Polsby-Popper Test

The Polsby-Popper Test is a mathematical measure of compactness developed to quantify the degree of gerrymandering of political districts. The method was developed by lawyers Daniel D. Polsby and Robert Popper. The formula for calculating a district's Polsby-Popper score is ${\displaystyle PP(D)={\frac {4\pi A(D)}{p^{2}}}}$, where ${\displaystyle D}$ is the district, ${\displaystyle p}$ is the perimeter of the district, and ${\displaystyle A(D)}$ is the area of the district. A district's Polsby-Popper score will always fall within the interval of ${\displaystyle [0,1]}$, with a score of ${\displaystyle 0}$ indicating complete lack of compactness and a score of ${\displaystyle 1}$ 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's redistricting commission in 2000.

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