Become a Patron

Russia: Understanding the Flagrant Vote-Rigging With Graphs

Often when election results from Russia are discussed with other people, one pedantic argument is constantly brought up. It is the fact that while we can feel and at some instances witness that Russian elections feature severe violations of electoral integrity, it is hard to conclusively prove the flagrant vote-rigging due to the lack of sufficient number of independent election observers. Most stations do not have independent observers and therefore it’s close to impossible to prove that results on those stations were modified and skewed to a desired direction.

Despite the initial hurdle, with the statistical analysis of election data it is possible to complement the picture and deduce improper tampering from the published election results. Golos, an independent democracy watchdog in Russia, regularly showcases the most flagrant cases and goes through the most common techniques used by the Russian government to rig the election results in its favour while keeping up a democratic façade. This article aims to explain the techniques to a broader foreign audience.

Election results everywhere adhere to a few statistical rules which people cannot go around. One of these is the observation that a distribution of electoral stations across certain variables like party support or voter turnout is most often unimodal—that there is only a single highest value—and the value decreases towards the end(s). Examples of these is for instance a traditional normal distribution or bell curve: it has only a single peak.

A simple normal distribution illustrating what it means to be unimodal: as we can see it has only one peak, in the middle
Graph: M. W. Toews (CC BY 2.5)

More concretely, if we plot a simple histogram of turnout in polling stations in case of free and fair elections, we see distribution on chart which will look similar to a bell; the number of polling stations will lay close to centre and have an average turnout, while low and extremely high turnouts would be uncommon. For example below is a distribution of turnout in polling stations in Finnish parliamentary elections of 2023.

Graph: Julius Lehtinen

Turnout by stations adheres very strictly to the normal distribution, but it is by no means the only variable to do so when it comes to elections. If we put turnout in polling stations and the votes in those polling stations towards a party on chart in case of free and fair elections, we would likewise see curve on chart which will look similar to a bell; the biggest total votes will lay close to centre, while low and extremely high turnouts would be uncommon and hence produce low vote totals. For example below is a distribution for different candidates depending on turnout in Poland in 2015.

As we can see, the distribution of votes on electoral stations falls under the above-described unimodality: they have clear and natural curve and the results form a structure that looks like a bell, as did the turnout graph. Curves like these adhere to the so-called 68–95–99.7 rule. That is, 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

But unlike in the exemplified Finnish parliament election in 2023 and Polish president election in 2015, last Russian regional election in 2023 has dozens of unexplainable anomalies which do not adhere to the statistical rules we find practically everywhere else in the free and fair elections.

Left image, x-axis: turnout, y-axis: sum of votes in stations with a certain turnout
Right image, x-axis: turnout, y-axis: results of each candidate in per cent, each dot is a candidate in a polling station
Graphs: Golos

For example, in Voronezh region a lot of electoral stations have anomalies and report identical turnout numbers of exactly 80%, 85%, 90% and 95%. If you compare the lefternmost image to the graph on Polish elections in 2015, you can notice that vote sums of the governing United Russia’s candidate do not draw such natural bell curve, Rather, in polling stations where the turnout was exorbitantly inflated, he received inconceivably high amount of votes. The authentic bell curve is the small bump with 15% to 20% turnout.

Results in stations with anomaly turnout indicate the need to provide specific results and reach target turnout no matter the cost. While such an indication of fraud could by some be discounted with all else being pristine, together with observed and validated electoral violations by independent observers, it paints a much more convincing and undeniable picture of wrongdoing.

Perhaps the most egregious recent case of wrongdoing happened in Moscow mayoral election in 2023. With the actual turnout being minuscule with corresponding small vote totals, the government candidate received two million fraudulent votes with certain polling stations with 100% turnout.

X-axis: turnout, y-axis: sum of votes in stations with a certain turnout.

Gathering the election data in Russia is not a task without complications: The Central Electoral Commission regularly obfuscates the data and hides it deep in its website portals, Golos member tells Europe Elects. It is not hard to notice why they do that, as the data sheds light to the flagrant malpractice and vote-rigging taking place routinely in Russia. Dekóder, a platform to bring Russian and Belarusian independent journalism to western audiences, has tallied similar graphics as presented in this article for many Russian elections along the years and collected them into one place.

Statistical analysis of election results can help uncovering wrongdoing in elections of an authoritarian regime, since the vote totals are extremely hard to tamper with while retaining the natural shapes and distributions. It complements the picture that independent electoral observers tell about the violations in the polling stations they managed to visit. And, ultimately, combined, we all can see through the democratic façade of Russia.

Written by Ariel Helimsky, edited by Julius Lehtinen