Barry Burden and Corwin Smidt have written this new article in SAGE Open. Here is the abstract:

A well-developed body of research offers ways to measure the partisan advantages that result from legislative districting. Although useful to researchers and legal practitioners, those studies also suffer from theoretical, empirical, and legal limitations. In this essay, we review measures of partisan bias and methods for both simulating election results under existing maps and simulating hypothetical maps. We start by describing the concept of partisan bias and how it has been measured. Then, we turn to new simulation methods that generate hypothetical election results or districts to judge the fairness of a map. While both kinds of evaluation are useful, we point to some unresolved questions and areas for future research.