Editor’s note (Oct. 4): Some of the numbers used in the original version of this column are based on an incorrect reading of efficiency-gap analysis. A correction reveals that the 2008 N.C. Senate efficiency gap skewed even more in Democrats’ favor. Learn more details here.

Those who want the U.S. Supreme Court to force changes in North Carolina’s election mapmaking process continue to tout the “efficiency gap.”

But one example from North Carolina’s recent election past demonstrates how that gap can mislead — especially if policymakers want to predict future election results.

“The efficiency gap counts the number of votes each party wastes in an election to determine whether either party enjoyed a systematic advantage in turning votes into seats,” according to a primer Eric Petry prepared for the Brennan Center for Justice at New York University’s law school.

To accept the efficiency gap argument, one must accept some questionable premises. First, as the quote suggests, efficiency gap analysis assumes that political parties “control” votes. Proponents don’t use the term “control,” but they assume that each party has a set number of voters whom they deploy within the electoral districts under consideration.

Second, voters who cast ballots for third parties or unaffiliated candidates play an insignificant role in efficiency gap calculations. Petry’s primer doesn’t consider that voters might stray from the binary choice of Democrat versus Republican.

Third, the efficiency gap depends on the novel concept of “wasted” votes. By definition, any vote cast for a losing candidate is wasted. Moreover, any vote cast for a winning candidate is wasted if that vote gives the winner one more vote than he needed to secure victory.

For example, Democrat candidate Jones beats Republican candidate Smith by a margin of 40,000 votes to 25,000 votes. Efficiency gap analysis calls for Republicans to count all 25,000 Smith votes as wasted. Democrats count 7,499 of Jones’ votes as wasted, since Jones needed just 32,501 votes to win with a bare majority of one vote more than 50 percent of the total votes cast.

In a more closely contested race, say 33,000 Jones votes prevailing over 32,000 Smith votes, efficiency gap proponents also would consider 32,499 votes, about 51 percent, to have been wasted between the two parties. Only the distribution of wasted votes would have changed.

To calculate the efficiency gap for a particular election map, add all wasted votes together for each major party. Subtract the smaller figure from the larger one. Then divide that net figure by the total number of votes cast. That number represents the efficiency gap.

Why calculate that number? The academics who devised this scheme believe that judges should consider an election map “presumptively unconstitutional” if its efficiency gap is too large. “For state legislative plans, the threshold is an efficiency gap of 8 percent or greater,” Petry explains.

This is no mere academic exercise. The U.S. Supreme Court will consider this fall whether a federal court in Wisconsin acted correctly in using efficiency gap analysis to throw out that state’s redistricting plan.

Let’s put the concept to the test.

For reasons that will become clear in time, I decided to apply efficiency gap analysis to the N.C. Senate election map used in 2008. Democrats who controlled the General Assembly in the 2000s drew the map. It was designed to elect as many Democrats as possible.

More than 3.7 million North Carolinians cast state Senate votes that year. This number, in and of itself, calls one of the efficiency gap’s assumptions into question. More than 4.3 million voters cast presidential ballots, all but about 40,000 of them for one of the two major-party presidential tickets.

If the parties “controlled” their voters, one might expect to see a closer correlation between the total number of state Senate votes and the number of votes for Barack Obama and John McCain. Instead, about 13 percent of voters who selected a Democratic or Republican presidential candidate cast no vote in a state Senate race.

Of the Senate votes, Democrats secured 1.9 million (52 percent) and Republicans a little more than 1.75 million (47 percent). As with the presidential race, roughly 40,000 voters chose another option. These third-party and write-in candidates affected the outcome of no individual Senate race, but they did represent more than 1 percent of the total vote. Their choices don’t fit inside the neat box of binary efficiency gap calculations.

Remove third-party votes, and Democrats beat Republicans, 52-48, in the overall statewide 2008 state Senate balloting. Democrats also won 30 Senate races. That’s 60 percent of the 50 Senate seats. In other words, a four-point victory in the overall vote total translated into a 20-point “margin” (60-40) in distribution of Senate seats.

