An interesting new study by Kevin Baas and Colin McAuliffe:

There are several legal and technical challenges to the establishment of a standard for limiting partisan gerrymandering, and a few methods have been proposed thus far. All methods for examining gerrymandering use observations of the results of one or more elections to make inferences about the tendency of a given redistricting plan to lead to biased outcomes. Here we propose an empirical Bayesian framework which allows an analyst to make such inferences accurately by using all available election results for the redistricting plan in question in a robust and consistent statistical model. The framework can be used with any gerrymandering metric.

Additionally, we propose a new measure of gerrymandering called the specific asymmetry which we believe will stand up better to judicial and technical tests than any other measure proposed thus far. The specific asymmetry does not rely on proportionality of seats and votes, is applicable to any level of statewide partisanship, does not require national results as a baseline, and measures bias at the popular vote that actually occurred as opposed to some other hypothetical popular vote. All other available metrics fall short in at least one of these aspects, which leaves them vulnerable to criticism and manipulation by those seeking to gerrymander or to defend an existing gerrymander.

We analyze the magnitude and persistence of partisan bias under a particular districting plan by using the empirical Bayesian model to compute the expected value of the specific asymmetry. This analysis technique is applied to the United States congressional elections from 1972-2016 to examine the total and net effects of partisan bias in recent history. We also examine the Act 43 map for the Wisconsin State Assembly, which is the subject of Whitford v. Gill.