The Science of Ballot-Box Stuffing

Sometimes election fraud can be laughably obvious. When Vladimir Putin took 99.8 percent of the vote in Chechnya in this year’s Russian presidential election, it probably wasn’t because the republic where he had violently crushed an armed insurgency a little more than a decade ago had developed an overwhelming affection for him. But sometimes, when the fraud is a bit subtler, more sophisticated methods of detection are needed.

Political scientists Bernd Beber and Alexandra Scacco of New York University have discovered an unusual method to detect rigged voting: looking only at the numbers. They came upon the idea somewhat by accident and wrote up their findings in the journal Political Analysis.

"We were in Nigeria for other fieldwork and got our hands on presidential election results from 2003 from the polling-station level," Beber explains. "We noticed that just looking at the return sheets, some of them looked off. But we couldn’t quite put our finger on it."

Try this experiment: Grab a pencil and, as quickly as possible, write down a string of 20 random numbers. You might think there’s no pattern to the numbers, but chances are you’re wrong. Psychologists have found that when making up long strings of numbers, people tend to overuse small digits, underestimate the number of times digits will repeat themselves, overuse pairs of adjacent digits like 2-3 or 7-8, and underuse pairs of distant digits like 1-7 or 9-2. In short, people aren’t very good at making up numbers that seem random.

When Beber and Scacco examined the results from the Nigerian election — where there had been widespread and credible accounts of fraud — they found several of these exact inconsistencies. In particular, local tabulators tended to overuse zero as the last digit in returns and underuse the number 2. Zeros were overused in general. When the authors applied the same analysis to a Swedish election where there had been no reports of fraud, they found no such inconsistencies.

The study also looked at Senegal’s controversial 2007 election, which returned President Abdoulaye Wade to power and in which fraud was alleged but not proven. Suspicious digits — particularly the abundance of zeros — again appeared in these returns, suggesting that Wade’s reelection might have been partially rigged. (He was finally removed from power after another controversial election this year.)

This method detects only numerical fraud in vote counting, not other methods like physically stuffing the ballot box or voter intimidation, but Beber and Scacco hope it can become part of the tool kit for international election monitors. They also freely admit that the publication of their research may help would-be election cheats improve their techniques, perhaps by employing a computerized random-number generator to eliminate unconscious habits or by tossing a couple of extra 2s into the mix.

"There’s a bit of an arms race between people engaging in election fraud and those trying to detect it," Beber says. "We’re going to have to keep innovating, but at least we’re making their job a little more difficult."