02405cam a22002657 4500001000700000003000500007005001700012008004100029100002500070245012700095260006600222490004200288500001800330520129300348530006101641538007201702538003601774690005701810690005501867700002301922710004201945830007701987856003802064856003702102w13456NBER20180424193207.0180424s2007 mau||||fs|||| 000 0 eng d1 aFryer, Roland G, Jr.10aMeasuring the Compactness of Political Districting Plansh[electronic resource] /cRoland G. Fryer, Jr, Richard T. Holden. aCambridge, Mass.bNational Bureau of Economic Researchc2007.1 aNBER working paper seriesvno. w13456 aOctober 2007.3 aThe 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aH70 - General2Journal of Economic Literature class. 7aK19 - Other2Journal of Economic Literature class.1 aHolden, Richard T.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w13456.4 uhttp://www.nber.org/papers/w1345641uhttp://dx.doi.org/10.3386/w13456