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The Equal Districts Efficiency Gap: Fundamental Gerrymandering Theory and an Analysis and Modification of the Efficiency Gap

The ‘efficiency gap’ method has gained notoriety recently by playing an important role in framing the Gill v Whitford gerrymandering case decided in Wisconsin and 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.’ 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 tables presented to the district court in the Gill v Whitford case to show that such tables can be heavily manipulated, gerrymandered in ways that the efficiency gap does not measure. Wasted votes are then shown to be biased toward districts with higher voter turnout. Then, , it is shown that wasted votes are not needed, nor are tables, as the table calculations can be reduced to a two-variable equation, which when comparing redistricting plans, boils down to a one-variable equation that provides little insight into gerrymandering. 
Finally, this paper corrects the bias found in the efficiency gap with the ‘equal districts efficiency gap equation’ which produces a more accurate efficiency gap measure. The equal districts efficiency gap shows that to date, efficiency gap calculations in literature have been biased, including those presented to the courts, and that any gerrymandering calculation that uses numbers such as ‘party X’s statewide votes’ or ‘statewide wasted votes’ is inherently biased. 
Throughout this paper, examples are given to help clarify what seems to be general confusion in scientific literature as to what a vote is and what a seat (or a district) is in gerrymandering analysis. To date, some measures of bias use votes as a basis and others use seats, with no clarification as to why one is used over the other. This paper shows that, as a fundamental principle, all equations concerning gerrymandering should be written in reference to seats (districts), not votes.