Election mathematics 2011: addition

The editors of the Trinity Option asked me to comment on Sergei Shpilkin’s article, paying special attention to the weaknesses in his argumentation. Since I am thus invited to play the role of devil's advocate, I hasten to warn the reader of my position. I have no doubt that these elections were held with huge falsifications in favor of the party in power: there is a lot of documentary evidence of this. Like S. Shpilkin, I believe that statistical analysis of the results can help assess the scale of these falsifications and estimate the real results. According to various estimates, the real result of United Russia is 30-40%; my own estimate is 38% [1].

Having made this necessary preface, I turn to the comments.

1. I’ll start the list of weaknesses with one of the strengths. The only indisputable statistical evidence of falsification is the sharp peaks in the histogram of votes for United Russia: detailed histograms show sharp peaks every 5%, starting from 65% (just in case, I note that at 50% of the sharp peak, clearly visible on some graphs, on Actually no - it's an artifact of integer distributions). The probability of such regular peaks occurring by chance is astronomically small [2], and they are especially strong in regions such as Bashkortostan and North Ossetia. Below these peaks there are about a million additional votes for United Russia, which does not change their final result very much (by about 1%). But there can be no doubt about the man-made origin of the peaks: we see the order based on the voting results.

2. The rest is more difficult. All methods for assessing the scale of falsification are based on the fact that the correlation between turnout and United Russia results is considered the result of stuffing and additions. Indeed, in many countries, turnout is distributed more or less normally (see Fig. 2 in the article by S. Shpilkin), and there is no correlation between turnout and results. But there are also countries where there is no doubt about the integrity of the elections, and the picture nevertheless resembles the situation in Russia: a clear correlation is visible between turnout and the results of different parties. Among them are England [3], Germany [4] and Israel [5].

The example of Germany is especially interesting: this correlation practically disappears if we move on to considering individual lands, i.e. Oddities in the general German graphs and distributions arise due to the strong heterogeneity of the regions. Russia is a huge and very heterogeneous country; there is every reason to believe that even in a crystal-clear election, this heterogeneity could lead to “suspicious” correlations. However, S. Shpilkin in his article analyzes all-Russian data in its entirety.

In fact, if you carry out an analysis for each region separately, you will find out a lot of interesting things: in some regions there is no correlation, and turnout is distributed exactly according to Gaussian (but the United Russia results are different in each of these regions). In some regions, the official results clearly have no relation to the actual expression of the will of citizens (Chechnya with a turnout above 99.5%; Vladikavkaz with a result of exactly 75% for United Russia in almost every polling station; Dagestan, where the number of votes for United Russia in dozens of polling stations is a multiple of one hundred [6]). But in some regions we still see a clear correlation between turnout and votes for United Russia. Can the fear be considered exhausted?

3. Unfortunately, no. In addition to the difference between regions, there is at least one more important heterogeneity: the traditionally strong difference in Russia between urban and rural areas. It was this difference that V. Churov and co-authors referred to in their article criticizing S. Shpilkin’s approach [7]. If both turnout and support for the party in power in rural areas is higher than in urban areas (and both seem quite likely), then looking at the entire region will show a correlation in the absence of a causal relationship. Using the names of territorial election commissions, we can roughly divide urban and rural areas within each region.

If this is done, the picture will become even more interesting: it turns out that in many regions the correlation between turnout and the result of the United Russia is entirely due to the village: the city votes compactly, demonstrating quite reasonable values ​​of turnout and the result for the United Russia, but in the countryside the turnout varies in a wide range, and the higher it is, the higher the result of the EP. These are, for example, the Voronezh, Omsk and Ulyanovsk regions. There are two possible explanations for this. First: by dividing the country into regions and distinguishing between cities and villages, we eliminated all important heterogeneities; remaining correlations are a sign of fraud. Second: the villages in these regions really vote this way. Let’s say that in these regions, rural support for United Russia is very high, but turnout in different areas varies greatly and depends, for example, on the activity of local agitators. In this case, the more people come, the greater the result of the United Russia will be. Is it possible to somehow refute this attempt at explanation? Purely statistically, this is hardly possible, but there remains hope for KOIBs.

4. Alas, with COIBs everything is also not so clear. There are regions where quite a lot of KOIBs were installed in rural areas, and at the same time, areas with KOIBs also demonstrate a high correlation between turnout and the result of the United Russia (not all regions are like this, but this is exactly the case, for example, in the Bryansk and Saratov regions). What is this: evidence of the true nature of voting in rural areas or that in these areas the falsifiers were either not afraid of KOIBs, or simply recalculated the results manually, which they had every right to do? The fact that KOIBs are not a panacea for falsification is clearly shown by the examples of Dagestan or Tuva, where polling stations with KOIBs quietly demonstrate an implausible level of turnout.

On the other hand, in Moscow, the EP result for areas with COIBs is significantly lower than for the city as a whole. But if you look at the geography of these areas more closely, it turns out that they are mainly concentrated in just three districts of the city (Mitino, Strogino and Zelenogradsky district) and, thus, cannot be considered a representative sample [8]. In St. Petersburg, all KOIBs were installed in Kronstadt - in essence, in another city. Finally, you need to be very careful when combining results from different regions: the difference between the EP result in areas with and without KOIBam within the same TECs (here I follow the very reasonable approach of S. Shpilkin) on average across regions is only about 6%. This clearly indicates fraud in areas without COIBs, but rather modest ones. The gigantic difference that S. Shpilkin writes about (between 37 and 54%) arises only when all regions are united, which does not seem entirely correct.

5. Finally, about the accuracy of various estimates of unfalsified results. Shpilkin's method gives 34%. The same method, applied to each region separately, gives a total of 32% [9]. A method based on cutting off areas with turnout exceeding a certain limit—again 34%. If for each region we set separate boundaries for the city and the village, then the result will be 38% [1]. Finally, the preliminary results of the FOM exit poll (there is reason to doubt the final results) were 43%, with 30% of respondents refusing to answer - very roughly we can assume that if these people had answered, United Russia would have received 40 percent. The real result, according to apparently lies within the boundaries outlined by these numbers.

In conclusion - about pleasant things. Thanks to the work of S. Shpilkin, statistical analysis of election results just a few days after December 4 literally exploded the Russian blogosphere (see p. 9). Look at the list of quotes for this short note: almost all of them are blog posts by a variety of people from different countries of the world, who together, in the shortest possible time, did a great job of analyzing the election results. Such well-coordinated and effective cooperation could be the envy of any international scientific collaboration. I hope this work will continue [10].

Dmitry Kobak,
postgraduate student at Imperial College London

1. http://kobak.LivejournaL.com/101512.html

2. http://kobak.livejournal.com/102646.html

3. http://users.livejournal.eom/_ab_/139002.html

4. http://jemmybutton.livejournal.com/1359.html

5. http://levrrr.livejournal.com/31427.html

6. http://gegmopo4.livejournal.com/72536.html

7. Churov V.E., Arlazarov V.L., Solovyov A.V., Election results. Analysis of electoral preferences: http://cikrf.ru/banners/illuziya/itogi_160908.html

8. http://oude-rus.livejournal.com/551503.html

9. http://dmitrykogan.livejournal.com/46452.html

10. Shen A. Elections and statistics: the case of “United Russia” (2009, 2011). www.lif.univ-mrs.fr/~ashen/elections.pdf