Polsby–Popper test

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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,^[1] though it had earlier been introduced in the field of paleontology by E.P. Cox.^[2] The formula for calculating a district's Polsby–Popper score is $PP(D)={\frac {4\pi A(D)}{P(D)^{2}}}$ , where $D$ is the district, $P(D)$ is the perimeter of the district, and $A(D)$ is the area of the district.^[3] A district's Polsby–Popper score will always fall within the interval of $[0,1]$ , with a score of $0$ indicating complete lack of compactness and a score of $1$ indicating maximal compactness.^[4] 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.^[5] The method was chosen by Arizona's redistricting commission in 2000.^[6]

References

↑ Polsby, Daniel D.; Popper, Robert D. (1991). "The Third Criterion: Compactness as a procedural safeguard against partisan gerrymandering". Yale Law & Policy Review. 9 (2): 301–353.
↑ 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
↑ Crisman, Karl-Dieter, and Jones, Michael A. The Mathematics of Decisions, Elections, and Games pg. 3
↑ Miller, William J., and Walling, Jeremy D. The Political Battle Over Congressional Redistricting pg. 345
↑ Ansolabehere, Stephen, and Palmer, Maxwell A Two Hundred-Year Statistical History of the Gerrymander pp. 6–7
↑ Monorief, Gary F. Reapportionment and Redistricting in the West pg. 27

[1] Polsby, Daniel D.; Popper, Robert D. (1991). "The Third Criterion: Compactness as a procedural safeguard against partisan gerrymandering". Yale Law & Policy Review. 9 (2): 301–353.

[2] 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

[3] Crisman, Karl-Dieter, and Jones, Michael A. The Mathematics of Decisions, Elections, and Games pg. 3

[4] Miller, William J., and Walling, Jeremy D. The Political Battle Over Congressional Redistricting pg. 345

[5] Ansolabehere, Stephen, and Palmer, Maxwell A Two Hundred-Year Statistical History of the Gerrymander pp. 6–7

[6] Monorief, Gary F. Reapportionment and Redistricting in the West pg. 27

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Polsby–Popper test

See also

References