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…