TY  - JOUR
AU  - Fryer,Roland G., Jr
AU  - Holden,Richard T.
TI  - Measuring the Compactness of Political Districting Plans
JF  - National Bureau of Economic Research Working Paper Series
VL  - No. 13456
PY  - 2007
Y2  - October 2007
UR  - http://www.nber.org/papers/w13456
L1  - http://www.nber.org/papers/w13456.pdf
N1  - Author contact info:
Roland G. Fryer, Jr
Department of Economics
Harvard University
Littauer Center 208
Cambridge, MA  02138
Tel: 617/495-9592
Fax: 617/495-8570
E-Mail: rfryer@fas.harvard.edu

Richard T. Holden
University of Chicago
Booth School of Business
Room 528
5807 S Woodlawn Ave
Chicago,IL 60637
Tel: 773.834.3184
E-Mail: richard.holden@chicagobooth.edu
AB  - 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.
ER  -