Mathematics Colloquium
Computational Challenges in Redistricting
Speaker: Jonathan Mattingly, Duke University
Location: Warren Weaver Hall 1302
Date: Monday, November 11, 2024, 3:45 p.m.
Synopsis:
The U.S. political system is built on representatives elected from geographically defined regions, creating the need for designing these districts. Every ten years, following the U.S. Census, new political districts must be drawn. When this redistricting process is manipulated for partisan advantage, it’s known as gerrymandering.
But how can we identify and understand gerrymandering? Can it always be recognized when it happens? If one party receives over 50% of the vote, is it fair if it wins less than 50% of the seats? What exactly do we mean by “fair”? And how can mathematics help answer these questions? How does the geography of a state—where various groups live and the shape of the state itself—inform these answers?
Our ability to tackle these questions is still evolving, presenting fascinating mathematical research opportunities. These topics draw on areas like computational statistics, statistical physics, combinatorics, high-dimensional probability, Markov Chain theory, and modern data science.
So far, this work has been a collaboration between lawyers, mathematicians, computational scientists, and policy advocates. Legal debates are increasingly shaped by mathematical frameworks, while the mathematical approaches are refined to incorporate policy considerations. This exchange has been vital in effectively informing policymakers and the courts. The challenge of understanding gerrymandering has also spurred the creation of new computational algorithms, which, in turn, raise further mathematical questions. The next wave of redistricting analysis will need to be even more sophisticated, employing advanced sampling and mathematical modeling methods inspired by computational chemistry, Bayesian sampling, and computational statistical mechanics.
There’s also an opportunity to be proactive. Instead of waiting to respond in court, there’s a chance to influence the initial redistricting process. We can shape the discussion by examining the impact of factors like communities of interest, incumbency, or proposed procedural changes to redistricting laws.
For me, these questions began with an undergraduate research project in 2013 and have since led me to testify in several court cases, including Common Cause v. Rucho (which reached the U.S. Supreme Court), Common Cause v. Lewis, Harper v. Lewis, and Harper v. Hall/Moore. Related concepts have been central in numerous cases, with computational scientists providing key testimony.