For voters around the world, including the millions of Americans who will cast ballots in the midterms up to and on November 6, an election is democracy in action—an opportunity to make their voices heard, have a say in how their government is run and, if necessary, throw the bums out. It is a thoroughly political exercise, or so it would seem.

But to Peter Klimek, who works in the emerging field of electoral forensics, an election is something else as well. “Basically it is a huge, standardized social experiment,” he says. “What you are doing is taking the population of a country and segmenting it into different subpopulations—the eligible voters in their separate polling stations. Then you are having each one of them answer the same questions.”

And because huge experiments like elections follow the law of large numbers,  a bedrock principle of probability, those answers from the voting data should show “certain statistical regularities,” says Klimek, who studies complex systems at Medical University of Vienna. When they do not, when there are instead statistical anomalies, that other F–word—fraud—may be the reason.

That appears to be the case with the results of Turkey’s 2017 constitutional referendum and its 2018 presidential election, which Klimek and colleagues analyze in a paper published earlier this month in PLOS ONE. Using their own set of statistical tools, the researchers identified multiple irregularities in both elections that they attribute to systematic ballot stuffing (submission of multiple ballots per person during the election) and voter rigging (defined as coercion or intimidation of voters). In the case of the constitutional referendum they wrote, “removing such ballot-stuffing characteristic anomalies from the data would tip the overall balance from a majority of ‘No’ to a majority of ‘Yes’ votes.” Klimek says, “We’ve showed that you can develop a unique tool set that allows you not only to screen a data set for potential signs of fraud but also to identify the specific methods used.” One of the most important features of such forensic tool kits (others in the field have created their own) is their portability. They can be used to analyze elections around the world, and a physical presence is not necessary. All that’s required is the voting data, ideally at the level of individual polling stations, which can usually be downloaded from official government Web sites.

There is clearly a need. A 2010 analysis of data from elections conducted in more than 170 countries between 1978 and 2004, published on the Social Science Research Network, found signs of some cheating in 61 percent of the countries, and major problems in 27 percent of them. Since the early 2000s various research groups, including Klimek’s, have used forensic tools to examine elections in multiple countries including Venezuela, Kenya, Cambodia, South Africa, Bangladesh and Argentina.

Although the new paper from Klimek’s group includes a disclaimer that it is “by no means direct proof of electoral fraud,” it makes a strong case the Turkish elections were marred by malpractice. And, the authors wrote, the patterns of irregularities in the two elections, held 14 months apart, were barely distinguishable from each other. “We found exactly the same malpractices in exactly the same districts in 2018 as we did the year before,” Klimek says. Making that kind of connection is key to preventing fraud in future elections, he adds. “If you want to get some policy-relevant actions out of this kind of research, you need to be able to tell what happened with which likelihood in which geographical area,” he notes.

The researchers worked with data from the official Web site of the Turkish election commission. To detect signs of ballot stuffing, they used the number of voters, the number of valid ballots cast (turnout) and the total votes tallied by the winners (‘Yes’ in 2017’s referendum and for Pres. Recep Tayyip Erdogan in 2018) to create an “election fingerprint” for each of the polling stations they analyzed.

For the 2017 referendum, they crunched the numbers from 153,701 stations, grouped in 28,447 neighborhoods. For the 2018 election, they looked at 168,377 stations in 44,796 neighborhoods. When the data was plotted in two dimensions and compared with standardized fingerprints from trustworthy elections with normal distributions, Klemik’s team found “highly significant statistical support” for ballot stuffing in 11 percent of the polling stations they analyzed. (Ballot stuffing inflates both turnout and the percentage of winning votes.)

Election fingerprint analysis also turned up evidence of possible voter rigging at small, rural polling stations—which are less likely to be monitored by poll observers than large urban stations are, and where it is easier to identify the political leanings of individual voters. “That makes it much easier to conduct certain malpractices,” Klimek says, such as intimidating voters with an excessive police or military presence.

Walter Mebane, a professor of political science and statistics at the University of Michigan and co-author of a 2017 guide to election forensics for the U.S. Agency for International Development, urges caution when attributing election anomalies to possible fraud. “The problem is that many of the patterns that look irregular according to many statistical methods can be produced by strategic behavior, or normal politics,” he says. “You can tell that the pattern was manipulated or looks unusual, but you can’t tell why.”

Figuring out the “why” is the next big challenge, according to Mebane, a pioneer of the field. “Politics is weird, to use a technical term. All kinds of bizarre things can happen. I think the limit of election forensics, and this is the frontier of my research right now, is to try to see how well we can discriminate frauds from human behavior.”

An even more basic challenge faces researchers who want to use forensic tool kits to analyze U.S. elections—getting the data. “The way elections take place and are administered in the U.S. is not really up to the quality standards in other countries,” says Klimek, who tried and failed to apply some of his methods to the 2008 election. “The data quality was not good enough.” In most states, access to voter registration data is restricted mainly to the political parties, the candidates and some companies that work with them, Mebane says. 

After a 2016 presidential election marred by allegations of foreign meddling, the midterm contest looms amid concerns about voter suppression in Georgia and other states as well as unsubstantiated claims of widespread voter fraud by undocumented aliens. The most unexpected takeaway from electoral forensics may be that it is easier to analyze Russian elections than those in the U.S. “It’s really not much work to do this kind of analysis once you’ve got the data,” Klimek says. “With the algorithms we are talking about, it can be done in a couple of hours.”