As with pretty much any Russian election over the past decade, evidence of electoral fraud has begun to surface. Reports of "carousel voting," paid voters being shuttled by bus to vote at multiple polling stations, ballot stuffing, and an impossible figure of "107% turnout" in a Chechen precinct all suggest some degree of manipulation. Was this fraud then systematic or idiosyncratic? In the wake of the 2011 Duma elections, many Russian bloggers used statistical analysis techniques to uncover strange patterns in the reported results for United Russia. Scott Gelbach posted an English summary of some of these findings. Do the same observations hold for the presidential election?
I gathered the precinct-level data reported by the Russian Election Commission and looked at the three main "problematic" distributions. The first is vote shares across precincts:
The distribution is certainly less skewed than it was for United Russia, which can be attributed to the fact that the genuine popularity of Putin compared to his party decreased the necessity of much falsification. Nevertheless, one again sees the distribution suspiciously widen at the right end and the existence of a significant number of precincts where essentially everyone voted for Putin is likewise odd, particularly given the anecdotes from regions like Chechnya. However, the non-normality of this distribution is not necessarily conclusive evidence of fraud. It does, however, illustrate a heavily skewed and non-competitive electoral system. More odd are the spikes in the precinct counts at what appear to be the round numbers and simple fractions in the 60 to 80 percent range. Gelbach notes a similar phenomenon in the results for United Russia, though it is certainly less pronounced here
What of the distribution of turnout*? Gelbach argues that this should be roughly normal "to the extent that voters are making idiosyncratic decisions about whether to vote rather than do something else." Yet again, one sees an upward sloping tail on the right end and a huge spike at 100.
Grouping the turnout data into smaller intervals, one sees some spikiness at crucial benchmarks, though it is less pronounced compared to the results from December:
Finally, turnout and percentage vote for Putin are highly correlated:
As with United Russia's voting percentage, Putin's results are strongly associated with turnout. As a number of people have pointed out, this does not necessarily indicate fraud. For example, a strong GOTV campaign may mean that a candidate tends to get more voters as turnout increases. Yet as Gelbach noted: "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." In the case of Putin's results, the relationship is not as strong (again, owing to the fact that Putin's actual level of popularity is still relatively high). Nevertheless, the correlation at the upper levels of turnout is such that it's difficult to conclude that manipulation was insignificant.
Again, the patterns in the electoral results are suggestive of some fraud, but the degree appears to be lower than in December. This may be partly due to the decreased necessity of boosting Putin's results. Indeed, the curious decision to install web-cams at all polling places may be evidence that the Kremlin, knowing that the incumbent would win handily, wanted to keep overt reports of fraud to a minimum. As Josh Tucker commented, if the election was meant as a signal to the public that Putin remains popular, compromising footage of ballot stuffing and ham-handed manipulation would weaken the message. So while there is a disincentive to commit visible fraud, there is still a logic behind committing less clearly observable fraud (Andrew Little wrote a good post recently on this point). So the statistical evidence combined with anecdotal reports from observers strongly suggests that systematic cheating, while much less blatant than in the Duma elections, likely occurred.
Part 2 of this post will apply some more advanced statistical techniques to examine the variation in fraud levels across the different regions.
*I compute turnout as (Number of Valid Votes + Number of Invalid Votes)/(Number of Registered Voters). The Russian electoral commission site does not give a clear percentage figure of turnout.