Many criticize statistical processing: they say it is soulless, lifeless. But there are cases when it is precisely statistics that provide vivid and simply unsurpassed arguments. The distribution of votes cast for different parties across different polling stations during the recent elections in Russia. Only the distribution, nothing more...
Дмитро Шабанов
[A few words about how this was written. I found some interesting images in LiveJournal and posted a short description of them here. According to the terms of my work at "Computerra," the topics of the columns must not touch on politics. Nevertheless, I asked permission from Computerra's editor-in-chief, Kirill Tikhonov, to write a column analyzing these graphs. He found a way out of the conflict between the rules of the game and my wish, and suggested I post this text on the Computerra site, in the "Blogs" section: https://blogs.computerra.ru/20964. So now I am replacing, on this page, the text that was originally posted with a new, more detailed one. I am grateful for links to other pages where similar graphs are discussed. For example, similar graphs are posted here: https://hist-kai.livejournal.com/243639.html, but in discussing them the author arrives at a conclusion I do not agree with. Falsifications of 5-7% stand behind the small peaks near "round" numbers, while the tail stretched to the right itself gives a more serious distortion. How this relates to exit-poll results, I do not know. I trust more these statistically comprehensible results, based on official ballot records. After criticism and questions from readers I wrote a continuation. It is here] The psyche of different people processes incoming information differently. Some try to believe only what their own eyes see. Others come to understand that their sense organs often deceive them and begin to search for a point of support that can be trusted. But what can help in such a search, since everything we receive, we receive through our imperfect senses? Can one find some reliable support, for example, in politics? Do you know how old the common joke is about the three qualities of a person that occur in any pairwise combination, but never all three together in one person: intelligence, honesty, and party loyalty? No, no, it was not born in the era of stagnation. It was already known in Athens in the time of Pericles. I "got hooked" on an acute experience of political life seven years ago. There were scandalous elections in Ukraine. The party of power (with the support of Russian political technologists) crudely pushed its candidate. If the cast-iron foreheads hadn't tried so excessively hard, they would have pulled it off. Strangely enough, once at dizzying heights, our "elite" loses touch with reality and forgets that excessive action breeds excessive reaction. At the time I even went as an observer for the final round of the elections. I saw falsifications, and stopped some of them. At least in the small town where I observed, at most polling stations the candidate in whose favor they falsified won, while at "my" station it was the other, oppressed one. A victory? Probably. Unfortunately, it did not lead to an improvement in quality of life. Maybe there was a slight rise in the sense of one's own dignity. Time passed. Now, when those elections are recalled, it is often said that in one half of the country the result was falsified in favor of one person, and in the other half in favor of another. That's probably true. How did my experience relate to the actual picture? Today it's hard to say, and I've even come to doubt the adequacy of my own memories. Now Russia is feverish. I am a regular reader of "Yezhednevny Zhurnal," "Novaya Gazeta," and "Ekho Moskvy." I read the descriptions of election violations officially reported by observers. But what these sites write about is only a small and non-random sample! Maybe these observers are wrong, and elsewhere there lie other statements describing opposite violations? Can one be sure that the associates of Mr. Zhirinovsky or Mr. Zyuganov are better than the associates of the leaders of the party of power? How can one see the picture as a whole, without taking a partisan position (so as to lose neither intelligence nor decency)? And suddenly, while wandering the web, I found something that made the picture entirely clear to me. Thank you, statistics! Now I know what one can rely on even in politics: the regularities that follow from the natural and exact sciences. This is the distribution of votes cast for different parties at different polling stations. Just the distribution, nothing more.
Distribution of polling stations (across all of Russia) by the number of votes cast for the most successful parties (taken from oude-rus.livejournal.com/542295.html). Each point on the curve is the number of stations at which the given party received a certain percentage of votes. Let me start from the very beginning. A variable quantity influenced by a great many independent factors acquires a quite definite distribution. One of the simple ways of demonstrating this was devised by Francis Galton (a first cousin of Charles Darwin, by the way). Here is an inclined board. Shot rolls down it from above. The pellets collide with each other and with pins sticking out of the board, and accumulate at the bottom.
