In the aftermath of the 2011 Duma elections, the Russian blogosphere was abuzz with allegations of electoral fraud. Many of these were anecdotal or purely rhetorical in nature; some were more concrete, but variegated or ambiguous. A prime example of these were opinion polls and exit polls, which variably supported and contradicted the Kremlin’s claims that fraud was minimal. But there was also a third set of evidence. Whatever problems Russia may have, a lack of highly skilled mathematicians, statisticians and programmers certainly isn’t one of them. In the hours and days after the results were announced, these wonks drew on the Central Electoral Commission’s own figures to argue the statistical impossibility of the election results. The highest of these fraud estimates were adopted as fact by the opposition. Overnight, every politologist in the country – or at least, every liberal politologist – became a leading expert on Gaussian distributions and number theory.

While I don’t want to decry Churov, the head of the Central Electoral Commission, for making subjects many people gave up back in 8th grade fun and interesting again, I would like to insert a word of caution: lots of math and numbers do not necessarily prove anything, and in fact – generally speaking – the more math and numbers you have the less reliable your conclusions (not making this up: the research backs me up on this). Complicated calculations can be rendered null and void by simple but mistaken assumptions; the sheer weight of figures and fancy graphs cannot be allowed to crowd out common sense and strong diverging evidence. Since the most (in)famous of these models asserts that United Russia stole 15% or more of the votes, it is high time to compile a list of alternate models and fraud estimates that challenge that extremely unlikely conclusion – unlikely, because if it were true, it would essentially discredit the entirety of Russian opinion polling for the last decade.

In this post, I will compile a list of models built by Russian analysts of the scale of electoral fraud in the 2011 Duma elections. I will summarize them, including their estimates of aggregate fraud in favor of United Russia, and list their possible weak points. The exercise will show that, first, the proper methodology is very, very far from settled and as such all these estimates are subject to (Knightian) uncertainty; but second, many of them converge to around 5%-7%, which is about the same figure as indicated by the most comprehensive exit poll. This is obviously very bad but still a far cry from the most pessimistic and damning estimates of 15%+ fraud, which would if they were true unequivocally delegitimize the Russian elections.

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