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Mathematics Colloquium

Duke University

Title: Quantifying Gerrymandering: Separating Natural Bias from Partisan Bias in Redistricting
Date: Friday, March 1, 2019
Place and Time: Room 101, Love Building, 3:35-4:25 pm
Refreshments: Room 204, Love Building, 3:00 pm

Abstract. Gerrymandering changes the outcome of an election; but what would have happened in the election had no gerrymandering occurred? My research group seeks to answer this question using Markov Chain Monte Carlo algorithms that sample the space of district plans. In sampling this space, we generate an ensemble made of thousands of a-political district plans that comply with traditional redistricting criteria. When the ensemble is combined with historical election data, we reveal a range of typical election outcomes. We then compare the ensemble's typical range with an enacted plan to determine whether the enacted plan is an extreme outlier and therefore a partisan gerrymander.

There are three principle challenges of this work: (1) to develop redistricting criteria, (2) to sample the space of redistricting plans that meet this criteria, and (3) analyze the ensemble of sampled plans. Although the first challenge is primarily a legal and political challenge, the latter two challenges provide a rich environment for applied mathematics that I will discuss in this talk.

This approach is being used in several court cases. Most prominently, it comprises part of the evidence in Common Cause v Rucho, a federal case challenging the constitutionality of the North Carolina Congressional district plan. This case will be heard in the United States Supreme Court in late March, where the ideas behind this approach will be tested in a legal setting.