xeromass
12-08-2014, 10:55 AM
in Russia. With math. Sorry.
Statistical anomalies in 2011-2012 Russian elections revealed by 2D correlation analysis (http://arxiv.org/pdf/1205.0741v2)
http://shrani.si/f/2R/sa/4fxGp1j5/volitve.jpg
Figures 1A and 1E show 2D histograms of the number of ballots in favour of UR/Putin as a function of turnout and respective vote share at each polling station. Apart from the main clusters at ~52% turnout and ~30% votes for UR and ~60%/55% for Putin, there are two prominent features at both plots that clearly distinguish them from other participants' histograms (Figs. 1D,H):
(i) an unusual cluster of votes in the vicinity of 95% turnout, and
(ii) a long tail of votes beginning at the central peak which shows a high correlation of the results with the turnout (marked by black curves, known in 2D spectroscopy as the centre line slope). The clusters at 90-100% turnout yield ~3.5 million ballots for the winners in both elections and can be traced back to six republics of North Caucasian Federal District, and Republics of Mordovia, Bashkortostan, and Tatarstan. In each of these nine regions, there are a number of constituencies that exhibit voting results with extremely low dispersion across polling stations, significantly lower than dispersion value imposed by binomial model (e.g., 25 constituencies with p < 0.0001 for parliamentary and 9 constituencies for presidential elections, see Table S1 and Methods). This suggests that the results in these constituencies were artificially fixed to certain percentage values.
It is instructive to consider a projection of the 2D histograms onto the vertical axis, which gives a distribution of the number of ballots cast for UR and Putin depending on their results at every polling station (Figs. 1B,F). The unique feature of these histograms is sharp peaks located at "round" numbers of 65%, 70%, 75% etc. The periodic character of these peaks is evident from the Fourier spectra that show prominent harmonics at 1/5 %^-1 (insets).
By far the highest peak in both cases is located at 99.5% and originates solely from a single region of Chechen Republic. Other peaks can also be traced back to particular constituencies, but are usually not confined to a single region. These peaks, which are highly statistically significant (see Table 1 and Methods), comprise ~1.4 million ballots for UR and ~1.3 million ballots for Putin. The supernatural character of the peaks strongly suggests that the votes for the winners were manipulated a posteriori to fix the vote shares at appealing round values.
Statistical anomalies in 2011-2012 Russian elections revealed by 2D correlation analysis (http://arxiv.org/pdf/1205.0741v2)
http://shrani.si/f/2R/sa/4fxGp1j5/volitve.jpg
Figures 1A and 1E show 2D histograms of the number of ballots in favour of UR/Putin as a function of turnout and respective vote share at each polling station. Apart from the main clusters at ~52% turnout and ~30% votes for UR and ~60%/55% for Putin, there are two prominent features at both plots that clearly distinguish them from other participants' histograms (Figs. 1D,H):
(i) an unusual cluster of votes in the vicinity of 95% turnout, and
(ii) a long tail of votes beginning at the central peak which shows a high correlation of the results with the turnout (marked by black curves, known in 2D spectroscopy as the centre line slope). The clusters at 90-100% turnout yield ~3.5 million ballots for the winners in both elections and can be traced back to six republics of North Caucasian Federal District, and Republics of Mordovia, Bashkortostan, and Tatarstan. In each of these nine regions, there are a number of constituencies that exhibit voting results with extremely low dispersion across polling stations, significantly lower than dispersion value imposed by binomial model (e.g., 25 constituencies with p < 0.0001 for parliamentary and 9 constituencies for presidential elections, see Table S1 and Methods). This suggests that the results in these constituencies were artificially fixed to certain percentage values.
It is instructive to consider a projection of the 2D histograms onto the vertical axis, which gives a distribution of the number of ballots cast for UR and Putin depending on their results at every polling station (Figs. 1B,F). The unique feature of these histograms is sharp peaks located at "round" numbers of 65%, 70%, 75% etc. The periodic character of these peaks is evident from the Fourier spectra that show prominent harmonics at 1/5 %^-1 (insets).
By far the highest peak in both cases is located at 99.5% and originates solely from a single region of Chechen Republic. Other peaks can also be traced back to particular constituencies, but are usually not confined to a single region. These peaks, which are highly statistically significant (see Table 1 and Methods), comprise ~1.4 million ballots for UR and ~1.3 million ballots for Putin. The supernatural character of the peaks strongly suggests that the votes for the winners were manipulated a posteriori to fix the vote shares at appealing round values.