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Lattice Studies of Gerrymandering Strategies

Published online by Cambridge University Press:  11 November 2020

Kyle Gatesman  and
James Unwin Open the ORCID record for James Unwin [Opens in a new window]
Kyle Gatesman
Affiliation:
Johns Hopkins University, Baltimore, MD21218USA. Email: kgatsm1@jhu.edu
James Unwin*
Affiliation:
University of Illinois at Chicago, Chicago, IL60607, USA. Email: unwin@uic.edu Simons Center for Geometry and Physics, Stony Brook, NY11794, USA
*
Corresponding author James Unwin
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Abstract

A new theoretical method for examining gerrymandering is presented based on lattice models of voters, in which districts are constructed by partitioning the lattice. We propose three novel algorithms for constructing equal-population, connected districts which favor the gerrymanderer and incorporate the spatial distribution of voters. Due to the probabilistic population fluctuations inherent to our voter models, Monte Carlo techniques can be applied to study the impact of gerrymandering. We use the method developed here to compare our different gerrymandering algorithms, show approaches which ignore spatial data lead to (legally prohibited) disconnected districts, and examine the effectiveness of isoperimetric quotient tests.

Keywords

spatial voting modelMonte Carlo methodslattices
Type
Article
Information
Political Analysis , Volume 29 , Issue 2 , April 2021 , pp. 167 - 192
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of the Society for Political Methodology

