Polsby–Popper test

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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


  1. w:compactness measure of a shape
  2. w:Daniel D. Polsby
  3. 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.
  4. 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
  5. Crisman, Karl-Dieter, and Jones, Michael A. The Mathematics of Decisions, Elections, and Games pg. 3
  6. Miller, William J., and Walling, Jeremy D. The Political Battle Over Congressional Redistricting pg. 345
  7. Ansolabehere, Stephen, and Palmer, Maxwell A Two Hundred-Year Statistical History of the Gerrymander pp. 6–7
  8. w:redistricting in Arizona
  9. Monorief, Gary F. Reapportionment and Redistricting in the West pg. 27