Evaluating the Efficiency Gap as a Measure of Proportionality and Competition

Posted by Theodore Landsman on May 31, 2017

As legal director Drew Penrose discussed last December, one of the most important developments for electoral reform last year was a challenge to partisan gerrymandering in Wisconsin -- a case that holds the promise to shake up unfair maps across the nation. FairVote hopes to contribute an amicus brief to the case that will discuss the potential of fair representation remedies. Here research analyst Theo Landsman steps back to review the idea of fair legislative elections through the lens of FairVote's support for fair representation as the long-term reform solution to breakdowns in our legislative elections.

In 2004, the U.S. Supreme Court issued a landmark ruling that courts can hear cases about gerrymandered redistricting maps in Vieth v Jubelirer. However, until the courts possessed  a discernable and manageable standard by which to assess whether a map was illegally politically gerrymandered, the issue would be considered a non-justiciable political question. Until late 2016, no court had found an acceptable standard by which to assess whether a map was gerrymandered. Consequently,  even when legislators admitted that the map was deliberately gerrymandered, no cases challenging the validity of a gerrymandered map had been successful.

The “efficiency gap” was first proposed by Stephanopoulos and McGhee in a 2015 paper, and it has emerged as a way to prove evidence of bias that even defenders of distorted maps could not deny. This new criterion has paved the way for a three judge panel to strike down Wisconsin's state assembly map on the grounds of an unconstitutional partisan gerrymander. Should the decision be upheld by the Supreme Court, the efficiency gap calculation will likely be critical in many other redistricting cases. The impact that this criterion has had already cannot be denied. However, the question remains, is the efficiency the ideal measure of fairness in redistricting and legislative apportionment, and how does it fair compared to other measures?  

Wisconsin is in many ways an ideal example of a problematic partisan gerrymander. At the start of the 2013 session, the state legislature had only 54 Democrats and 78 Republicans, despite Obama carrying the state by 3.5 points in the 2012 election. Assuming the presidential vote is indicative of vote in state elections, which has become more and more reliable, this is a much greater deviation than any reasonable standard would allow. Moreover, this deviation is far larger than what we would expect from single winner district inefficiencies (which ought to cancel eachother out), or differences between presidential and midterms electorates. This obvious partisan distortion, with clear evidence of bias, begs the question of why the efficiency gap was necessary at all.

While the original formulation of the efficiency gap is more complicated, if we assume equal numbers of votes are required to win every seat in a given legislative chamber (which is, unfortunately, far from true for Congress), the math becomes quite simple. The efficiency gap proposes that every 1% increase in vote count for either party above 50% should correspond to a 2% increase in seats won. Bias is measured as the deviation from this standard. Proportionality, on the other hand, provides that winner’s margin percentage should equal the seat margin percentage. Perfect efficiency by the efficiency gap standard would be if the percent of the vote margin could be doubled to get the percent of the seat margin.

While no one besides perhaps Stephanopoulos and McGhee themselves has compiled the detailed vote tallies for each state legislative seat that would allow for a complete comparison, our state legislative seat level presidential partisanship data (via DailyKos) can provide a replacement with which to calculate an approximate simplified efficiency gap. While using presidential partisanship obscures many interesting local trends, such as the survival of regional democratic parties in appalachia and the south, it is enough of an acceptable substitute that Stephanopoulos and McGhee use it themselves for state elections where candidates ran unopposed. Moreover presidential partisanship has been shown to be a better predictor of open seat results than state election history, and is typically seen as a better indicator of partisan lean than elections which feature incumbents.  

As the graph below shows, the empirical trend in state legislative districting is somewhere between the efficiency gap hypothesis and proportionality, with a 2.7% general bias towards Republicans. This complicates any assessment of which criterion is truer to the overall trend in redistricting, but does show that both the efficiency gap hypothesis and proportionality hold key lessons for how our representative system can be improved.

The efficiency gap formulation of bias does not significantly change our conclusions as to which types of redistricting schemes perform better or worse. However, the contrast of the efficiency gap as compared to a proportionality criterion does raise issues. As shown in the scatter plot below, since proportionality and approximate efficiency are arrived at using the same variables, we can project both standards onto a simple graph, and contrast it with the empirical trend in relationship of seat margin to vote share (the trendline).



Of particular concern is the area between the perfect proportionality criterion and the 0 efficiency gap criterion lines, which contains a significant number of state chambers. In this area, assigning a chamber a worse efficiency gap score amounts to punishing the legislature for behaving in a more proportional way. Kentucky, for example, had an almost perfectly proportional Senate in 2012, but given its significant Republican lean, would have an approximate efficiency gap of about 10% against Republicans. Interestingly, two of the states with chambers in this area; the Wyoming and Arizona chambers, have ongoing challenges to their redistricting procedure. In these cases, the efficiency gap argument, and it’s differences from the proportionality argument, could make a significant difference in whether a challenge to district maps succeeds, and what sort of district map replaces the current gerrymander.

One notable impact of the efficiency gap criterion is that under it only 3 Democrat-controlled legislatures show bias towards Democrats across both chambers, and only West Virginia, which has its own complicated history of non-traditional partisanship, does so by more than four points. By contrast, 25 Republican-controlled chambers show significant bias towards Republicans, and in 12 of those the bias is significant enough to give them control over the legislature when partisanship indicates they should not have it. This fact in particular makes the efficiency gap an advantageous metric for civil rights groups in Republican-controlled states who are seeking to prove a non-symmetrical or intentional bias in redistricting procedure. Moreover, in the vast majority of these cases, proportionality and efficiency arguments would suggest the same solution, redistricting these states to provide more opportunities for Democratic challengers.

However, the question remains of whether the efficiency gap is a better metric for measuring bias against the minority party in the redistricting process. Given that it is twice as sensitive to partisan shifts as proportionality, we would expect maps designed with the efficiency gap in mind to be more competitive. There is an extraordinary lack of competition in US legislative elections, and this argument alone would create a compelling case for legislatures  to eliminate the efficiency gap, a goal which this data shows may prove more viable in single winner districts with plurality voting, just as it has already proven more viable for the purposes of legal challenges.  Indeed, a competitive efficiency gap neutral map may do significantly more to combat perceptions of bias than packing democratic and republican partisans into extremely Democratic or Republican districts, which is probably the easiest way to achieve uniform proportionality in a single winner system.

Yet even a redistricting map with no efficiency gap will often be disproportional, and some maps that are already proportional, either due to chance or legislative compromise, may encounter pressure to abandon their current more proportional maps as they adapt to the new standard.  Creating a more responsive map may still be a worthwhile outcome, but this choice is only forced on us by our single-winner system. Multi-winner districts with ranked choice voting would achieve dramatic gains in efficiency and representation. Using RCV in multi-winner districts would eliminate the majority of wasted votes while also bringing our legislative maps closer to proportional representation. As we move toward a more representative and inclusive government, we applaud the efforts of political scientists and lawyers to create more responsive and competitive maps, and we look forward to a day when Fair Representation Voting ensures  universal proportionality and competition.


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