Statistical detection of systematic election irregularities
Another way to visualize the intensity of election irregularities is the cumulative number of votes as a function of the turnout (Fig. 6). For each turnout level, the total number of votes from units with this level or lower is shown. Each curve corresponds to the respective election winner in a different country with average electorate per unit of comparable order of magnitude. Usually, these cumulative distribution functions (cdfs) level off and form a plateau from the party’s maximal vote count. Again, this result is not the case for Russia and Uganda. Both show a boost phase of increased extreme fraud toward the right end of the distribution (red circles). Russia never even shows a tendency to form a plateau. As long as the empirical vote distribution functions remain invariant under data aggregation (as discussed above), the shape of these cdfs will be preserved as well. Note that Fig. 6 shows that these effects are decisive for winning the 50% majority in Russia in 2011.
https://www.pnas.org/content/109/41/16469