Metaphorically, we suspect the Russians may be giving us the statistical finger. They appear to be sending signals that they are on to election forensics researchers — while continuing to cheat, obviously, right in front of us.

AD

AD

Some background: Tests used in election forensics research assume that when elections are clean, we see certain patterns in the vote counts, while deviations from those patterns may indicate manipulation.

The 2016 Russian election

So what happened in Russia? In the September Duma election, Russians cast two ballots. One ballot was called “proportional representation.” On that one, they voted for a party — and then legislative seats were divvied up among the parties to match the proportion of the vote each party won.

AD

On the other ballot, Russians voted for a particular candidate running for a single-member district seat, as a U.S. candidate would.

AD

Half the seats were allocated in each way. A similar mixed voting system was used between 1993 and 2003.

The 2011 Duma election was marred by allegations of fraud and massive protests. And so in 2016, Russia worked hard to build up the election’s credibility — for instance, by appointing a new head of the election commission.

At the same time, Russia restricted citizens’ ability to register as candidates, form party blocs or campaign, and they shifted Election Day to the fall, discouraging many voters. They also limited international observers’ ability to evaluate the election.

AD

Observers report fewer cases than in 2011 of vote rigging or conflicts between the observers and election committees. But observers did report ballot stuffing and other violations. According to a polling agency closely aligned with the state, exit polls show that the pro-government United Russia party should have received 44.5 percent of the vote — but official tallies recorded that UR won with 55 percent of the vote.

Many voters chose to ignore or to boycott the election, but the Kremlin apparently used regional political machines to manipulate votes — and report an overwhelming victory for the party of power.

AD

The Russian government denies any allegations of electoral violations.

AD

What makes us think the totals were fraudulent?

Here’s one answer. Methods developed by New York University political scientist Arturas Rozenas show that too many precincts report that United Russia won more than 50 percent of the vote in numbers that can be evenly divided by five: 55 percent, 65 percent, 70 percent, 75 percent, 80 percent, 85 percent, 90 percent, 95 percent or even 100 percent (analysis details are here).

We’ve found similarly obvious patterns in vote percentages in Russian national elections from 2000 to 2016. This kind of fraud can function as a signaling mechanism by which regional governors display their loyalty to the Kremlin. An article by Ashlea Rundlett and Milan Svolic presents analogous analysis showing that agents who commit frauds may do so in ways that allow their efforts to be detected.

AD

AD

We also used a positive empirical model of election frauds, and found two kinds of fraud indicators were vastly higher in 2016 than in earlier years’ elections: incremental fraud, in which some votes appear to be redirected to the winner, and extreme fraud, in which almost all votes go to the winner, which of course is extremely unlikely. In 2016, we concluded that about 3.6 percent of votes recorded for United Russia (nearly two million votes) were fraudulent. Manufacturing votes from nonexistent voters appeared to predominate over stealing votes from other parties.

And then we find 4.187, which is a very special number

So where’s the finger?

Consider the following statistics for Russia’s 2016 election. We computed both turnout and the total vote for every party that was reported as having more than a million votes in the proportional representation election.

This paper, written for a grant funded by USAID, describes in detail what all these statistics are.

AD

AD

But to see the oddity, here’s what you have to know. These are among the statistics often cited as indicators of election anomalies. When several of these indicators differ significantly from what was expected, there’s a high probability that the election included fraud.

Almost across the board, the statistics differ significantly from expectations.

There are two exceptions.

And this is the special moment. The exceptions are too perfect.

An article by Luis Pericchi and David Torres argues that Benford’s Law (which implies that smaller digits occur more frequently than larger digits) can help us detect anomalies. Chapter 9 in this book of essays about Benford’s Law points out that, given that, the mean of vote counts’ second digits should be 4.187.

AD

To four significant figures, that is the value observed for the mean of the second digit (2BL) of the number of voters in each of 96,869 precincts.

AD

This article by Berndt Beber and Alexandra Scacco argues that each of the 10 possible last digits of vote counts should occur equally often, in which case their mean is 4.5. That is the value observed for the mean of the last digit (LastC) of the votes in each precinct for United Russia.

Those two statistics are perfect. The Russians appear to be telling folks like us that they have pretty good skills at faking vote data. What’s more, the other elections since 2004 have similarly perfect digits in votes for Putin or United Russia.

AD

The Russian government denies any allegations of electoral violations.

They know we’re watching. We know they know we’re watching.

But given the variety of tasks they need to accomplish with the elections, they cannot pass every test in the election forensics tool kit. Signaling happens for domestic political reasons. Apparently they aren’t simply faking all the votes. Instead, they appear to just add a few (millions).

Kirill Kalinin is a PhD candidate in political science at the University of Michigan.