A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans
Abstract
We describe a Markov chain on redistricting plans that makes relatively global moves. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing a graph into a partition with a specified number elements which each correspond to a different district. The partitions satisfy a collection of hard constraints and the measure may be weighted with regard to a number of other criteria. When these constraints and criteria are chosen to align well with classical legal redistricting criteria, the algorithm can be used to generate a collection of non-partisan, neutral plans. This collection of plans can serve as a baseline against which a particular plan of interest is compared. If a given plan has different racial or partisan qualities than what is typical of the collection plans, the given plan may have been gerrymandered and is labeled as an outlier.
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Scholars@Duke
Gregory Joseph Herschlag
I am interested in studying techniques to understand fairness in redistricting. I am also interested in computational fluid dynamics and high-performance computing.
Jonathan Christopher Mattingly
Jonathan Christopher Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day. He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.
His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.
Since 2013 he has also been working to understand and quantify gerrymandering and its interaction of a region's geopolitical landscape. This has lead him to testify in a number of court cases including in North Carolina, which led to the NC congressional and both NC legislative maps being deemed unconstitutional and replaced for the 2020 elections.
He is the recipient of a Sloan Fellowship and a PECASE CAREER award. He is also a fellow of the IMS and the AMS. He was awarded the Defender of Freedom award by Common Cause for his work on Quantifying Gerrymandering.
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