lauantai 10. joulukuuta 2011

Russian legislative elections 2011 - statistical evidence of vote fraud.

You probably have heard about alleged vote fraud in the Russian legislative election 2011. You might even have seen videos about cases of vote rigging. The ruling party dismisses allegations, because even if some of the cases may have been proven, there are too few of these cases to jeopardize the legitimacy of the whole election. Some of the opposition disagrees with this and is taking it to the streets. There were over 95000 polling stations in the election and of course election observers were not present in all of them. So few Russian citizens wondered if there would be some statistical support to the claims of systematic vote rigging. I have gathered information from three different Russian blog-posts that present such statistics. There are thousands of different reasons that can slightly alter the vote turnout at any given polling station. Some of these reasons affect the turnout positively, some of them negatively, but since the reasons are mainly random it is extremely unlikely that the turnout of a certain polling station differs a great deal from the average turnout of the elections. Usually when you plot the polling station by their turnout percentage you get a Normal distribution . Here's a picture:

 In the above picture the X-axis shows vote turnout and the Y-axis shows amount of polling stations. From left to right the four curves represent Mexican legislative election 2009, second round of Polish presidential election in 2010, Bulgarian legislative election in 2009 and Swedish legislative election in 2010. Tendency towards a normal distribution is obvious. Now let's take a look if Russian elections in 2011 follow the same logic:

 You can see the normal distribution all the way to the 55% turnout. Then something strange happens. For some reason turnout significantly larger than the mean is far more likely than turnout significantly lower than the mean. This cannot be explained by existence of very small polling stations since the results are weighted. So maybe it's just one of those Russian things like excessive alcohol consumption. Let's take a look at the previous four election in Russia:

 The pale brown curve is for the 2003 legislative election, the dark brown curve is for the 2007 legislative election, the light blue curve is for the 2004 presidential election and the dark blue curve is for the 2008 presidential election. Once again we observe normal distribution until the 55% turnout mark. But take a look at those spikes at 70%, 75%, 80%, 85%, 90% and 98%! There are two ways to explain this. First explanation is that for some unknown reason voters of large amount of polling stations coordinate their actions by setting a target turnout. The second explanation is that there is systematic vote fraud at some of the polling station with specific target amount of votes. Take for example the 98% spikes in the curves. Imagine that you are committing a vote fraud. You don't want to get caught and 100% turnout is easily proven false as soon as one of the citizens of the area tells that he didn't vote since he was out of town. So, since you live in Russia and not North Korea, you make the turnout 98%. Take for example the 2011 legislative election in Chechnya: the turnout is 93.31% and 99.48% of votes go to United Russia party. One could use the argument that the even percentage spikes are there because of very small polling stations. In a polling station with 20 voters all of the possible turnout outcomes end with 5 or 0. But there are not that many small polling stations, and even if there were, you would expect the similar spikes at polling stations with low turnout.

 So, now that we concluded that there is something fishy about Russian election, the next question is who benefits from this? The opposition blames the United Russia party, which holds the majority of lower and higher house parliament, as well as the presidential seat. United Russia denies vote fraud. Accusing opposition of vote rigging would take away the legitimacy of the election and if you're the one in power you don't want to do that. One might ask why would United Russia, Putin or Medvedev resort to vote fraud despite the fact that they are truly popular in Russia and would get a majority or close to a majority of parliament seats/votes even without the fraud. That is a fair question, but politics is a game that has wide array of possible outcomes, not just win or lose. It is a completely different thing to do what you want when you can claim a mandate of 80% of the people instead of just half. But is there evidence that the United Russia is benefiting from vote fraud? Imagine that you are going to a polling station and that you already know who are you going to vote. At the door to the polling station you find out that the turnout there is already over 40%/60%/80%. Does that influence your vote? Probably not. Let's take a look the next picture.

