Following Russia’s parliamentary elections on December 4, a link was posted to Reddit reporting an impossibly high turnout (99.51%) and near unanimous support (99.48%) for Putin’s ruling party, United Russia, in the last location one would expect it: the republic of Chechnya. Even if relations with the secessionist region have improved since the Second Chechen War, both the turnout and United Russia’s vote share are a complete joke. This absurdity prompted a more thorough examination of all regions, many of which were also plagued by irregularities. In this post, I will give some detailed visualizations of both region- and precinct- level election data, and point out some highly likely instances of fraud.

The data is taken from the Central Election Commission’s own (semi)-official results. The precinct-level data alone consisted of 2,743 Excel files totaling 146 MB. From it, the results across all of Russia are divided into:

Regions: 135 Sub-regions: 2,744 Precincts: 94,573

In the plot below, the vertical axis is United Russia’s vote share divided by the entire voting age population (all the eligible voters, not just those who voted). The horizontal axis is the sum of all other parties’ vote shares, over the same set of people. It follows that the turnout of the vote is equal to the sum of these two values. Lines of equal turnout would have a -45° angle (i.e. a slope of -1); obviously, all data points are confined to the lower left triangle (0-100% turnout).

The colors of the dots have no meaning other than its ordering: regions or precincts that are adjacent on the Election Commission’s official results have similar colors. In the “per-precinct” plots for each region below, the ordering is done first by sub-region, then by precinct (PEC) number. Therefore, all the precincts belonging to a sub-region have similar colors, which is a good way to spot systematic vote-rigging or manipulation across a sub-region.

The regional results can be further broken down into sub-regions and precincts:





(Large Version – 2MB)

I will focus on two basic types of vote fraud:

Ballot stuffing: when one person casts multiple votes, or where unused ballots are fraudulently filled in and cast by election officials. However, since you can’t decrease other parties’ vote counts via this method, the total number of votes always increases and the apparent turnout is inflated. Such increases in total votes would come entirely from one party, which in an honest election would be highly unnatural. By plotting the votes from all precincts onto a graph, these telltale signs can be detected.

Misreporting: when vote totals are fabricated after votes are counted, either at the voting station, or even during central tabulation by the Commission (which is feasible if results at each station are not publicly posted). These often come with telltale signs, such as orderly patterns in turnout/vote shares on a graph, where one would expect randomness. It can also crop up as skewed distributions or those that simply don’t make sense.

I think the government has taken the position that, while there exist some “isolated” activity of fraud which ought to be investigated (and which by now is too obvious to admit otherwise), these “incidents” are of little consequence overall and ultimately don’t affect the validity of the election. Therefore, no need to redo the election. However, the data itself suggests otherwise.

What I just plotted is a frequency distribution of vote share for each party in each of the country’s 94,573 precincts. While the six opposition parties each have support clustered at around 10% or less, they sum to over 30% (which is all that matters, since Russia uses proportional representation). This seemingly has a higher mean than even United Russia’s blue line, but thanks to its long tail to the right, United Russia’s curve actually had a higher mean, allowing it to just barely (almost, conveniently) eke out a majority in the parliament this time around (visually, it is hard to believe the blue curve has the higher mean, but it is true). Compare it to the 2007 elections below, which was quite the opposite situation: the incumbents handily defeated the combined opposition.

In this year especially, the long tail for United Russia is a curious outcast among the more symmetric distributions for the other parties. For speculation, I’ve included an unscientific estimate of what United Russia’s actual vote share likely was, had there been no inflation of its figures. I’ve taken the liberty, of course, to assume the distribution ought to be Gaussian, which “ICM laureate” Sergey Kusnetsov points out is not always true. Nevertheless, that is beside the point. Even if the true distribution given the current voter sentiment and geography was not Gaussian, it should not differ to this degree.

U.S. Election: a comparison

Here are similar plots from the 2008 U.S. presidential election to show, relatively speaking, what an honest election should look like. (Of course, in the U.S. the problem is that it doesn’t matter who you elect!). I have plotted both candidates’ votes as a fraction of the total VAP (voting age population) in each region. The data has been broken down by state, as well as by county.





The above graphs show characteristics of a fair election: a single, gaussian-distributed cluster, low variance in voter turnout (between 50-65%), and relatively few counties with extreme support for either candidate. These same features are lacking in the Russian election.

Regional analysis: Obvious fraud

Chechen Republic

The plot for Chechnya frankly speaks for itself, and even looking at the tables on the Commission’s website, you’d be crazy not to notice something amiss. This is the initial outrageous result that led me to investigate all the regions.

