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Measuring the Compactness of Political Districting Plans


  • Roland G. Fryer Jr.
  • Richard Holden


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

  • Roland G. Fryer Jr. & Richard Holden, 2011. "Measuring the Compactness of Political Districting Plans," Journal of Law and Economics, University of Chicago Press, vol. 54(3), pages 493-535.
  • Handle: RePEc:ucp:jlawec:doi:10.1086/661511

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    Cited by:

    1. 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.
    2. Stephen Coate & Brian Knight, 2007. "Socially Optimal Districting: A Theoretical and Empirical Exploration," The Quarterly Journal of Economics, Oxford University Press, vol. 122(4), pages 1409-1471.
    3. 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.
    4. Filipe R. Campante & Quoc-Anh Do, 2010. "A Centered Index of Spatial Concentration: Expected Influence Approach," Sciences Po publications info:hdl:2441/7t0dp4mp828, Sciences Po.
    5. Chambers, Christopher P. & Miller, Alan D., 2013. "Measuring legislative boundaries," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 268-275.

    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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