A comparison of gerrymandering metrics
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We compare and contrast twelve functions that have been proposed for the purpose of quantifying partisan gerrymandering. We consider functions that, rather than examining the shapes of districts, utilize only the partisan vote distribution among districts: partisan bias; the efficiency gap and several of its variants; the mean-median difference and the equal vote weights measure; the declination and one variant; and the lopsided-means test. We determine which historical elections are viewed as the most extreme outliers under each measure. As part of this examination, we highlight elections for which various pairs of measures arrive at very different conclusions. We also compare the measures' evaluations on a number of hypothetical elections.
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