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The Polsby–Popper test is a mathematical
compactness measure of a shape The compactness measure of a shape is a numerical quantity representing the degree to which a shape is compact. The meaning of "compact" here is not related to the topological notion of compact space. Properties Various compactness measures are us ...
developed to quantify the degree of
gerrymandering In representative democracies, gerrymandering (, originally ) is the political manipulation of electoral district boundaries with the intent to create undue advantage for a party, group, or socioeconomic class within the constituency. The m ...
of political districts. The method was developed by lawyers Daniel D. Polsby and Robert Popper, though it had earlier been introduced in the field of paleontology by E.P. Cox. The formula for calculating a district's Polsby–Popper score is PP(D) = \frac , where D is the district, P(D) is the perimeter of the district, and A(D) is the area of the district. A district's Polsby–Popper score will always fall within the interval of ,1/math>, with a score of 0 indicating complete lack of compactness and a score of 1 indicating maximal compactness. 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. The method was chosen by
Arizona Arizona ( ; nv, Hoozdo Hahoodzo ; ood, Alĭ ṣonak ) is a state in the Southwestern United States. It is the 6th largest and the 14th most populous of the 50 states. Its capital and largest city is Phoenix. Arizona is part of the Fou ...
's
redistricting commission In the United States, a redistricting commission is a body, other than the usual state legislative bodies, established to draw electoral district boundaries. Generally the intent is to avoid gerrymandering, or at least the appearance of gerryman ...
in 2000.Monorief, Gary F
Reapportionment and Redistricting in the West
pg. 27


See also

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Isoperimetric inequality In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n ...


References

{{DEFAULTSORT:Polsby-Popper test Gerrymandering