Declination

A gerrymander designs districts with the win/loss threshold in mind, to ensure that more districts of the favored party end up on the winning side of the threshold. A neutral map designs districts for other reasons, and does not treat the win/loss threshold as special. Declination uses this fact to identify partisan differences around the threshold, as in the plot below.

Declination graph showing unfair example R: center of mass for Republican seats, D: center of mass for Democratic seats, and Win/Loss threshold.

The declination metric treats threshold-related asymmetry in the distribution of votes across districts as indicative of partisan gerrymandering. To calculate declination, we take the angles of the lines between each party’s mean vote share in the districts they won and the point on the 50% line between the mass of points representing each party. We then take the difference between those two angles and divide by π/2 to convert the result from radians to fractions of 90 degrees. We then do a further adjustment to account for differences in the number of seats across legislative chambers.

For more about declination, see Gregory Warrington's Election Law Journal article, Quantifying Gerrymandering Using the Vote Distribution, paper Introduction to the Declination Function for Gerrymanders, and Eric McGhee’s report Assessing California’s Redistricting Commission: Effects on Partisan Fairness and Competitiveness.

Compare declination to three other metrics, partisan bias, mean-median difference, and the efficiency gap.

North Carolina 2016

Under North Carolina’s 2016-2018 congressional plan, the Democratic mean vote share in districts they won was 12% higher than the Republican mean vote share in districts they won.

NC
+ D
Balanced
+ R

Georgia 1972

Under Georgia’s 1972-1980 congressional plan, the Republican mean vote share in districts they won was 4.9% higher than the Democratic mean vote share in districts they won.

GA
+ D
Balanced
+ R