The Republic of Dagestan – Makhachkala

In this region, highly regular patterns become visible in the precinct results once placed on this raw vote vs. raw vote graph. The red lines indicate not only that numbers were forged, but that whoever was responsible really lacked creativity. One red cluster follows almost exactly the line y = 3*x, and another seems to be dictated by y + x = 95%. A blue line, if my eyes are not mistaken, follows y = 10*x. How could voters at different precincts have possibly coordinated themselves to produce such orderly results? (By the way, this is not simply due to very small numbers, such as 3 votes out of 4. The larger dots represent precincts that had hundreds of eligible voters). Finally, there is the overwhelming, 80%+ average vote share for a single party, a level unheard of in most democratic elections.

The impossibly high turnouts and simultaneously lopsided vote shares (a.k.a. points clustered into the upper left corner of the graph) seem to be endemic to the autonomous republics (for a complete listing, see below). If there is a good, legitimate reason for this occurring, I have yet to hear it. Smaller sample size alone wouldn’t explain this, since it would imply greater variance, whereas these regions show just the opposite. Perhaps the physical inability to vote for other parties, if not outright miscounting of votes, is the real culprit.

Republic of Bashkortostan – Sterlitamak

The telltale green and purple clusters below are not only suspicious but reflect a lack of statistical understanding on the part of whomever made them up (if that is the case). The green cluster in particular seems far too concentrated to have occurred by chance, and is in fact responsible for the small red dot you see in the plot above.

Kabardino-Balkaria

The figures in the next plot are very strange indeed, as if every single ballot that wasn’t used was secretly filled in with “United Russia”. Whoever conjured them also seemed to think people will blindly believe these mythical turnout rates of over 95%:

Chelyabinsk region – Magnitogorsk

This is, surprisingly, the first region we see that has any points in the “legitimate” zone around (x = 30%, y = 20%). Again we see that consistent and implausible clusters around y=60% and 90% percent suggest false reporting, likely the work of a single official.

If this doesn’t convince you, have a look at the same region in 2007:

Moderately obvious fraud

Not all instances of fraud necessarily involve absurdly high vote shares. In some regions it was made to be not so dramatic: only a 10-20% inflation of United Russia’s vote share, yet indefensible under statistical scrutiny.

St. Petersburg

There is, at the very least, a manipulation of vote counts as betrayed by the decisive line formation in the centre. Whoever fabricated the numbers clearly lacked the creative acumen to do anything other than set United Russia’s total to the sum of all other parties’ times a constant. If you checked, you would see that the linear cluster in the 2011 plot is exactly described by y = 6/7 x. (It’s rather appalling in itself that they could not find someone more statistically competent to do their bidding, in a nation so highly ranked in math competitions).

Whether the other cluster to the top-left is also fraudulent is uncertain, but its existence is awfully strange. Moreover, by looking at the bottommost cluster for this year (evidently the legitimate cluster) and seeing how much support United Russia has lost since 2007, you can understand why they’ve had to fudge the votes.

Tyumen Region

The plot for Tyumen region below shows again two distinct patterns of rigging: first, the insane precincts with greater than 80% United Russia support, but also the red and green clusters around y=50-70% which are still way off the expected values (but whose “other party” votes seem to be typical), and is likely indicative of heavy ballot stuffing.

Less obvious fraud

City of Moscow

The individual regions in Moscow (see “Plots for all regions” below) seem to be distributed strangely, but the nature of the rigging does not become obvious until all its regions are pooled as one. In this composite plot of all 3,373 precincts in the city, one can clearly see a bimodal distribution, or two distinct clusters. The bottom cluster is located near the main clusters seen in other cities, and should be the legitimate one, while the more dispersed, larger cluster above it is likely of fraudulent origin. What you see here could either be vote stuffing or miscounting taken at a massive scale.

Credit goes to Maxim Pshenichnikov for having done this exact same analysis in greater detail; I am just including the idea here for the sake of completeness.

Chelyabinsk region – Zlatoustovskaya

The plot for this region has one large cluster, and everything appears to check out, with only a few extreme (six or so) outliers above y=60%. But could perhaps even one outlier be too much? Looking at the other graphs, and at how tightly packed the main cluster is here, the answer is yes: a single point located that far away would take an enormous coincidence. It’s safe to say that all six of these precincts’ results are probably bogus.

Conclusion

These examples have shown that vote rigging is much more widespread and dramatic than it appears, and indeed decisively changed the outcome of the election. We saw unexpectedly regular patterns at the small scale, which help explain the anomalies in the big picture, and we compared different types of irregularities. Those in Russia who are protesting these results ought to settle for nothing less than a complete re-do of the election, under better scrutiny. Since Medvedev does not seem willing to allow this, the next few days and weeks will be very interesting to watch.

Plots for all 135 regions

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