We hypothesize that if election results are manipulated or forged, then, due to the well-known human attraction to round numbers, the frequency of reported round percentages can be increased. To test this hypothesis, we analyzed raw data from seven federal elections held in the Russian Federation during the period from 2000 to 2012 and found that in all elections since 2004 the number of polling stations reporting turnout and/or leader’s result expressed by an integer percentage (as opposed to a fractional value) was much higher than expected by pure chance. Monte Carlo simulations confirmed high statistical significance of the observed phenomenon, thereby suggesting its man-made nature. Geographical analysis showed that these anomalies were concentrated in a specific subset of Russian regions which strongly suggests its orchestrated origin. Unlike previously proposed statistical indicators of alleged electoral falsifications, our observations can hardly be explained differently but by a widespread election fraud.
"Integer percentages as electoral falsification fingerprints." Ann. Appl. Stat. 10 (1) 54 - 73, March 2016. https://doi.org/10.1214/16-AOAS904