sampling theory) and data analysis, respectively. In this talk, I will discuss how our research group at Duke has analyzed gerrymandering. I will discuss the sampling methods we employ and discuss several recent algorithmic advances. I will also mention several open problems and challenges in this field. These sampling methods provide rich grounds both for mathematical exploration and development and also as a practical and relevant algorithm.