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Lattice Studies of Gerrymandering Strategies

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  • Kyle Gatesman
  • James Unwin

Abstract

We propose three novel gerrymandering algorithms which incorporate the spatial distribution of voters with the aim of constructing gerrymandered, equal-population, connected districts. Moreover, we develop lattice models of voter distributions, based on analogies to electrostatic potentials, in order to compare different gerrymandering strategies. Due to the probabilistic population fluctuations inherent to our voter models, Monte Carlo methods can be applied to the districts constructed via our gerrymandering algorithms. Through Monte Carlo studies we quantify the effectiveness of each of our gerrymandering algorithms and we also argue that gerrymandering strategies which do not include spatial data lead to (legally prohibited) highly disconnected districts. Of the three algorithms we propose, two are based on different strategies for packing opposition voters, and the third is a new approach to algorithmic gerrymandering based on genetic algorithms, which automatically guarantees that all districts are connected. Furthermore, we use our lattice voter model to examine the effectiveness of isoperimetric quotient tests and our results provide further quantitative support for implementing compactness tests in real-world political redistricting.

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  • Kyle Gatesman & James Unwin, 2018. "Lattice Studies of Gerrymandering Strategies," Papers 1808.02826, arXiv.org.
  • Handle: RePEc:arx:papers:1808.02826
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    File URL: http://arxiv.org/pdf/1808.02826
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    1. Chambers, Christopher P. & Miller, Alan D., 2010. "A Measure of Bizarreness," Quarterly Journal of Political Science, now publishers, vol. 5(1), pages 27-44, April.
    2. Puppe, Clemens & Tasnádi, Attila, 2009. "Optimal redistricting under geographical constraints: Why "pack and crack" does not work," Economics Letters, Elsevier, vol. 105(1), pages 93-96, October.
    3. Katerina Sherstyuk, 1998. "How to gerrymander: A formal analysis," Public Choice, Springer, vol. 95(1), pages 27-49, April.
    4. Altman, Micah & McDonald, Michael P., 2011. "BARD: Better Automated Redistricting," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i04).
    5. John N. Friedman & Richard T. Holden, 2008. "Optimal Gerrymandering: Sometimes Pack, but Never Crack," American Economic Review, American Economic Association, vol. 98(1), pages 113-144, March.
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