Is this unconstitutional, according to the efficiency gap? No.

[Editor’s note: Italicized paragraphs that follow include incorrect numbers. Click the link in the editor’s note at the top of the column to get the correct data.]

A district-by-district analysis suggests that Republicans “wasted” more than 1.4 million (82 percent) of their votes, while Democrats wasted fewer than 1.3 million (67 percent) of their votes. Republicans “wasted” 152,500 more votes than Democrats. That yielded an efficiency gap of roughly 4 percent, whether the total vote count includes or excludes those pesky third-party votes.

That’s well short of the 8 percent standard for a “presumptively unconstitutional” election map. Dig a little deeper, though, and you can see how efficiency gap analysis could prove deceptive.

To reach the “presumptively unconstitutional” level of 8 percent, Republicans would have had to have “wasted” about 298,000 more votes than Democrats. That’s roughly 145,000 more wasted votes than those actually cast by Republicans in 2008.

It’s not hard to devise a scenario that would have accomplished that goal.

Democrats won 10 of the 50 state Senate races in 2008 with no opposition in the general election. Republicans won 10 open seats of their own, plus they won another race in the 17th District with competition from a Libertarian, but no Democrat.

If you’re searching for a real-life sign of uncompetitive election districts, it would be harder to find one than an uncontested race. Add a little competition to those races, though, and the efficiency gap actually increases — even to a level that academics would deem to be a sign of an unconstitutional partisan gerrymander.

Had a Libertarian not filed in the 17th District, another 17,440 Republican votes could be counted as “wasted,” since the incumbent would have needed just a single vote to win the seat.

If Republicans had offered even token opposition in some of the 10 uncontested races won by Democrats, it’s clearly plausible to assume that some votes cast for the victorious incumbent would have gone instead to the Republican challenger: votes from Republicans, Libertarians, unaffiliated voters, and even some Democrats who didn’t like the incumbent.

If Republicans had run candidates in the seven uncontested races with the highest Democratic vote totals, and if those losing Republican challengers had flipped just 10,000 votes apiece — still losing by margins of anywhere from 84-16 to 82-18 — the switch in “wasted” votes would have been high enough for the efficiency gap to reach the “presumptively unconstitutional” level. If Republicans had run candidates in every race, flipping just 7,000 votes apiece in the districts with uncontested Democratic wins would have accomplished the same goal.

That’s a lot of “ifs,” but they are not implausible. Only one major-party candidate earned fewer than 20,000 votes (19,666) in a contested 2008 state Senate race. That losing candidate secured 23 percent of the vote in a three-way race. The scenario above assumes that token opposition could have achieved just a fraction of that vote total.

Under our alternate scenario, honest efficiency gap advocates would call on judges to step in and strike down the state Senate map used in 2008 as overly partisan. In their view, the judicial branch should not permit such blatant disregard for the right of political parties to maintain a relatively balanced number of “wasted” votes.

Even under real-life circumstances, efficiency gap advocates would look at the 4 percent gap and suggest that election maps gave Democrats as many as two extra seats (4 percent of 50) than they would have won under maps drawn to minimize “wasted” votes.

But how would they explain the fact that two years later, using the same maps, Republicans swamped Democrats. GOP Senate candidates outpolled Democratic opponents, 59-41, in head-to-head competition and won a supermajority of Senate seats that has persisted to this day.

That question — unanswerable by efficiency gap analysis — explains why this observer chose the 2008 state Senate elections. While the analysis performed above said nothing about the impact of an election wave featuring Barack Obama and a revived Democratic Party, nothing about the data could have predicted the countervailing impact of the 2010 Tea Party response.

Numbers don’t lie. But they don’t always tell the whole story, either. Those who think they can project future election results using an efficiency gap should keep this recent history in mind.

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