  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.
