Browsing by Author "Herschlag, Gregory"

Now showing 1 - 8 of 8
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    A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans
    Carter, Daniel; Hunter, Zach; Herschlag, Gregory; Mattingly, Jonathan
    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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    Mathematically Quantifying Gerrymandering and the Non-responsiveness of the 2021 Georgia Congressional Districting Plan
    (2022-03-12) Zhao, Zhanzhan; Hettle, Cyrus; Gupta, Swati; Mattingly, Jonathan; Randall, Dana; Herschlag, Gregory
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    Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
    Autry, Eric A; Carter, Daniel; Herschlag, Gregory; Hunter, Zach; Mattingly, Jonathan C
    We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. 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 of elements which each correspond to a different district. The districts satisfy a collection of hard constraints and the measure may be weighted with regard to a number of other criteria. The multi-scale algorithm is similar to our previously developed Merge-Split proposal, however, this algorithm provides improved scaling properties and may also be used to preserve nested communities of interest such as counties and precincts. Both works use a proposal which extends the ReCom algorithm which leveraged spanning trees merge and split districts. In this work we extend the state space so that each district is defined by a hierarchy of trees. In this sense, the proposal step in both algorithms can be seen as a "Forest ReCom." We also expand the state space to include edges that link specified districts, which further improves the computational efficiency of our algorithm. The collection of plans sampled by the MCMC algorithm 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 of plans, the given plan may have been gerrymandered and is labeled as an outlier.
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    Non-reversible Markov chain Monte Carlo for sampling of districting maps
    Herschlag, Gregory; Mattingly, Jonathan C; Sachs, Matthias; Wyse, Evan
    Evaluating the degree of partisan districting (Gerrymandering) in a statistical framework typically requires an ensemble of districting plans which are drawn from a prescribed probability distribution that adheres to a realistic and non-partisan criteria. In this article we introduce novel non-reversible Markov chain Monte-Carlo (MCMC) methods for the sampling of such districting plans which have improved mixing properties in comparison to previously used (reversible) MCMC algorithms. In doing so we extend the current framework for construction of non-reversible Markov chains on discrete sampling spaces by considering a generalization of skew detailed balance. We provide a detailed description of the proposed algorithms and evaluate their performance in numerical experiments.
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    Optimal Legislative County Clustering in North Carolina
    (2019-11-22) Carter, Daniel; Zach, Hunter; Herschlag, Gregory; Mattingly, Jonathan
    North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate of the U.S. Supreme Court. Given that counties must be split, the North Carolina legislature and courts have provided guidelines that seek to reduce counties split across districts while also complying with the "one person, one vote" criteria. Under these guidelines, the counties are separated into clusters. The primary goal of this work is to develop, present, and publicly release an algorithm to optimally cluster counties according to the guidelines set by the court in 2015. We use this tool to investigate the optimality and uniqueness of the enacted clusters under the 2017 redistricting process. We verify that the enacted clusters are optimal, but find other optimal choices. We emphasize that the tool we provide lists all possible optimal county clusterings. We also explore the stability of clustering under changing statewide populations and project what the county clusters may look like in the next redistricting cycle beginning in 2020/2021.
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    Redistricting: Drawing the Line
    (2017-04-12) Bangia, Sachet; Graves, Christy Vaughn; Herschlag, Gregory; Kang, Han Sung; Luo, Justin; Mattingly, Jonathan C; Ravier, Robert
    We develop methods to evaluate whether a political districting accurately represents the will of the people. To explore and showcase our ideas, we concentrate on the congressional districts for the U.S. House of representatives and use the state of North Carolina and its redistrictings since the 2010 census. Using a Monte Carlo algorithm, we randomly generate over 24,000 redistrictings that are non-partisan and adhere to criteria from proposed legislation. Applying historical voting data to these random redistrictings, we find that the number of democratic and republican representatives elected varies drastically depending on how districts are drawn. Some results are more common, and we gain a clear range of expected election outcomes. Using the statistics of our generated redistrictings, we critique the particular congressional districtings used in the 2012 and 2016 NC elections as well as a districting proposed by a bipartisan redistricting commission. We find that the 2012 and 2016 districtings are highly atypical and not representative of the will of the people. On the other hand, our results indicate that a plan produced by a bipartisan panel of retired judges is highly typical and representative. Since our analyses are based on an ensemble of reasonable redistrictings of North Carolina, they provide a baseline for a given election which incorporates the geometry of the state's population distribution.
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    Segregation and Integration in Dallas County: What Do Demographic Differences Between Neighborhoods tell us About the Political Preference of those Neighborhoods?
    (2019-12-06) Odim, Onuoha
    How does environment affect how people decide to vote? If a person lives in a more diverse environment, does that change their fundamental political preference? This research uses both racial demographic information of voters in Dallas County and aggregate election results to draw a conclusion about the voting preference of individuals living within the county depending on the makeup of their precinct. Using 2010 census data to identify the demographic composition of every precinct in Dallas County, this research finds that the white population in the county is heavily concentrated in the north-central region, the black population in the south-central region, and the Hispanic population in the west-central region. Using Texas’ 2010 Gubernatorial Election results to identify the electoral outcome of every precinct in Dallas County, this research finds that the north-central region leans Republican, the south-central region leans heavily Democratic, and the west-central region leans slightly Democratic. Through measuring neighborhood level segregation and integration and comparing varying levels of demographic makeup in precincts with voting outcome, this research identifies the relationship between voting preference and the white, black and Hispanic populations. By investigating patterns of segregation in Dallas at both the precinct and county levels, this research finds that segregation polarizes voting preference. This research concludes that in Dallas, a small black population may polarize Hispanic voters to lean heavily Democratic in the absence of a white population.
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    The Signature of Gerrymandering in Rucho v. Common Cause
    (South Carolina Law Review, 2019) Chin, Andrew; Herschlag, Gregory; Mattingly, Jonathan