Specifically, we use two statistical methods to detect anomalies that are often linked to election fraud. Finding such anomalies does not prove that fraud in fact happened but it would raise doubts and justify calls for further investigation. Since results are often hard to interpret in an absolute sense, we use 2012 parliamentary election as the benchmark in our analysis since the election was perceived as dubious.
Tool #1: Voter turnout and party shares
Perhaps the most popular form of fraud is to throw in voter ballots for a party. An implication of this “trick” is that one should see a correlation between the turnout of voters and the share of votes going to a given party. However, the interpretation of such correlation may be more complicated in cases where the distribution of voters’ party preference and their activity is not random. For example, people in region A may be more energized than people in region B. To the extent people in region A favor party X rather than party Y, which is favored in region B, we would observe a correlation between turnout and the share of votes going to party Y without fraud taking place. One can address a concern like this by controlling for characteristics of various regions.
We run such an analysis* on the data from the 2012 and 2014 parliamentary elections to put the results from 2014 in perspective. We find that in the 2012 election, the share of votes going to the Party of Regions, the winner of 2012 election and the party of the ex-president Viktor Yanukovych, was strongly positively related to voter turnout. Specifically, the estimate suggests a one percent increase in voter turnout associated with about 0.24 percent increase in the share of votes that went to the Party of Regions. We can rule out that this estimate is by chance. In contrast, the estimates for all other parties, except Svoboda, are negative. This result is consistent with the view that the Party of Regions was “stealing” votes from other parties. Note that the coefficient on the Communist party is the most negative suggesting that the Communist party suffered the most from such “stealing.”
In contrast, the share of votes going to People’s front, the winner of the 2014 election, does not show any correlation with voter turnout. Poroshenko bloc, the second most popular party in the 2014 election, does show a positive correlation between the share of votes going to the party and voter turnout. This is potentially troubling, but the degree of the correlation is much smaller than that of the Party of Regions in 2012 – the sensitivity of the Poroshenko bloc share to turnout is five times smaller than that of the Party of Regions. Overall, the results for the 2014 election from this test indicate that the scope of fraud — if it occurred – was much smaller than in 2012.
Tool #2: Voter turnout and contribution of extreme stations
Fraud is likely to be concentrated in a relatively small number of polling stations, but these stations can bring a significant share of votes at the national scale. It is suspicions if a bulk of votes comes from a handful of polling stations with very high turnouts. Obviously, some polling stations can have large turnouts, but, statistically, they should make little difference for the total number of votes going to any given party. Intuitively, it is possible statistically to have high turnout rates for polling stations with a few registered voters. But high turnout rates are not very likely to happen in polling stations with a large number of voters. For example, if a polling station has five registered voters, it is relatively likely that all five voters show up and vote. In contrast, if a polling station has 10,000 potential voters, it is extremely unlikely that all 10,000 would show up.
One way to detect this anomaly is to examine the cumulative contribution of polling stations as a function of turnout. If everything is fair, one should observe that as turnout approaches 100 percent, the share of votes going to a given party at the national level flattens. In other words, a flat part of the cumulative distribution signals that these extreme polling stations make no effect for the results at the national level. On the other hand, if the cumulative distribution rises with turnout close to 100 percent, there is a reason to worry: These polling stations not only have statistically unlikely turnouts but also votes unusually concentrated for a given party.
Figure 1 below plots such cumulative distributions for the Party of Regions in 2012, the People’s front in 2014, and the Poroshenko bloc in 2014. Note that for the last two parties the curves are flat after about 90 percent turnout. In contrast, the curve for the Party of Region continues to rise all the way up to 100 percent. This positive slope is a clear sign of potential fraud: large districts had unusually high voter activity and these districts were atypically strongly in favor of the Party of Regions. Again, when we put the 2014 election vis-a-vis the 2012 election, it suggests less evidence of fraud in 2014.
Mark Twain once famously said that there are three types of lies: “Lies, damned lies, and statistics.” Apparently, he was not aware of elections in Ukraine where results could tell lies far worse than statistics could tell. Our statistical tools suggest that the scale of election fraud in the 2014 election was considerably smaller than in the 2012 election. To the extent one believes in statistics, he or she can take our results as a sign of science approving of the election results in 2014.
Ukraine has a mixed electoral system, with 53.2 percent of seats allocated under party lists and 46.8 percent allocated in 198 constituencies. Our analysis was conducted only for the party lists. A part of the public discussion in Ukraine focuses on the question of whether Ukraine should move to 100 percent party list system in order to remove alleged abuse in the individual constituencies. Hence, it would be valuable to complement the analysis in this post with that of the anomalies in the remaining 198 constituencies. It is also extremely interesting to consider the counterfactual composition of the new Ukrainian parliament if the turnout in the east affected by the security crisis were on par with that in the rest of the country.
[Data: 2014: 99.52 percent voting stations covered, stations located abroad not included; 2012: 99.59 percent voting stations covered, stations located abroad not included]
*Here are the details of the regression analysis: