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We introduce simulated packing and cracking as a technique for evaluating partisan-gerrymandering measures. We apply it to historical congressional and legislative elections to evaluate four measures: partisan bias, declination, efficiency gap, and mean-median difference. While the efficiency gap recognizes simulated packing and cracking in a completely predictable manner (a fact that follows immediately from the efficiency gap's definition) and the declination does a very good job of recording simulated packing and cracking, we conclude that both of the other two measures record it less well. This variation is especially notable given the frequent use of such measures in outlier analyses. [ABSTRACT FROM AUTHOR]

We compare and contrast 14 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 a supplementary appendix the most extreme outliers for each measure among historical congressional and state legislative elections. [ABSTRACT FROM AUTHOR]

One way to assess the presence of gerrymandering is to analyze the distribution of votes. The efficiency gap, which does this, plays a central role in a 2016 federal court case on the constitutionality ofWisconsin'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 U.S. congressional and state legislative plans from recent decades to identify candidate gerrymanders. [ABSTRACT FROM AUTHOR]