# Polsby–Popper test

The **Polsby–Popper test** is a mathematical compactness measure of a shape ^{[1]} developed to quantify the degree of gerrymandering of political districts. The method was developed by lawyers Daniel D. Polsby^{[2]} and Robert Popper,^{[3]} though it had earlier been introduced in the field of paleontology by E.P. Cox.^{[4]} The formula for calculating a district's Polsby–Popper score is , where is the district, is the perimeter of the district, and is the area of the district.^{[5]} A district's Polsby–Popper score will always fall within the interval of , with a score of indicating complete lack of compactness and a score of indicating maximal compactness.^{[6]} 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.^{[7]} The method was chosen by Arizona's redistricting commission ^{[8]} in 2000.^{[9]}

## See also

- Wikipedia: w:Isoperimetric inequality
- The original text of this article was copied and adapted text from the English Wikipedia article "Polsby–Popper test) (<https://en.wikipedia.org/w/index.php?title=Polsby%E2%80%93Popper_test&oldid=1068226643>).

## References

- ↑ w:compactness measure of a shape
- ↑ w:Daniel D. Polsby
- ↑ 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
- ↑ w:redistricting in Arizona
- ↑ Monorief, Gary F. Reapportionment and Redistricting in the West pg. 27