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Measuring the Compactness of Political Districting Plans

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  • Roland G. Fryer, Jr
  • Richard T. Holden

Abstract

The United States Supreme Court has long recognized compactness as an important principle in assessing the constitutionality of political districting plans. We propose 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. We prove that any compactness measure which 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, requiring us to solve for each state's maximal compactness; an NP-hard problem. Using two properties of maximally compact districts, we prove they are power diagrams and develop an algorithm based on these insights. The correlation between our index and the commonly-used measures of dispersion and perimeter is -.22 and -.06, 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 their average vote increases is significantly greater under maximally compact districting plans, relative to the existing plans.

Suggested Citation

  • Roland G. Fryer, Jr & Richard T. Holden, 2007. "Measuring the Compactness of Political Districting Plans," NBER Working Papers 13456, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:13456 Note: LS PE POL
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    1. repec:cup:apsrev:v:67:y:1973:i:03:p:947-950_14 is not listed on IDEAS
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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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