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Voting Rights, Markov Chains, and Optimization by Short Bursts

Author

Listed:
  • Sarah Cannon

    (Claremont McKenna College)

  • Ari Goldbloom-Helzner

    (Brown University)

  • Varun Gupta

    (University of Pennsylvania)

  • JN Matthews

    (University of Chicago)

  • Bhushan Suwal

    (Boston University)

Abstract

Finding outlying elementsin probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider the problem of maximizing the number of simultaneous majority-minority districts in a political districting plan. An unbiased random walk on districting plans is unlikely to find plans that approach this maximum. A common search approach is to use a biased random walk: preferentially select districting plans with more majority-minority districts. Here, we present a third option, called short bursts, in which an unbiased random walk is performed for a small number of steps (called the burst length), then re-started from the most extreme plan that was encountered in the last burst. We give empirical evidence that short-burst runs outperform biased random walks for the problem of maximizing the number of majority-minority districts, and that there are many values of burst length for which we see this improvement. Abstracting from our use case, we also consider short bursts where the underlying state space is a line with various probability distributions, and then explore some features of more complicated state spaces and how these impact the effectiveness of short bursts.

Suggested Citation

  • Sarah Cannon & Ari Goldbloom-Helzner & Varun Gupta & JN Matthews & Bhushan Suwal, 2023. "Voting Rights, Markov Chains, and Optimization by Short Bursts," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-38, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09994-1
    DOI: 10.1007/s11009-023-09994-1
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    References listed on IDEAS

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    1. Daryl DeFord & Moon Duchin & Justin Solomon, 2020. "A Computational Approach to Measuring Vote Elasticity and Competitiveness," Statistics and Public Policy, Taylor & Francis Journals, vol. 7(1), pages 69-86, January.
    2. Sophia Caldera & Daryl DeFord & Moon Duchin & Samuel C. Gutekunst & Cara Nix, 2020. "Mathematics of Nested Districts: The Case of Alaska," Statistics and Public Policy, Taylor & Francis Journals, vol. 7(1), pages 39-51, January.
    3. Maria Chikina & Alan Frieze & Jonathan C. Mattingly & Wesley Pegden, 2020. "Separating Effect From Significance in Markov Chain Tests," Statistics and Public Policy, Taylor & Francis Journals, vol. 7(1), pages 101-114, January.
    4. Gregory Herschlag & Han Sung Kang & Justin Luo & Christy Vaughn Graves & Sachet Bangia & Robert Ravier & Jonathan C. Mattingly, 2020. "Quantifying Gerrymandering in North Carolina," Statistics and Public Policy, Taylor & Francis Journals, vol. 7(1), pages 30-38, January.
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