Eric McGhee has posted this draft on SSRN. Here is the abstract:
There has been a recent surge in work on measuring partisan bias in single-member (SMD) redistricting plans. A classic SMD gerrymander is “efficient”: it “cracks” a party’s supporters so they barely lose many seats, and “packs” the remainder in a few seats that the party wins by large margins. This essay classifies these new metrics and proposes a simple principle for evaluating each metric as a gauge of this efficiency. It finds that only methods that measure the packing and cracking directly through the counting of wasted votes can serve as consistent measures of the concept. Indeed, measures of symmetry in the seats-votes curve not only fail to consistently measure efficiency, but suffer from internal contradictions in certain circumstances. Further examination of the wasted votes measures reveals that only a modified version of the “efficiency gap” — a measure active in ongoing litigation — can serve as a measure of efficiency under a wide range of electoral circumstances. Among the rest, there is considerable variation in their ability serve as appropriate measures of the concept.