Efficiency gap

The efficiency gap is the difference between the two parties' wasted votes, divided by the total number of votes.[1][2]

The efficiency gap is a measure devised by University of Chicago law professor Nicholas Stephanopoulos and political scientist Eric McGhee in 2014.[3] The metric has notably been used to quantitatively assess the effect of gerrymandering, the assigning of voters to electoral districts in such a way as to increase the number of districts won by one political party at the expense of another.[1][4]

Stephanopoulos and McGhee argued that in a non-partisan redistricting with two roughly equally popular parties, the efficiency gap would be close to zero, with a similar number of wasted votes from either party. They advocated defining illegal gerrymandering as when the efficiency gap goes above 7% or below -7%. If the gap exceeded 7%, then Stephanopoulos and McGhee argued that this could allow the party with fewer wasted votes to control the state for the duration of the validity of the map.[5][6]

Mira Bernstein and Moon Duchin argue that the Efficiency Gap is a useful starting point and should be built upon with additional measures, like the compactness measure of a shape to prevent against gerrymandering.[7]

Citing in part an efficiency gap of 11.69% to 13% in favor of the Republicans, in 2016 a U.S. District Court ruled in Gill v. Whitford against the 2011 drawing of Wisconsin legislative districts. It was the first U.S. Federal court ruling to strike down a redistricting on the grounds of favoring a political party. In the 2012 election for the state legislature, Republican candidates had 48.6% of the two-party votes but won 61% of the 99 districts. The court found that the disparate treatment of Democratic and Republican voters violated the 1st and 14th amendments to the US Constitution.[8] The State appealed the district court's Gill v. Whitford ruling to the Supreme Court,[5] which said that the plaintiffs did not have standing and sent the case back to the district court. Consequently, existing gerrymandered district maps were used in the 2018 elections. For the State Assembly, 54% of the popular vote supported Democratic candidates, but the Republicans retained their 63-seat majority. The efficiency gap, estimated to be 10% in 2014, increased to 15% based on 2018 election results.[9] The efficiency gap can be represented as a seat advantage, for example in 2017 the two US states with highest efficiency seat advantage of 3 seats were North Carolina and Pennsylvania, Rhode Island had one of the highest positive efficiency gaps, while Florida has one of the highest negative efficiency gaps.[10][11]

The following example illustrates the efficiency gap calculation.[2] There are two parties, A and B. According to the original paper,[1] wasted votes for the winner (say A) are those "beyond the 50 per-cent threshold needed" i.e., beyond 50% plus one or A-((A+B)/2+1) or more simply (A-B)/2-1, if A-B is even, like here, otherwise use int((A-B)/2). There are 500 voters divided into 5 districts with 100 voters each. In the recent election, Party A had about 45% of the votes but won 4 of the 5 districts, as follows:

The efficiency gap is the difference in the two party's wasted votes, divided by the total number of votes.

• All votes for a losing candidate are wasted .
• To win a district, 51 votes are needed, so the excess votes for the winner are wasted votes.

Efficiency gap = ${\displaystyle {\frac {222-23}{500}}=39.8\%}$ in favor of Party A.

Party A has less than half the votes, but far more of Party B's votes are wasted.

• Gerrymandering
• Evaluative Proportional Representation

• Amy, Douglas J. (2000). Behind the Ballot Box: A Citizen's Guide to Voting Systems. Praeger/Greenwood. ISBN 0-275-96585-6.