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Measuring the Compactness of Political Districting Plans

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  • Fryer, Roland Gerhard
  • Holden, Richard

Abstract

We develop a measure of compactness based on the distance between voters within the same district relative to the minimum distance achievable, which we coin the relative proximity index. Any compactness measure that satisfies three desirable properties (anonymity of voters, efficient clustering, and invariance to scale, population density, and number of districts) ranks districting plans identically to our index. We then calculate the relative proximity index for the 106th Congress, which requires us to solve for each state’s maximal compactness—a problem that is nondeterministic polynomial-time hard (NP hard). The correlations between our index and the commonly used measures of dispersion and perimeter are −.37 and −.29, respectively. We conclude by estimating seat-vote curves under maximally compact districts for several large states. The fraction of additional seats a party obtains when its average vote increases is significantly greater under maximally compact districting plans relative to the existing plans.

Suggested Citation

  • Fryer, Roland Gerhard & Holden, Richard, 2011. "Measuring the Compactness of Political Districting Plans," Scholarly Articles 13456931, Harvard University Department of Economics.
    • Handle: RePEc:hrv:faseco:13456931
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    1. Taylor, Peter J., 1973. "A New Shape Measure for Evaluating Electoral District Patterns," American Political Science Review, Cambridge University Press, vol. 67(3), pages 947-950, September.
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    Cited by:

    1. Kai Hao Yang & Alexander K. Zentefis, 2023. "Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications," Cowles Foundation Discussion Papers 2355, Cowles Foundation for Research in Economics, Yale University.
    2. Anton Kolotilin & Alexander Wolitzky, 2020. "The Economics of Partisan Gerrymandering," Discussion Papers 2020-12, School of Economics, The University of New South Wales.
    3. Michael Geruso & Dean Spears & Ishaana Talesara, 2019. "Inversions in US Presidential Elections: 1836-2016," NBER Working Papers 26247, National Bureau of Economic Research, Inc.
    4. Quoc-Anh Do & Filipe R. Campante, 2009. "Keeping Dictators Honest: the Role of Population Concentration," Working Papers 01-2009, Singapore Management University, School of Economics.
    5. repec:hal:spmain:info:hdl:2441/7t0dp4mp8288lr2u6l7j8uk4li is not listed on IDEAS
    6. Samuel Bazzi & Matthew Gudgeon, 2021. "The Political Boundaries of Ethnic Divisions," American Economic Journal: Applied Economics, American Economic Association, vol. 13(1), pages 235-266, January.
    7. Stephen Coate & Brian Knight, 2007. "Socially Optimal Districting: A Theoretical and Empirical Exploration," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1409-1471.
    8. Belin Thomas R & Fischer Heidi J & Zigler Corwin M, 2011. "Using a Density-Variation/Compactness Measure to Evaluate Redistricting Plans for Partisan Bias and Electoral Responsiveness," Statistics, Politics and Policy, De Gruyter, vol. 2(1), pages 1-27, May.
    9. Aaron R Kaufman, 2020. "Implementing novel, flexible, and powerful survey designs in R Shiny," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-15, April.
    10. Baghersad, Milad & Emadikhiav, Mohsen & Huang, C. Derrick & Behara, Ravi S., 2023. "Modularity maximization to design contiguous policy zones for pandemic response," European Journal of Operational Research, Elsevier, vol. 304(1), pages 99-112.
    11. Andrei Gomberg & Romans Pancs & Tridib Sharma, 2023. "Electoral Maldistricting," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1223-1264, August.
    12. Eduardo Álvarez-Miranda & Camilo Campos-Valdés & Maurcio Morales Quiroga & Matías Moreno-Faguett & Jordi Pereira, 2020. "A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter," Mathematics, MDPI, vol. 8(9), pages 1-26, August.
    13. Quoc-Anh Doy & Filipe R. Campante, 2009. "Keeping Dictators Honest : the Role of Population Concentration," Governance Working Papers 22076, East Asian Bureau of Economic Research.
    14. Filipe Campante & Quoc-Anh Do, 2010. "A Centered Index of Spatial Concentration: Expected Influence Approach," Working Papers hal-03460167, HAL.
    15. repec:spo:wpmain:info:hdl:2441/7t0dp4mp8288lr2u6l7j8uk4li is not listed on IDEAS
    16. Kai Hao Yang & Alexander K. Zentefis, 2022. "Gerrymandering and the Limits of Representative Democracy," Cowles Foundation Discussion Papers 2328, Cowles Foundation for Research in Economics, Yale University.
    17. Katsuya Kobayashi & Attila Tasnádi, 2019. "Gerrymandering in a hierarchical legislature," Theory and Decision, Springer, vol. 87(2), pages 253-279, September.
    18. Kai Hao Yang & Alexander K. Zentefis, 2023. "Monotone Function Intervals: Theory and Applications," Papers 2302.03135, arXiv.org, revised Apr 2024.
    19. Chambers, Christopher P. & Miller, Alan D., 2013. "Measuring legislative boundaries," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 268-275.
    20. Artés, Joaquín & Richter, Brian Kelleher & Timmons, Jeffrey F., 2019. "The Value of Political Geography: Evidence from the Redistricting of Firms," Working Papers 291, The University of Chicago Booth School of Business, George J. Stigler Center for the Study of the Economy and the State.

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    More about this item

    JEL classification:

    • H70 - Public Economics - - State and Local Government; Intergovernmental Relations - - - General
    • K19 - Law and Economics - - Basic Areas of Law - - - Other

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