Here’s why statisticians are calling Putin’s constitutional plebiscite the most fraudulent vote in Russia’s recent history

Researchers who study Russia’s electoral statistics believe that the recent nationwide plebiscite on constitutional amendments is the most dishonest vote the country has seen since the year 2000. According to statisticians, their “tests” have revealed a number of red flags that support these claims: from a statistical point of view, the official results in many precincts can’t be attributed to fair voting processes. Researchers say that the only explanation is that somehow, officials responsible for tallying the votes changed the results. According to official data from Russia’s Central Election Commission, a little more than half of the country’s eligible voters supported the changes to the constitution. But if you exclude all of the “excess” votes from precincts that don’t pass statistical “tests,” it turns out that less than a third of Russia’s voters supported the amendments.

How electoral statisticians find red flags

Since the 1990s, Russian researchers from a number of fields have been developing a theory of statistical analysis for elections, based on the idea that the results of a fair vote (established by counting the actual number of ballots cast) look different than voting results chosen “by hand” (in other words, a falsified result). 

Physicist Sergey Shpilkin has been Russia’s most well-known electoral statistics researcher since the end of the 2000s. According to his theory, there are a few ways to “test” for potential electoral fraud. Red flags include:

• An increase in the percentage of votes cast for the leading candidate (or in this case, the authorities’ desired result) at a precinct with high turnout (relative to the proportion observed in a precinct with lower turnout). This can indicate that unused ballots are being thrown in as votes in favor of the desired candidate or result. Researchers say that during a fair election, the distribution of votes should look proportional, regardless of the turnout.
• The appearance of two visible “clusters” in the distribution of polling stations in terms of voting results and turnout: one with relatively low turnout and a relatively low percentage of votes in favor of the leading candidate, and one with very high turnout and a high percentage of votes for the front runner. In this case, the average results for the region or the country may fall somewhere in the middle (between the two the clusters). This can indicate that the results in precincts belonging to the high-turnout cluster were falsified, in order to increase the regional or countrywide average.
• Precincts (especially those with high turnout) having voting results and turnout numbers that end in 5% or any repeated number. If these results are especially common, they will stand out on a graph and look like the teeth of a saw — peaking at 65 percent, 70 percent, and 75 percent, for example, — or form a straight line tied to a particular number (for example, in Russia’s 2016 parliamentary elections, 140 polling stations in Saratove saw 62 percent of voters cast their ballot for the ruling party, United Russia). This can mean that election officials adjusted the results to a particular number. 

So what happened during the plebiscite? 

Sergey Shpilkin and his colleagues have revealed that according to the three aforementioned “tests,” Russia’s nationwide vote has become the most falsified in the country’s recent history.

• In more than half the regions with turnout starting at 50 percent, many precincts saw the number of votes in favor grow faster than the number of votes against.
• Graphs mapping the distribution of votes and voter turnout show two clearly visible clusters: those with approximately 45 percent turnout saw 65 percent vote in favor of the amendments and 35 percent vote against, while those with 80 to 100 percent turnout saw between 70 and 100 percent support. The average turnout for the country was 65 percent and only a few precincts saw 77 percent of voters vote in favor. The graph shows one dense spot in this area, representing the results from precincts in Kazan.

• Two clusters and a disproportionate increase in supporting votes were also identified in precincts with high voter turnout, including in Moscow, where the results in the last few elections have typically looked relatively realistic. The anomalies this time around were likely made possible by the peculiarities of the voting process: the plebiscite was spread out over the course of a week and most of the votes were cast remotely — without being monitored by election observers.

• Finally, the distribution graph does in fact look like a saw, with large “teeth” corresponding to 65, 70, 75, 80, 85, and 90 percent turnout. According to researchers, the “peaks” in the vote on constitutional amendments have outflanked all previous federal elections in the 2000s.

What does this mean?

According to Shpilkin’s model, 65 percent of voters who cast their ballots supported the amendments to the constitution (the official result was 77.92 percent), while actual voter turnout was around 45 percent (the official number was 67.97 percent). As such, around 30 percent of Russia’s voters (32 million people) voted in favor of the amendments — not 52.95 percent of eligible voters or 57.7 million people, as the Central Election Commission claimed. This means that there could have been more than 20 million falsified votes favoring the changes.

Is there another explanation? 

On the one hand, Shpilkin’s model has clear limitations: in reality, for example, the distribution of voter turnout doesn’t have to be “normal” — as the model suggests. This means that the model can consider biases, which theoretically could arise due to disparities in the distribution of voters across precincts, as falsifications. However, these disparities still can’t explain the official results of Russia’s elections over the past 16 years. 

On the other hand, the model has the potential to miss a number of instances of possible fraud: for example, it considers the unusually high voter turnout in many parts of the Russian Caucasus “realistic.” Elections in these regions are known for having nearly 100 percent turnout with almost all precincts showing full approval for the authorities’ preferred candidate — as such, there are simply no “honest” precincts available for comparison, which could call the results into question.