It would seem that heated debates about the statistical analysis of election results are a thing of the past. The assessments (see, for example, [1], October 11, 2009), made «on the hot tracks» according to which there were falsifications, were met with criticism [2, 3]. While the first of these works can be described as a conflict of interest (one of the authors served as the chairman of the CEC at that time), the second one was written by a well-known and very qualified mathematician. In some cases, artifacts of data presentation (peaking at 50%) were taken as indications of falsification. In others, the «non-normality» of the distribution was taken as evidence of falsification. Additional confusion arose also because «normality» in the mathematical sense (proportionality of the Gauss function) is easily mixed with «normality» in the everyday sense («the election was normal»).

Since then, the situation has been clarified: presentation artifacts were identified, and various hypotheses explaining possible histogram shapes were tested in subsequent elections. Emotional blog posts were supplemented by detailed papers published in scientific journals in statistics [4, 5, 6], in which statistical evidence of falsification did not rely in any way on the assumption of normality (in the sense of Gauss) of distributions. The question of statistical analysis of elections (as a scientific, not public question) seemed more or less closed.

The peer-reviewed paper again raises the question about the incorrectness of the conducted statistical analysis. But it is based on a misunderstanding: the authors rightly point out and confirm with numerous examples that histograms of elections may well be very different from «Gaussian» and in the absence of falsification. They have probably not seen the papers cited above and suggest that the conclusions about fraud so far are based on a deviation from «Gaussianity».

The authors make political accusations as well: «to speak about “bona fide delusion” of the authors of “mathematical theories” of electoral behavior estimations, who disseminate unreliable information, in this case it is not necessary» (p. 4). In this connection, one can recall the speeches of Lysenko's students, who stated that «the terms, scales, and, most importantly, the results envisaged by the theory of Mendelism are unsuitable for our Soviet reality» [7], «as Lenin wrote,  …  statistics, which leads to depersonalization, turns into the emptiest and most harmful “game of numbers”» [8]. To this Kolmogorov, having made a correct statistical analysis of the works of the «Lysenkovians» and having established that they are quite consistent with the «pea laws» allegedly refuted by them [9], briefly remarked: «Kolman's work  …  is entirely based on a misunderstanding of the circumstances stated in our note».

It would be possible to follow his example and limit ourselves to what has been said (the authors argue against the thesis of «a priori Gaussianity» on which the analysis does not rely), but it is also possible to note the extreme carelessness of the authors in preparing the text. Reproducing one of the criticized graphs, they write (p. 17): «The results of voting in Chernogolovskaya TEC of the Moscow Region» raise “suspicions” of the authors-compilers of the charts. Meanwhile, on the graph they reproduced it is written «0 thousand anomalous votes» — as it is obvious, the authors not only did not understand the data, but even did not read the inscriptions on the figure they included in their work. In their defense, it can be noted that this inscription is in small (though quite legible) font.

The authors found it necessary to include in their paper «mathematical proof» of the well-known fact that convergence to the Gaussian distribution occurs when the system size tends to infinity (Section 5, «Peculiarities of mathematical modeling of the process»). However, it is difficult to make sense of this section even with the most sympathetic attitude and with a lot of experience in checking the work of twos. The authors write on p. 45, that «for all possible contributions of voting voters who cast ‘votes’ in each precinct» to be equally likely to be accounted for, the number of precincts must be equal

(where n — precinct size) and that «this unambiguously imposes a condition on the total number of voters equal to N = nY» (whereY = 2ⁿ , the authors instead write the sum of the binomial coefficients, probably unaware that it is equal to 2ⁿ). Two things can be observed in the authors' defense. First, this absurd reasoning applies to the correct statement. Second, section 5 itself, in terms of layout is a «copy-paste» of fragments of another text, done in T_EX system, in the form of halftone drawings, so perhaps claims about the content should be addressed to the author of this other text.