Quantifying Gerrymandering Using the Vote Distribution

Abstract

To assess the presence of gerrymandering, one can consider the shapes of districts or the distribution of votes. The efficiency gap, which does the latter, plays a central role in a 2016 federal court case on the constitutionality of Wisconsin's state legislative district plan. Unfortunately, however, the efficiency gap reduces to proportional representation, an expectation that is not a constitutional right. We present a new measure of partisan asymmetry that does not rely on the shapes of districts, is simple to compute, is provably related to the "packing and cracking" integral to gerrymandering, and that avoids the constitutionality issue presented by the efficiency gap. In addition, we introduce a generalization of the efficiency gap that also avoids the equivalency to proportional representation. We apply the first function to US congressional and state legislative plans from recent decades to identify candidate gerrymanders.

A Comparison of Partisan-Gerrymandering Measures

“…We include Bias and MM for reference even though it is immediate from their definitions that they are completely insensitive to uniform vote swings. We note that similar sensitivity analyses have been conducted for various measures using historical election results -see, for example, (Warrington, Mar 2018;McGhee & Stephanopoulos, 2015;Best et al, 2017). Also, it is worth mentioning that an alternative approach to sensitivity would be to add in random noise to the Democratic vote in each district.…”

“…We consider here only the two "vote-centric" versions of the efficiency gap given by EG 1 v and EG 2 v . Finally, (Warrington, Mar 2018) introduces the τ -Gap measure which weights votes according to a function parameterized by a non-negative real number τ . The idea behind the definition is that votes close to the fifty-percent threshold are less wasted than those at either extreme.…”

Declination as a Metric to Detect Partisan Gerrymandering

“…If party A is both packed and cracked, y will be close to 50% and z will be very large, resulting in a large Declination. Indeed, Warrington made a point of proving that the Declination detects certain definitions of packing and cracking [10]. But, while both the Efficiency Gap and the Declination focus on packing and cracking, their definitions get at packing and cracking through very different means.…”

“…This also allows the possibility of y = 1 2 or z = 1 2 (or both). While no specific range of values of the Declination has been suggested to indicate a lack of partisan bias, the implication of Warrington's construction and discussion of the Declination in [10] is that a Declination near 0 indicates that a districting map is fair. This gives rise to a natural question: Q: What kinds of election outcomes have δ = 0?…”

“…Warrington recently defined the Declination [10], which is based upon the number of seats won by Party A, the average vote share for Party A in districts it won, and the average vote share for Party A in districts it lost. The idea is that if party A has been packed, its average vote share in districts it won should be unusually high, and if party A has been cracked, its average vote share in districts it lost should be close to (but of course below) 50%.…”