Ray Wallin has posted this draft on SSRN. Here is the abstract:
Recently the ‘efficiency gap’ method has gained notoriety by playing an important role in framing the Gill v Whitford gerrymandering case decided in Wisconsin and soon to be heard by the US Supreme Court. The story of the efficiency gap is captivating as it frames all votes it deems unnecessary as ‘wasted votes,’ and it is the sum of these wasted votes that determines whether the outcome of an election is fair.
The first part of this paper uses two tables presented to the district court in the Gill v Whitford and shows that such tables can be heavily manipulated, gerrymandered in ways that the efficiency gap does not measure. The wasted votes in the tables will be shown to be biased toward districts with higher voter turnout, and under further scrutiny, it will be shown that wasted votes are not needed, nor are tables, as the table calculations can be represented in a two-variable equation, which when comparing redistricting plans, will boil down to a one-variable equation that provides little insight into gerrymandering.
The second part of this paper derives a corrected efficiency gap equation, the ‘equal districts efficiency gap equation,’ which produces a more precise efficiency gap measure. The equal districts efficiency gap will show that to date, efficiency gap calculations in literature have been biased, including those presented to the courts, and that a gerrymandering calculation that uses numbers such as ‘party X’s statewide votes’ or ‘statewide wasted votes’ is inherently biased.
But the main purpose of this paper is a clarification of what seems to be general confusion in the literature as to what a vote is and what a seat (or a district) is in gerrymandering calculations. It is shown that, as a fundamental principle, all equations concerning gerrymandering should be written in reference to seats (districts), not votes.