Polsby–Popper test: Difference between revisions

▲The '''Polsby–Popper test''' is a mathematical [[compactness measure of a shape]] developed to quantify the degree of [[gerrymandering]] of political districts. The method was developed by lawyers [[Daniel D. Polsby]] and Robert Popper,<ref>{{cite journal|last1=Polsby |first1=Daniel D. |author1-link=Daniel D. Polsby |first2=Robert D. |last2=Popper |year=1991 |title=The Third Criterion: Compactness as a procedural safeguard against partisan gerrymandering |journal=Yale Law & Policy Review |volume=9 |issue=2 |pages=301–353 |url=https://digitalcommons.law.yale.edu/ylpr/vol9/iss2/6 }}</ref> though it had earlier been introduced in the field of paleontology by E.P. Cox.<ref>Cox, E.P. 1927. "A Method of Assigning Numerical and Percentage Values to the Degree of Roundness of Sand Grains." ''Journal of Paleontology'' 1(3): pp. 179–183</ref> The formula for calculating a district's Polsby–Popper score is <math>PP(D) = \frac {4\pi A(D)} {P(D)^2}</math>, where <math>D</math> is the district, <math>P(D)</math> is the perimeter of the district, and <math>A(D)</math> is the area of the district.<ref>Crisman, Karl-Dieter, and Jones, Michael A. [https://books.google.com/books?id=xdZzBAAAQBAJ&pg=PA3&lpg=PA3 The Mathematics of Decisions, Elections, and Games] pg. 3</ref> A district's Polsby–Popper score will always fall within the interval of <math>[0,1]</math>, with a score of <math>0</math> indicating complete lack of compactness and a score of <math>1</math> indicating maximal compactness.<ref>Miller, William J., and Walling, Jeremy D. [https://books.google.com/books?id=3dEaMt1NKYYC&pg=PA345 The Political Battle Over Congressional Redistricting] pg. 345</ref> Compared to other measures that use dispersion to measure gerrymandering, the Polsby–Popper test is very sensitive to both physical geography (for instance, convoluted coastal borders) and map resolution.<ref>Ansolabehere, Stephen, and Palmer, Maxwell [http://www.vanderbilt.edu/csdi/events/ansolabehere_palmer_gerrymander.pdf A Two Hundred-Year Statistical History of the Gerrymander] pp. 6–7</ref> The method was chosen by [[Arizona]]'s [[redistricting in Arizona|redistricting commission]] in 2000.<ref>Monorief, Gary F. [https://books.google.com/books?id=VYICdjpivIQC&pg=PA27 Reapportionment and Redistricting in the West] pg. 27</ref>