Galton's apparatus. The shot that has rolled down has formed a characteristic bell-shaped distribution. Increasing the number of independent factors, we arrive at a distribution described by the Gaussian (the function described by Carl Friedrich Gauss). Otherwise this distribution is called normal. The distribution of polling stations by the number of votes cast for a fairly popular party is a quantity whose distribution should be close to normal. I should note that if the probability of a given party receiving even a single vote at a station is a rare event, the distribution becomes Poissonian. Perhaps this happened with the "green" party shown in the graph. But if parties are voted for fairly often (and the remaining parties shown in the figure meet this condition), the distribution approaches normal. A strange thing! The distributions of three parties are more or less bell-shaped, but the fourth one (could you have guessed which one without the graph?) is not! So the results of one party were influenced not by many random factors (individual voter preferences and many other random events) but by one factor. Falsification. The "brown" party shows a long "tail" stretched to the right, into the region of implausibly high values. On this "tail" spikes are visible corresponding to round numbers. I cannot find any other explanation for them except that this is the result of carrying out orders like: "...and if it's less than 60%, you'll answer with your heads!" The same kind of spikes are visible at the top of the distribution for the "red" party — they were bitten down to round numbers when they gained too much. But here is a more homogeneous sample, the Moscow one. The bells have become more slender and neat (the differences between regions of the country, which stood out from among the many random factors, have disappeared). Violations are noticeable for two parties. Something was tampered with for the "green" one, while the result for the "light blue" one was inflated, and grandiosely so.
Distribution of polling stations by the number of votes cast for the most successful parties, in Moscow (this and the next graph are taken from onsb.org/elections-moscow-2011-12-07.html). Note: the color codes for the parties differ from those in the previous figure! How was this done? There is an answer to that too. Here is another Moscow picture. Look: at stations where turnout (according to the official records) was 50% or 80%, the results for most parties remained roughly the same. But for the "light blue" party the points form two clouds: a horizontal one and a sloped one. Where the count was honest, the level of votes for this party remained relatively constant; these points form the horizontal cloud. Where turnout (on paper) was raised through ballot stuffing, the number of votes for this party rose steadily, forming the sloped cloud.
The dependence of the number of votes cast at Moscow polling stations for each party on the turnout at each station. Can these graphs be explained some other way? In theory, yes. I did not create them; they were downloaded from the addresses I indicated. The authors of these graphs claim they created them based on data from the Central Election Commission. Do you suppose that the Central Election Commission's website holds different data? Check it! As for me, I believed these graphs. Behind every point that stands out from the statistically regular picture lies a serious crime, committed by a group of persons by prior conspiracy. The instigators are politicians and administrations of various levels; the perpetrators, most often, are schoolteachers and housing-office employees. Imagine: if all the falsifiers were jailed, as the law requires, education would become depopulated! And can you imagine a person writing an official statement to transfer their son or daughter from one school to another, giving as the reason that they don't want their child to study at a school where the teachers are falsifiers and criminals? Several consequences follow from what has been said. Global ones. Most likely, the election result has been falsified on a mass scale and to such an extent that it can only be annulled. One can, of course, estimate how much a given party actually received. But those who planned and carried out the deception (and it is they who have run, and probably will continue to run, Russia's fate) will never acknowledge such a result. Local ones. Where, on the graphs presented, does the result shown at your polling station lie, at the school where your children study or where your acquaintances work? Perhaps one should ask how the people who took part in the crime are feeling? Every blue point in the sloped cloud on the last graph is the result of the criminal actions of an entire group of Muscovites, mostly educated and socially active people. They have families, friends, colleagues, a circle of people whom they respect and who respect them... And that's just in Moscow. What is to be done? From my point of view (the point of view of an outside observer) — warn the rank-and-file falsifiers, forgive those who have repented, and hold new elections. And don't forget to build statistical distributions from the new results, and then thoughtfully analyze their features!
