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Recently, scholars from law and political science have introduced metricswhich use only election outcomes (and not district geometry) to assess thepresence of partisan gerrymandering. The most high-profile example of such atool is the efficiency gap. Some scholars have suggested that such tools shouldbe sensitive enough to alert us when two election outcomes have the samepercentage of votes going to political party $A$, but one of the two awardsparty $A$ more seats. When a metric is able to distinguish election outcomes inthis way, that metric is said to satisfy the efficiency principle.  In this article, we show that the efficiency gap fails to satisfy theefficiency principle. We show precisely how the efficiency principle breaksdown in the presence of unequal voter turnout. To do this, we first present aconstruction that, given any rationals $1/4< V<3/4$ and $0<S<1$, constructs anelection outcome with vote share $V$, seat share $S$, and EG = 0. (Forinstance, one party can get 26% of the vote and anywhere from 1% to 99% of theseats while the efficiency gap remains zero.) Then, for any election with voteshare $1/4<V<3/4$, seat share $S$, and EG= 0, we express the ratio $\rho$ ofaverage turnout in districts party $A$ lost to average turnout in districtsparty $A$ won as a function in only $V$ and $S$. It is well known that when alldistricts have equal turnout, EG can be expressed as a simple formula in $V$and $S$; we express the efficiency gap of any election as an equation only in$V, S,$ and $\rho$. We also report on the values of $\rho$ that can be observedin actual elections.

The Efficiency Gap, Voter Turnout, and the Efficiency Principle