Elections are full of numbers. Misuse those numbers, and you might end up making arguments that are full of something else.

For instance, partisans rely on voting statistics to complain about the “disparate impact” particular election policies have on different racial and ethnic groups. Observers such as Thomas Sowell have exposed the inherent flaw within the “disparate impact” argument.

“The implicit assumption is that without ‘discriminatory intent’ these statistics would reflect the percentages of people in the population,” Sowell writes. “But no matter how plausible that outcome might seem on the surface, it is seldom found in real life, and those who use this standard are seldom, if ever, asked to produce hard evidence that it is factually correct, as distinct from politically correct.”

Pundits and political observers also err when they seek to extrapolate too much information from statistical averages.

Let’s say 2,000 people cast votes on a weekday during an early-voting period, while 400 cast votes on a Sunday. One might surmise the weekday option is more popular with voters.

But Democrats on the N.C. State Board of Elections, presented earlier this year with similar numbers from Craven County’s 2012 voting record, contended that the Sunday option was more popular because that day featured a higher number of “voters per hour” than any weekday.

Implicit in their argument was the notion that the volume of voters would remain high on Sunday if the number of voting hours had increased. But an equally plausible counterargument would suggest the number of Sunday voters might have remained relatively close to 400, whether a polling site had been open for four or eight hours. Without additional evidence, it’s impossible to know whether the “voters per hour” statistic offers valuable information.

The latest example of questionable election numbers involves something called an “efficiency gap,” discussed in a recent Raleigh News & Observer column by Harvard law professor Noah Feldman. Two other professors developed the concept. The efficiency gap purports to show the ill effects of gerrymandering in electoral redistricting.

“To measure the efficiency gap, you first tally up the votes wasted by each side,” Feldman explains. “For the winners in a district, that’s the total votes beyond what was needed for victory. For the losing side in a district, it’s all the votes cast. Then, for each party, you divide the wasted votes by the total number of votes cast. That yields a rough measure of vote efficiency for each party.”

The party victimized by gerrymandering “has a much lower efficiency,” Feldman writes.

Not just an academic exercise, calculation of an efficiency gap in Wisconsin’s state legislative elections played a role in a recent court ruling. The gap helped persuade a three-judge federal panel that state election maps violated the U.S. Constitution’s equal protection clause. It’s the first time a court has struck down an election map because of “partisan” gerrymandering.

While clever, the efficiency gap statistic strikes this observer as problematic. If Feldman’s description is accurate, the concept is based on the notion that both major political parties control a bloc of votes and that votes not cast for those parties’ preferred candidates are “wasted.”

But that’s not how elections work.

Yes, the two major political parties can use voter registration data and past election results to gauge how many votes they might expect to win in a particular election district. They don’t control those votes.

Voters control those votes. And their voting decisions can defy statistical models.

North Carolina’s legislative elections during the 2000s offer a useful historical example.

In four separate elections from 2000 to 2006, conducted under three different sets of election maps, the two major parties collected a relatively consistent share of the total legislative vote.

In each of those elections, House Republicans collected 51-52 percent of the total vote. Democrats collected 47-49 percent in three of the elections, with a 44 percent share in the outlier year of 2002. Despite the GOP’s slight — but consistent — “victory” margin, Democrats won control of the House in each election. (Actually, Republicans won 61 of the 120 House seats in 2002, but future felon Jim Black’s scheming helped keep the House in Democrats’ hands.)

On the Senate side, the two parties faced a continuous battle for total vote supremacy. Democrats won in 2000 (50-49 percent), Republicans won in 2002 (51-46 percent) and 2004 (50-48 percent), and Democrats won again in 2006 (52-48 percent). Regardless of those closely contested statewide campaigns, Democrats maintained majorities of actual Senate seats after each election.

Election maps clearly favored Democrats. One suspects an efficiency gap analysis would show more “wasted” votes for Republicans. Their frequent majorities in the statewide vote did not translate into GOP control of either legislative chamber.

But that’s not the end of the story. Attempts to analyze only these four election years would omit the key factor of changing voter preferences.

Fast forward to 2008. Using the same election maps as 2006, voters shifted gears. For the first time in the decade, Democrats won the popular vote in N.C. House contests (54-44 percent). While that represented a swing of 5-6 percentage points toward Democrats, the vote in statewide Senate races was relatively constant from 2006 to 2008, as Democrats won with a 52-47 percent margin.

Those victories gave Democrats a 68-52 majority among the 120 House seats and a 30-20 majority within the Senate.

Jump ahead another two years, with the same election maps, and the picture changes dramatically again. The total share of N.C. House votes flipped by 14 percentage points back toward Republicans, as they secured a 59-40 percent margin in total votes and completely reversed the total number of House seats under the two parties’ control, with the GOP taking a 68-52 majority.

The Senate, which had experienced only minor changes in total vote share from 2000 to 2008, saw an 11-point swing in 2010. Republicans outpolled Democrats, 59-41 percent, statewide. They also turned the Democrats’ 30-20 Senate majority into a 31-19 margin favoring the GOP.

As a reminder, Republicans secured these large advantages using election maps drawn by Democrats to benefit Democrats — a goal Democrats had succeeded in achieving during election after election earlier in the decade.

It’s unclear whether an efficiency gap analysis could capture these major shifts accurately. Why? Because it says nothing about voters’ shifting preferences.

Voters’ decisions can vary based on a number of factors, including the candidates and issues in a particular race, other elections on the ballot that year, even the weather on Election Day.

The “efficiency gap” concept ignores these real-world factors. It also fails to account for a candidate who consistently earns bipartisan support. Or for a district in which the incumbent is so popular that no credible challenger wishes to spend time and money trying to unseat him. Whose votes are “wasted” in these scenarios?

Partisan gerrymandering is bad. North Carolina ought to pursue an alternative. But this new statistical tool appears to fall short of bridging the gap between academic theory and electoral reality.

Mitch Kokai is an associate editor of Carolina Journal.