Polsby–Popper Test
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The Polsby–Popper test is a mathematical
compactness measure of a shape Compactness measure is a numerical quantity representing the degree to which a shape is compact. The circle and the sphere are the most compact planar and solid shapes, respectively. Properties Various compactness measures are used. However, the ...
developed to quantify the degree of
gerrymandering Gerrymandering, ( , originally ) defined in the contexts of Representative democracy, representative electoral systems, is the political manipulation of Boundary delimitation, electoral district boundaries to advantage a Political party, pa ...
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 method was chosen by
Arizona Arizona is a U.S. state, state in the Southwestern United States, Southwestern region of the United States, sharing the Four Corners region of the western United States with Colorado, New Mexico, and Utah. It also borders Nevada to the nort ...
'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 gerrym ...
in 2000.


Definition

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. Only a perfectly round district will reach a Polsby–Popper score of 1. 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.


Contradiction to other measures

Fairness criteria for gerrymandering can stand in contradiction to each other. For example, there are cases in which, in order to sufficiently fulfill the
One man, one vote "One man, one vote" or "one vote, one value" is a slogan used to advocate for the principle of equal representation in voting. This slogan is used by advocates of democracy and political equality, especially with regard to electoral reforms like ...
criterion and a low
efficiency gap Efficiency is the often measurable ability to avoid making mistakes or wasting materials, energy, efforts, money, and time while performing a task. In a more general sense, it is the ability to do things well, successfully, and without waste. ...
, one needs to take a low Polsby–Popper compactness into account.


See also

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Isoperimetric inequality In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. '' Isoperimetric'' ...


References

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