Why Statistics Only Support 3%-6% Fraud

Remember Sergey Shpilkin? He is the mathematician, blogging as [info]podmoskovnik, who estimated 16% fraud for the Duma elections (also the one whom the WSJ plagiarized off). He got this figure by assuming that in a fair election, the share of the vote for each candidate at each level of turnout had to be a constant factor.

This is, of course, a flawed assumption, as I argued extensively in Measuring Churov’s Beard. First, that would imply that elections in countries such as Israel, Germany, and the UK – where the share of the vote for right-wing parties rises with turnout – are also falsified. Second, it is further refuted by Russian opinion polling evidence: Rural Russians are both more more likely to vote than urban ones, and more of them would vote for Putin.

This influence of electoral sub-groups partially explains United Russia’s “fat tail” to the right of a turnout / share of the vote graph (although NOT the spikes at 80%, 85%, 90%, and 100%, or the general “bump” in that region). As such, we can say with confidence that the level of falsifications was significantly lower than 16%, i.e. around the 6% or 7% indicated by FOM’s exit poll.

Anyhow, Shpilkin repeated his exercise for the 2012 Presidential elections, and the fraud figure he got was much lower this time, at 6% (official result: 63.6%; result according to this method: 57.5%). Using the same method Kobak got 57%. Here is a graphical comparison of the two elections using Shpilkin’s graphs:

The bottom axis is turnout in the 2011 Duma election, and the vertical axis is percentage of the vote. The green line is the vote for non-UR parties, the blue line is the vote for UR, the cyan line is the vote for UR if it remained strictly proportional to the votes for the other parties on the right hand side of the graph as well as the left, and the purple line denotes the anomalous part of the votes for UR. The latter are 16% of all the votes, and are taken by Shpilkin to be synonymous with falsifications.

This graph shows the exact same for the 2012 Presidential elections, just replace UR above with Putin. The anomolous part of the graph is visibly much less, at 6% of the total votes.

Of course, as acknowledged by Shpilkin himself in discussions with another mathematician Dmitry Kobak (if not in the media), this method is flawed, and a more accurate approach would be to break down this analysis by region, with separate graphs for cities and villages. This approach, which is far more accurate, yields 59% for Putin, i.e. about 4% something falsifications. (I.e., almost exactly matching the results of the FOM exit poll, at 59.3%, and the VCIOM exit poll, at 58.3%).

One caveat is that the separation between “cities” and “rural” may still be too crude, even at regional levels; there are still significant differences between voting patterns in bigger towns and smaller towns, for instance, with the latter closer to the profile of villages (i.e. higher turnout, and more votes for Putin. This may trim down the fraud by half of to one percentage point.

(A similar exercise for the Duma elections yielded a result of 39% for United Russia. Since this way of estimating fraud gives plausible results for the Presidential elections, this has made me reevaluate my old estimate of 5%-7% fraud in the Duma elections, based off the results of the FOM exit poll, to perhaps 8%-9%.)

There are three further points I’d like to make then:

(1) The Presidential election, though still very sub-par, was not just modestly but A LOT cleaner than the Duma ones. The absolute lowest feasible “floor” on Putin’s real result is around 57% (note: confirmed by properly adjusted figures from observers). This is well above the critical 50% mark that the radical opposition and Western journalists claim that Putin actually got.

(2)  I was predicting that Putin would get about a real result of 56%-57%, as in the forecasts of the major polling agencies, and about 2%-3% of fraud would raise it to 58%-60% (hence, I predicted 59%). In reality, his real result was probably 59%-60%, with still higher than what I expected fraud of 4% raising it to 63.6%.

(3) As the adjusted Shpilkin/Kobak statistical method appears to be reliable, the real level of fraud in the Duma elections may well have been closer to 10% than to 5%, which would begin raising real questions about its legitimacy.


  1. Rashabasha says:

    Elections are like an erection. Dysfuction cannot be measured only by calculating the percenteage of the fairness during the actual action. It all begins much more earlier, and underlying causes can be traced back to physical and psychological conditions of the holder. We should not forget that dysfunction is usually also an indicator of a more severe or even pathological condition.

    Now if you argue that you have got around 95% it is obvious that for most of us it is definitely not enough. Flaccidness of the whole thing is evident.

    But all is not lost yet – at least Russia is not suffering dysfuntion in silence, but many are openly admitting there is a problem. That is the first step towards a more pleasurable life.

  2. yalensis says:

    So, if BOTH elections had been fair and accurate, according to Shpilkin/Kobak method, then Putin would still be Prez, but KPRF would have majority in Duma? Now THAT would be interesting political layout! I said at the time Ziuganov should have been given the Speaker post. If nothing else, just to shut him up. He is a bitter, bitter old man.

  3. Alexander Mercouris says:

    The one thing I would say about this is that I would be careful making assumptions about the parliamentary elections because a particular statistical model produces results that correspond with one’s assumptions about the presidential elections. These are two different elections and should be studied on their own terms. Bear in mind that a 39% result for United Russia in the parliamentary elections is far lower than both the opinion poll and exit poll results would lead one to suppose. It would suggest either that those poll results are completely wrong or that they are fixed in advance in the way that some (eg. Eugene Ivanov) says. I find that very difficult to believe in either case. Also it would imply that United Russia is polling 20% below Putin, which I find difficult to credit given that the party is associated with him.

    My own opinion for the little it’s worth is that fraud levels in both the parliamentary and the presidential elections were about the same at around 5% with electoral fraud firmly embedded in the political culture in certain regions where it works in the interests of local politicians. In national terms fraud in these places tends to work in favour of the ruling party be that the CPSU in 1989 and 1990, Yeltsin in 1996 or Putin and United Russia now. The reason the question of electoral fraud in the presidential election has caused so much less of a stir than it did in the parliamentary election is not because it was necessarily less but because in the parliamentary election the result was so much closer. In the presidential election Putin’s win was so decisive that it was not seen to matter.

  4. I would like to see a comparison of “authoritarian” Russia’s 5% fraud with that of the self-anointed beacons of democracy in the west. Without a context anything bigger than zero can be spun as evidence of lack of democracy. The 5% fraud was totally irrelevant for the results of this election. But even a much smaller level of fraud made the difference between minority and majority for Canada’s Harper regime. The 2000 US presidential election would be another example where Gore had to concede to Bush because of the shenanigans in Florida.

    I would say that Russia’s polling system + 5% fraud is vastly superior to the first past the post racket in the west. A government should not have a majority or win when it gets 40% of the popular vote. I know that Germany and other European states have better polling systems, but they are not the organizing core of western foreign policy and play second fiddle to the US.

  5. Alexander Mercouris says:

    Dear Kirill,

    One point that is rarely discussed though I have heard it mentioned is that the electoral boundaries of Congressional districts are now so tightly drawn as to make it extremely difficult in the great majority of cases to oust the incumbent. Also one simply cannot compare the cost of Russian elections with that of elections in the US, which is off the scale. It seems to me that the US and the UK have bad electoral systems that operate reasonably though not completely honestly and that Russia has a good electoral system but one which is still implemented in places but not everywhere in a dishonest and flawed way. The aim now should be to improve the electoral system by working hard to reduce fraud where it exists. The web cameras were a start but in the worst places such as the northern Caucasus that is an immense challenge and one that is closely tied up with the economic, social and security situation there.