Picture on the left is about Russian legislative election 2007, the second picture is from Moscow city parliament election in 2009. Every dot represents the amount of votes that a party had at a polling station. The X-axis is for turnout of the polling station and the Y-axis is for the percentage of votes a party had at that station. Different colors represent different parties. Take a guess what party the purple dots represents. That's right, United Russia. Now lets take a look at the 2011 election results from Moscow:

The Y-axis is for the amount of polling stations, the X-axis is the vote percentage. We see curves for five different parties, four of them are close to the normal distribution curves and one of them belongs to the United Russia. You see two spikes: one at 30% which is what surveys predicted for United Russia and one at 50-55% which is what was probably United Russia's own target. Now the vote result in the city of Magnitogorsk:

This is a curve of United Russia votes in Magnitogorsk, a South Russia city with a population of 400000. I guess the people there are really divided or something. And then there's the last picture about the correlation between the vote turnout and the vote percentage of United Russia:

In conclusion, I would say that the vote fraud was definitely there, but it's to early to tell how much it affected the result. United Russia would probably have been the biggest party even without the fraud. But that's not the point. The point is that a rigged election does not give legitimacy to the new Duma. Even without the vote fraud there's still the issue of not allowing all opposition parties to take part in the elections and the lack of freedom of press. I, as a citizen of Russia voted in these elections at a Russian embassy in Helsinki. Yabloko party received 25% of the votes here, 22 points more than in Russian regions while United Russia got less than 20%. Is it because people with more "western" views are more likely to migrate from Russia or because of the free press here? That is a topic for a whole other discussion.


22 kommenttia:

Anonyymi kirjoitti...

No, I think that's because people with more "western" views are ready to sell Russia for a dollar or so and don't care if they motherland is accused of practically everything wrong on planet Earth while the "true democratic" country (blink, US) with big stick is ruining other countries and doing everything they can to make things stay the same. United Russia IS most popular party in Russia, THERE IS free speech in Russia, elections ARE legitimate and if somebody did rig it I would blame the opposition (well if we can't win, let's make it at least look not legit, right?) that is so eager to tear apart everything that was achieved during the years of Medvedev/Putin tandem.

Dennis Granau

Anonyymi kirjoitti...

That's some rhetoric there, but how do you explain the statistics Dennis?

Anton kirjoitti...

Ah, yes. The classical "they lynch black people in US"-defence.

If disagree with the evidence provided in the post, please tell us why the statistics are wrong or provide links to different kind of information. Using caps lock to tell us you completely disagree is very close to trolling.

Anonyymi kirjoitti...

Dennis, your comment sounds a bit like a huffy, little patriot. Like "and don't care if they motherland is accused of practically everything wrong on planet Earth " This is a very clear and easy to follow article on one topic: election fraud.
And your idea that the US (a county with big problems concerning human rights and the tendency of their democracy, I fully agree) is running the hole movement here is really scary. If your conspiracy mind goes so far imagining that all these people on the streets in Russia are under control of US influence in one way or another: Wow, you considere your fellow countrymen really weak and the US ridiculously strong. Which would also mean that something went very wrong in Russia.

I dont agree with that. I think real patriotism is to have an open eye on things happening in your country and to react consciously and brave the moment you see that things are going down the drain. (Instead of patriotism you could even say: sympathy for people effected by the state control) I have immense respect for all the people on the streets in Russia now.

artied kirjoitti...
Kirjoittaja on poistanut tämän kommentin.
artied kirjoitti...

Thanks for this..clear, concise, well illustrated and linked.

Is there any chance of getting the links to the raw/original data?

Anton kirjoitti...

To get the original data go here:

Click the region you want to study, find a link that says: Выборы и референдумы

Then find a link that says "Выборы депутатов Государственной Думы Федерального Собрания Российской Федерации шестого созыва" and then find a link that says "Сводная таблица предварительных итогов голосования". Then click on of the links in the upper row of the table and you'll get the stat's for all of the polling stations in the area.

If you want to investigate futher, use google translate :)

voldemarz kirjoitti...
Blogin hallinnoija on poistanut tämän kommentin.
voldemarz kirjoitti...

About the graph of the results in Moscow you said "The X-axis is for the amount of polling stations, the Y-axis is the vote percentage."

It's other way around.

Anton kirjoitti...

Thanks, fixed it.

achompas kirjoitti...

Anton, this is an excellent article. Is there any way you can zip this data up into a file and post it somewhere? If not, no worries--I'll get to work with Google Translate. :)

Alex kirjoitti...

There's another analysis in English at and I've also posted some copies of the raw data pulled from the web site, including some with with all english headers since some people have problems opening the Russian files.

Anonyymi kirjoitti...

First set of statistics only proves that a large number of Russians voted at a small number of stations, which is to be expected considering the size and distribution of population in Russia.

Second set of statistics doesn't really prove fraud either, it just suggests strangeness in the system. Like if UR had a rally or something, we see the same thing in America.

