A comparison of partisan-gerrymandering measures

TL;DR

This paper systematically compares fourteen measures for quantifying partisan gerrymandering, evaluating their effectiveness using hypothetical and historical elections to identify the most reliable metrics.

Contribution

It provides a comprehensive comparison of existing partisan gerrymandering measures and identifies the declination as the most effective among them.

Findings

The declination measure best avoids false positives and negatives.

Most measures struggle with accurately classifying elections as fair or unfair.

Historical outliers highlight differences in measure sensitivities.

Abstract

We compare and contrast fourteen measures that have been proposed for the purpose of quantifying partisan gerrymandering. We consider measures that, rather than examining the shapes of districts, utilize only the partisan vote distribution among districts. The measures considered are two versions of partisan bias; the efficiency gap and several of its variants; the mean-median difference and the equal vote weight standard; the declination and one variant; and the lopsided-means test. Our primary means of evaluating these measures is a suite of hypothetical elections we classify from the start as fair or unfair. We conclude that the declination is the most successful measure in terms of avoiding false positives and false negatives on the elections considered. We include in an appendix the most extreme outliers for each measure among historical congressional and state legislative elections.