Editor’s note (Oct. 4): Some numbers used in the original version of this column are based on an incorrect reading of efficiency gap analysis. Click here to learn about the error.

Perhaps Republicans in North Carolina’s state Senate shortchanged themselves when they drew the first map designed to preserve their supermajority. Their map could have aimed to give Republicans victories in 75 percent of Senate contests.

That’s a conclusion one might expect only a partisan Republican to endorse. But it’s also a logical response to an analysis of the “efficiency gap” associated with the 2010 election. That election handed control of the Senate to the GOP.

Some redistricting reform advocates tout the efficiency gap as an objective data point bolstering their argument against partisan gerrymandering. The U.S. Supreme Court could decide in its next term whether the gap proves sufficient as a basis to strike down a redistricting plan in Wisconsin. A lawsuit challenging North Carolina’s 2016 congressional map also points specifically to the efficiency gap.

But several recent Daily Journal columns have pointed to flaws in efficiency gap analysis.

It appears especially weak as a predictive tool. Last week, we learned that a 4 percent efficiency gap favoring Democrats in 2008 N.C. Senate elections (equivalent to adding two seats to Democrats’ victory) offered no clue that Republicans would swamp Democrats in the next election and turn a 30-20 deficit in Senate seats into a 31-19 supermajority.

Analysis of the 2010 Senate races leads to an even more troubling result for efficiency gap enthusiasts.

In an election cycle that favored Republicans up and down the ballot, the GOP won more than 1.46 million votes in 2010 state Senate races. Democrats won about 1 million votes, while Libertarians and unaffiliated candidates collected fewer than 12,000 votes statewide.

Head to head, Republicans outpolled Democrats, 59 percent to 41 percent. The GOP’s 31 victories gave them 62 percent of total Senate seats. By comparison, Democrats had beaten Republicans, 52-48, in 2008 but collected 30 Senate seats (60 percent).

Since the efficiency gap purports to convey the disparity between voters’ preferences and the size of the winning party’s electoral gain, one might expect a relatively small efficiency gap for the state Senate map in 2010. If North Carolina allocated legislative seats proportionally, as many European and Latin American countries do, the GOP could have expected to turn its 59 percent statewide vote total into 29 or 30 Senate seats. Perhaps its actual total of 31 wins shows evidence of some slight efficiency gap favoring Republicans.

The actual result is far different if one computes the gap district by district.

Remember that the efficiency gap depends on the concept of “wasted votes.” The analysis counts every vote cast for a losing candidate as wasted. It also considers any vote wasted if it gives the winning candidate more than the single vote needed to defeat his opponent.

Under this premise, Democrats wasted 664,786 votes in 2010. That’s nearly 66 percent of their total. At the same time, Republicans wasted 1,017,680 votes, nearly 70 percent of their total. In fact, Republicans “wasted” more votes than Democrats cast.

To calculate the efficiency gap, we subtract the Democrats’ wasted vote total from the Republicans’ total, then divide the result (352,894) by the nearly 2.5 million votes cast in 2010 state Senate races.

We find an efficiency gap of more than 14 percent … favoring Democrats.* Using the presumptions of efficiency gap analysis, this suggests that Democrats won 14 percent more seats in 2010 than they should have won. In a 50-seat Senate chamber, that translates into seven seats.

In other words, efficiency gap analysis suggests that the GOP’s 31-19 supermajority should have looked more like 38-12. Such a result would give Republicans more than 75 percent of state Senate seats.

(To be fair, the efficiency gap’s original authors are likely to take issue with a computation that makes no adjustments for the 2010 Senate election’s uncontested races. They might adjust the numbers to wipe out the Democrats’ efficiency gap advantage entirely.**)

This leads back to the proposition set forward in this column’s opening paragraph. The newly elected Republican majority drew an election map that has been used during the past three state Senate election cycles. In the 2012 election, Republicans picked up two more seats to build a 33-17 majority. They’ve since added two more seats and now hold a 35-15 majority. They’ve not come close to the 38-12 majority projected by the 2010 efficiency gap analysis.

To be clear, this column does not advocate an election map designed to produce that result. Nor does this author believe that even the most partisan Republicans think they could concoct a map that would produce that result.

What this exercise is designed to show instead is the inherently flawed nature of efficiency gap analysis. Treating the 2010 results seriously would lead an advocate to argue that the 14 percent gap favoring Democrats rendered the map “presumptively unconstitutional.”

It’s hard to imagine Republicans arguing in court that an election that gave them a Senate supermajority should be thrown out because of an efficiency gap favoring their opponents. On the other side, it’s impossible to imagine Democrats trying to persuade judges to throw out the map because of that gap. Democrats would be forced to argue for a new map even more favorable to Republicans than the one North Carolina has used since 2012.

North Carolina should reform its redistricting process. There’s no good reason to leave election maps in the hands of those who stand to benefit directly from those maps.

But there’s nothing efficient about a statistical tool that produces absurd results. The example of the 2010 N.C. state Senate election offers one more reason for electoral mapmakers and the courts to pay no mind to the efficiency gap.

Mitch Kokai is senior political analyst for the John Locke Foundation.


*This column derives a 14 percent efficiency gap favoring Democrats from a district-by-district computation of wasted votes. This is the method proponents typically use to describe how to calculate the gap. In the original 2014 law review article on the efficiency gap, its creators suggest a shortcut based solely on a comparison of the two major parties’ overall vote totals and their respective margins in total seats won. This simplification produces a result that never would show a gap favoring the minority party.

**Among the efficiency gap’s limitations, by its creators’ own admission, is the failure to account for uncontested races. Basic efficiency gap analysis calls for the winning party in an uncontested race to count all but one vote in the district as “wasted.” Proponents suggest adjustments that would reduce that number and add to the losing party’s “wasted” vote total. Using suggestions from the law review article, Republicans’ net wasted vote edge of 352,894 in the 2010 state Senate contests could swing to an edge of 73,100 wasted votes for Democrats. This would mean a 3 percent efficiency gap benefiting Republicans (meaning wins of an extra one or two seats).

This observer notes a problem with the recommended adjustment. The efficiency gap’s authors estimate that a losing party in an otherwise uncontested race would be likely to win more than one-third of the votes (34 percent for losing Republicans and 36 percent for losing Democrats). This seems overly generous. Drop the percentage to 25 percent for both parties, and the 2010 N.C. Senate efficiency gap swings back to 2 percent favoring Democrats (meaning a win of one seat they should have lost).

More important, adding mathematical adjustments to the mix takes away the efficiency gap’s promise as an objective tool for measuring partisan gerrymandering. A court that relies on this standard is wading into murky waters.