Could you send the raw data to me for analysis? It doesn't look like anyone did any post hoc.

My email:

Anton kirjoitti...

This should be the original data in exel form:

Bardamor kirjoitti...

You forgot to prove before that Democracy is not just a trick. And that statistics are not modern lie. Stop Mathematics, open your eyes, (French advise).

Anthony kirjoitti...

Interesting and thought provoking post. Speaking as an American, I can guarantee that the U.S. doesn't have the power to influence the protests in Russia one way or the other. Americans also don't speak with "one mind." We are a very heterogeneous group (and that includes our politicians). We can't even decide how to tackle important issues in our own country.

It's actually humorous sometimes to note that some people have replaced God or the devil with "the U.S." They ascribe any action to U.S. intervention or such (when usually the U.S. has nothing to do with it)...

Anonyymi kirjoitti...

Well, these graphs does not actually prove anything.

First of all you can never claim something "definitely" based ONLY on statistical/regression analysis. The cause/effect relation is totally forgotten - :-).

The assumption that there HAVE TO be normal distribution and no high correlation between turnout and % of vote is absolutely wrong. For example here - - is database of UK general elections 2010. This graphic - - shows correlation between turnout/vote for Conservative party (correlation coefficent is bigger than for United Russia :-) ) and here - - is distribution of votes for three major party (should be normal distribution :-) ).

Again if I understand correctly the results of election were pretty same as the results of opinion/exit polls conducted by independent and non-governmental Levada-center.

Anton kirjoitti...

Yes, you are right that you can't draw conclusions based on statistical analysis. The translation that I provided here was to support all of the other evidences that are very well documented.

Lack of correlation between the turnout and votes is a wrong assumption based on the graph you provided, but it fit's the allegation of the vote rigging.

Distribution of votes doesn't have to be normal, but in Russian elections it seems to be close to normal for all the other parties exept for UR. They also have these intresting spikes around convenient numbers, how do you explain those?

And what about vote distribution for the whole election, do you have examples of fair election where vote distribution is not normal or is only normal up to 55% like in Russia?

Votes were in line with the polls, but not the exit polls (40% to 48% for UR). In Moscow for example the the actual procentage of votes received by UR was 50% higher than the levada polls or exit polls predicted.

The craft of making polls is not as straight forvard as one might imagine. For some reason people don't always answer honestly to the polls and that's why pollmakers usually apply correction coefficent to their answers based on previous election. When opinions shift dramatically such coefficents do not give truthful polls (as happened in Finnish legislative election in 2011 for example). Only votes given in fair election count.

You also have to notice that election are about seats, not votes. You might need only slight rigging to make sure that your candidate get through. UR got 52,88% of the seats with only 49,33% of the votes.

Anonyymi kirjoitti...

What real evidence of fraud that MASSIVELY (not talking about some youtube-videos) affected result has Russian opposition? Any lawsuits started? I found that independent organization named "Golos" ( says that United Russia get 15.8 "extra" vote, but, if I understand correctly, it is also based on statistical analysis?
I would say that these spikes are result of fraud, but after all how much votes they bring to this downward trend of curve?

As far as I know the election fraud is identified (if we talk about mathematical methods) through polls/result ratio and analysis of voting time-series (e.g turnout or % of votes for ruling party cannot change dramatically from last elections), not such distribution analysis (I must admit, that I never seen such before :-)). As UK example shows central limit theorem doesn't actually work well when it is question about human behavior and these distributions can be whatever they are.

If I understand correctly organization called "ФОМ" has conducted exit polls that shows pretty same results for all Russia as official report and really different result for Moscow. So I would say that it was definitely election fraud at least in Moscow, but not so sure about other Russia.

Tatiana kirjoitti...

> It is a completely different thing
> to do what you want when you can
> claim a mandate of 80% of the
> people instead of just half.

True. But also, I think, their current concern was mostly a suitable make-up application. I.e. it's nobody's business to analyze e.g. some minor decline tendencies or what so ever of the all-mighty. And that's a kind of implicit thought that is generally quite widely accepted in Russia, I'm afraid...

Janne Pyykkö kirjoitti...

For the record, I checked the Finnish parliamentary elections 2007 and 2011 by using the same method. Image here: The original data is available at

Anonyymi kirjoitti...

I don't believe that the fraud (which indeed took place) can be detected and measured statistically.