The SINE function of the Russian elections

Several days ago we presented a preliminary analysis of the distribution of votes on polling stations in Russia. We borrowed the original graph from Maxim Pshenichnikov and crudely estimated the difference between the observed curve and that expected from normal distribution (Gaussian) of parties portions. All parties except United Russia showed the expected normal distribution, which is also observed during elections in other countries, where UR does not rule. Today we illustrate the difference and demonstrate quantitatively the difference. Moreover, we propose a simple functional dependence for those who want to carry our own research. Figure 1 reproduces the original distribution (brown curve), which depicts the number of polling stations in 0.5% bins as a function of the UR portion of votes - from 0% to 100%. we have approximated the original distribution with a normal one with mean=29% and stdev=5%. Black curve fits the left wing of the measured function and fails on the right one. When elections are honest, the distribution must be normal as the black line shows. However, the observed brown line is better approximated by a sine function shown by red line. We have found the following equation (not optimal):
s(V) = 637+403sin(V/18)
where  V is the portion of the UR votes (x-axis), s(V) is the number of polling stations in a given V-bin. The curve starts from 30%, where the normal distribution fails to fit the observed line. All in all, the elections’ results demonstrate a sine line of the UR success.
having this function one can easily estimate the number of polling stations with falcified elections and the number of voices falcified in favor of UR.

Figure 1. The number of polling stations in 0.5% bins (vertical axis) with a given portion of votes (between 0% and 100%) for the UR.

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