Electoral Fraud in Russia: Report from the Russian Blogosphere

The following is a guest post from Scott Gehlbach, a political scientist at the University of Wisconsin-Madison:

In a recent post on the Monkey Cage, Andrew Gelman writes that he was “not convinced” by a recent attempt to debunk evidence of fraud in Russia’s recent parliamentary elections, though he asserts that he knows “nothing about Russian elections” and suggests that “others can feel free to clarify.” There is, in fact, quite a bit of information floating around the blogosphere on December’s Duma elections, though most of it is in Russian and not accessible to the typical reader of the Monkey Cage. Here is my attempt at translation.

Some necessary context: The statistical analysis of electoral fraud in Russian elections dates to the pioneering work of Alexander Sobyanin, a Russian physicist who examined voting and turnout in the 1993 constitutional referendum. There is superb academic work on the topic by Mikhail Myagkov, Peter Ordeshook, and Dimitri Shakin, who built on and extended Sobyanin’s insights in a number of important publications, culminating in The Forensics of Electoral Fraud (Cambridge University Press, 2009). Finally, the bloggers Alexander Kireev and Sergei Shpilkin have provided some of the best real-time analysis of the recent elections.

The basic idea in all of this work is that electoral fraud should be evident in election data sufficiently disaggregated. In fact, certain anomalies are visible in the Russian elections using region-level data alone. Exhibit A is Chechnya, where both turnout and vote for United Russia were in excess of 99%. But we can do better, thanks to the generosity – or foolishness – of the Russian Electoral Commission, which makes precinct-level data freely available for download.

In practice, most analysis has focused on three indicators: the distribution of vote shares across precincts, the distribution of turnout across precincts, and the relationship between vote shares and turnout. Starting from the top, here is the distribution of precinct-level vote shares for United Russia:

As noted by various commentators, the distribution is not normal, though we would not necessarily expect it to be. The distribution of vote shares in Ukraine, for example, is typically bimodal, the consequence of a sharply divided political geography in which it is easier to get 10% or 90% of the vote than something in the middle. But the thickening right tail is suspicious, and the large number of precincts reporting that nearly everybody voted for United Russia is very suspicious. If you look closely, you also see spikes at familiar simple fractions: 3/4, 4/5, etc. Also informative is the dip in the distribution at 49%, reminiscent of the Soviet-era practice of just meeting the plan.

In contrast to vote shares, one might expect the distribution of precinct-level turnout to be approximately normal, to the extent that voters are making idiosyncratic decisions about whether to vote rather than do something else. Yet here too we see the ski jump from hell, with a huge swoop up as we approach 100%.

Further, if we group precincts into smaller bins, then again we see spikes at “target” levels of turnout.

Of course, we cannot tell from these figures alone whether targets are being set from above or are the result of some sort of decentralized competition among precincts, but it sure looks as though the election workers caught on cell-phone cameras stuffing ballot boxes knew they weren’t going home until they hit a certain number.

Finally, we can look at the relationship between vote shares and turnout at the precinct level. Here it is for United Russia:

United Russia does well where turnout is high. Of course, the Republican Party does well where turnout is high, and nobody who knows anything is alleging massive electoral fraud in the U.S. But the magnitude of the relationship in Russia is such that United Russia is scooping up essentially all of the marginal votes over a certain level. Maybe they’ve all just been reading Green and Gerber, but I doubt it.

So, what is one to make of all of this? The inference that has been drawn in the blogosphere, which it is probably clear I find compelling, is that there was substantial manipulation in some precincts that took the form of ballot-box stuffing for United Russia. Why those precincts and not others? One possibility is that vote rigging was discouraged where election observers were present. Indeed, United Russia did substantially worse in precincts with election observers, but unfortunately election observation was not randomly assigned. United Russia also did worse in precincts with electronic ballot-counting machines, but here too we don’t have a good experiment. We do, however, have another election just around the corner, and with it, more data…

6 Responses to Electoral Fraud in Russia: Report from the Russian Blogosphere

  1. crf January 27, 2012 at 2:57 am #

    Any info on the precincts that had 100%, or close to it, turnout?
    Are any very small? Are any military towns? Institutional?
    It is not clear that there wouldn’t be towns where 100% turnout wouldn’t occur.

  2. Andrew Gelman January 27, 2012 at 9:08 am #

    The following sentence does not make sense to me: “one might expect the distribution of precinct-level turnout to be approximately normal, to the extent that voters are making idiosyncratic decisions about whether to vote rather than do something else.” It makes no sense because turnout is subject to factors more important than “idiosyncratic decisions” and it makes no sense because there’s no reason to suspect a process based on such decisions to aggregate to a normal distribution. On the other hand, the gap at 49% seems suspicious, as does the scatterplot (which appears to be a simpler version of the multicolored scatterplot shown here and the graph with the spikes at round numbers (again shown, I believe more clearly, in the graph on that linked page).

    • Joshua Tucker January 27, 2012 at 10:57 am #

      Andy: Is there any good reason for the spikes at all the round numbers on the United Russia vote other than fraud?

      • Andrew Gelman January 27, 2012 at 2:26 pm #


        I can’t think of any—that’s why I agree that the numbers are suspicious—but I don’t know anything about Russian politics! The argument about the normal distribution is silly and wrong, but the spikes seem like they need an explanation.

        • szasulja January 30, 2012 at 7:01 am #

          Spikes are argued to be a consequence of “elementary number theory”. (though I lack the knowledge to judge whether it is a valid argument.)
          For details and A great summary of Russian election maths, in English see: sublimeoblivion.com/2011/12/26/measuring-churovs-beard/

  3. Wonks Anonymous January 30, 2012 at 7:38 pm #

    I thought it was supposed to be Democrats who did well when turnout is high. They have traditionally had an advantage in terms of identification/registration (although I’ve heard most recently that’s eroded), and many of their constituents are deterred by things like bad weather (urbanites less likely to own cars).