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Footnotes

Edited by Jeff Gill

References

Altman, M. 1998. “Modelling the Effect of Mandatory District Compactness on Partisan Gerrymanders .” Political Geography 17(8):989–1012.CrossRefGoogle Scholar
Altman, M. and McDonald, M. 2011. “BARD: Better Automated Redistricting.” Journal of Statistical Software 42(2011):4.CrossRefGoogle Scholar
Apollonioa, N. et al. 2009. “Bicolored Graph Partitioning, or: Gerrymandering at its Worst.” Discrete Applied Mathematics 157 17:3601.CrossRefGoogle Scholar
Bacao, F., Lobo, V., and Painho, M.. 2005. “Applying Genetic Algorithms to Zone Design .” Soft Computing 9(5):341–348.CrossRefGoogle Scholar
Benisek v. Lamone, 585 U.S.(2018).Google Scholar
Bium, H. 1964. A Transformation for Extracting New Descriptions of Shape, Symposium on Models for the Perception of Speech and Visual Form. Cambridge, MA: MIT Press.Google Scholar
Bowen, D. C. 2014. “Boundaries, Redistricting Criteria, and Representation in the US House of Representatives.” American Politics Research 42(5):856–895.CrossRefGoogle Scholar
Brownstein, R. 2018. “(CNN) Republicans and Democrats Increasingly Really Do Occupy Different Worlds.” CNN, June 12. www.cnn.com/2018/06/12/politics/republicans-democrats-different-worlds/index.html.Google Scholar
Castellano, C., Santo, F., and Vittorio, L.. 2009. “Statistical Physics of Social Dynamics.” Reviews of Modern Physics 81(2): 591.CrossRefGoogle Scholar
Chambers, C. P. and Miller, A. D. 2010. “A Measure of Bizarreness.” Quarterly Journal of Political Science 5(1):27–44.CrossRefGoogle Scholar
Chou, C. et al. 2014. “On Empirical Validation of Compactness Measures for Electoral Redistricting and its Significance for Application of Models in the Social Sciences .” Social Science Computer Review 32(4):534–543.Google Scholar
Chou, C.-I., Chu, Y., and Li, S.-P.. 2007. “Evolutionary Strategy for Political Districting Problem using Genetic Algorithm.” In International Conference on Computational Science. Berlin, Germany: Springer.Google Scholar
Chou, C.-I., and Li, S.-P. 2006. “Taming the Gerrymander: Statistical Physics Approach to Political Districting Problem .” Physica A 369(2):799–808.Google Scholar
Duchin, M. 2018. “Gerrymandering Metrics: How to Measure? What’s the Baseline?” arXiv:1801.02064.Google Scholar
Fifield, B. et al. 2015. A New Automated Redistricting Simulator Using Markov Chain Monte Carlo.Princeton, NJ: Princeton University.Google Scholar
Forman, S. L., and Yue, Y. 2003. “Congressional Districting Using a TSP-Based Genetic Algorithm.” In Genetic and Evolutionary Computation Conference. Berlin, Germany: Springer.Google Scholar
Friedman, J. N. and Holden, R. T. 2008. “Optimal Gerrymandering: Sometimes Pack, But Never Crack.” American Economic Review 98(1):113–144.Google Scholar
Gatesman, K., and Unwin, J. 2019. “Replication Data for Lattice Studies of Gerrymandering Strategies.” https://doi.org/10.7910/DVN/OP6EVF, Harvard Dataverse, V1.Google Scholar
Gill v. Whitford, 585 U.S.(2018).Google Scholar
Glassner, A. S., 2013. Graphics Gems. Cambridge, MA: Academic Press.Google Scholar
Herschlag, G., Ravier, R., and Mattingly, J. C.. 2017. “Evaluating Partisan Gerrymandering in Wisconsin.” arXiv:1709.01596.Google Scholar
Herschlag, G. et al. 2018. “Quantifying Gerrymandering in North Carolina.” arXiv:1801.03783Google Scholar
Hoare, C. A. R. 1961. “Algorithm 64: Quicksort.” Communications of the ACM 4(7):321.Google Scholar
Hodge, J., Marshall, E. and Patterson, G. 2010. “Gerrymandering and Convexity.” The College Mathematics Journal 41 4:312–324.CrossRefGoogle Scholar
Humphreys, M. 2011. “Can Compactness Constrain the Gerrymander? ” Irish Political Studies 26(4):513–520.Google Scholar
Macal, C. M., and North, M. J. 2005. “Tutorial on Agent-Based Modeling and Simulation.” In Proceedings of the Winter Simulation Conference. IEEE.CrossRefGoogle Scholar
Miller v. Johnson, 515 U.S. 900 (1995).CrossRefGoogle Scholar
Niemi, R. G., Groffman, B., Calucci, C., and Hofeller, T.. 1990. “Measuring Compactness and the Role of Compactness Standard in a Test for Partisan and Racial Gerrymandering.” Journal of Politics 52:1155.CrossRefGoogle Scholar
Oxtoby, J. 1977. “Diameters of Arcs and the Gerrymandering Problem.” The American Mathematical Monthly 84 3:155–162.CrossRefGoogle Scholar
Politicalmaps.org 2016. “What One Swing State Can Teach Us about Political Polarization in America.” Politicalmaps.org, November 6. http://politicalmaps.org/what-one-swing-state-can-teach-us-about-political-polarization-in-america/.Google Scholar
Polsby, D. and Popper, R. 1991. “The Third Criterion: Compactness as a Procedural Safeguard Against Partisan Gerrymandering.” Yale Law and Policy Review 9:301.Google Scholar
Puppe, C. and Tasnadi, A. 2009. “Optimal Redistricting Under Geographical Constraints: Why ‘Pack and Crack’ Does not Work .” Economics Letters 105(1):93.Google Scholar
Puppe, C. and Tasnadi, A. 2015. “Axiomatic Districting.” Social Choice and Welfare 44(1):31.Google Scholar
Roeck, E. C. Jr. 1961. “Measuring the Compactness as a Requirement of Legislative Apportionment.” Midwest Journal of Political Science 5:70–74.CrossRefGoogle Scholar
Schwartzberg, J. E. 1966. “Reapportionment, Gerrymanders, and the Notion of Compactness.” Minnesota Law Review 50:443–452.Google Scholar
Shaw v. Reno, 509 U.S. 630 (1993).Google Scholar
Sherstyuk, K. 1998. “How to Gerrymander: A Formal Analysis.” Public Choice 95:27.Google Scholar
Shiffman, D. 2012. The Nature of Code: Simulating Natural Systems with Processing. Magic Book Project.Google Scholar
Smith, A. R. 1979. “Tint Fill.” In Proceedings of the 6th Annual Conference on Computer Graphics and Interactive Techniques, pp. 276–283. Association for Computing Machinery.CrossRefGoogle Scholar
Vanneschi, L., Henriques, R., and Castelli, M.. 2017. “Multi-Objective Genetic Algorithm with Variable Neighbourhood Search for the Electoral Redistricting Problem .” Swarm and Evolutionary Computation 36:37–51.CrossRefGoogle Scholar
Wall, J. F. 2008. “Considering Opinion Dynamics and Community Structure in Complex Networks: A View Towards Modelling Elections and Gerrymandering.”Google Scholar
Wang, S. S.-H. 2016. “Three Tests for Practical Evaluation of Partisan Gerrymandering .” The Stanford Law Review 68:1263.Google Scholar
Young, H. P. 1988. “Measuring the Compactness of Legislative Districts.” Legislative Studies Quarterly 13 1:105–115.CrossRefGoogle Scholar
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