Measuring the compactness of political districting plans
By: Roland G. Fryer, Jr., Richard T. Holden.
Contributors: Holden, Richard T., 1974-; National Bureau of Economic Research.
Series: NBER working paper series -- working paper 13456.; Working paper series (National Bureau of Economic Research) -- working paper no. 13456.
Publisher: National Bureau of Economic Research
Published: 2007
Place of publication: Cambridge, Mass
Language: eng
Number of pages: 33
Subjects: Apportionment (Election law) -- United States; Election districts -- United States
Description: 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.
Notes: "October 2007."

Includes bibliographical references (p. 20-23).

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