A statistical study of the voting patterns in Turkey’s November 1 general election found strong evidence that is “consistent with widespread voting manipulation".

That was the conclusion of a paper released by assistant professor Erik Meyersson at Stockholm School of Economics entitled “Digit Tests and the Peculiar Election Dynamics of Turkey’s November Elections", and released on November 4.

The result of the elections came as a shock as the Justice and Development Party (AKP) of Turkish President Recep Tayyip Erdogan’s defied the almost universal polling consensus and won some 9 percentage points more than expected – just enough to rule alone, but not quite a constitutional majority.

Some have speculated that faced with external and internal instability Turks have turned to a strong leader to see them through uncertain times in what might be called a “Sultan complex". However, drilling down into the voting statistics Meyersson concludes that Sunday’s result was not so much an AKP victory as a defeat for the ultra-nationalist Nationalist Action Party (MHP).

“As in last elections, much of the change in voting seems to have occurred among nationalist as well as Kurdish voters, with this election seeing a difference of priority among them. Whereas June’s election was HDP’s to win, this one appears to have been to a large extent the nationalist MHP’s to lose,” Meyersson said in his paper.

Meyersson concentrated on the differences between June’s election and this one, where that time AKP was the recipient of the shock and had its majority grip on power broken after HDP entered parliament for the first time.

“Plotting the difference in vote share between November and June, the AKP’s gain appears to come predominantly at the expense of MHP. In some other cases, the vote swing seems to be driven by voters in Kurdish provinces leaving the other main opposition party pro-Kurdish and left-leaning Peoples’ Democratic Party (HDP) for AKP,” says Meyersson.

 

​The main statistical test the paper explores is the use of the so-called Benford’s Law that is a widespread statistical technique for spotting cheating in polls and has a big body of academic literature behind it.

The way it works is simple: in a fair vote the last number of the final tally for each polling station should be randomly distributed. As humans are very bad at generating random numbers if the vote count has been tampered with then this randomness is destroyed and a discernable pattern emerges.

Fun fair owners use Benford’s law and count the small change in the till in much the same way to catch attraction staff who have their hands in the till: dishonest employees tend to steal round numbers of notes and coins. The Benford distribution of final digits in the numbers should look something like this: 

A similar technique was used to show that Russia’s Duma election in 2011 was fixed and the authorities added an estimated 12% to the winning, and now ruling, United Russia party. Instead of a smooth Benford curve, the statistical analysis found there were spikes in the tally results ending with a 5 or a 0. The crooked vote counters naturally, and without thinking, were rounding up results in United Russia’s favour. The same spikes were seen in the votes for Just Russia (aka Fair Russia), the leading opposition party, which strongly suggests its votes were stolen and gifted to United Russia.

That result was so clearly unfair it led to the first mass street protests Russia has seen since president Vladimir Putin came to power more than a decade earlier.

 

Meyersson’s study finds a very similar thing seems to have happened last weekend. The analysis was complicated by the fact that some ballots only produced 300-350 ballot papers, which is too small a number to be a good statistical sample. To get round this problem Meyersson decided to use the June vote as the basis of the comparison for the randomness of the last number – but that also assumes the summer’s vote was free and fair.

Those caveats aside, the results are striking. As the chart below of the frequency of each of the appearance of the numbers from 0-9 in the last place of the final tally clearly show there are too few zeros in the AKP party vote counts and too many for MHP.  The same is true for HDP, but the number of zeros at the end of the tally for Republican People’s Party (CHP) were the same in both elections and conforms to the Benford distribution above.

These charts would be consistent with election officials stealing votes from MHP, and to a lesser extent from HDP, and giving them to AKP, but leaving the CHP vote tally untouched. Other charts in the paper suggest that unlike the Russian 2011 election, officials were rounding MHP results down to the nearest whole number and giving the difference to AKP. 

Meyersson goes on to drill into more detail and compares the votes in the five biggest cities as well as look at a sample of vote results in small rural cities and towns were election observers are less likely to go. The same results are repeated at all levels. Finally, Meyersson looked at the voting in the 35 provinces where MHP won more than 20% last time round, against its 10% share of the overall election.

“In this ‘nationalist sample’, even though the AKP’s last digits do not differ systematically from the previous elections, both that of CHP and MHP do. And as before, it shows abnormally large occurrences of lower last digits and smaller occurrences of larger last digits, Meyersson concluded.

Finally as a control Meyersson tested these results with another test based on separate research by Beber and Scacco, which show that in fixed elections officials have a habit of number pairs in adjacent places when making up results (12, 34, 65, etc) when again the distribution of numbers inside the final tally result should be random.

In a table that measures this frequency of number pairs Meyersson found that, “In all but one cases does  the occurrences of adjacent digits change between November and June for the MHP, and for the HDP there is a statistically significant change in the five largest provinces sample.”

“Overall, this analysis shows evidence that would be consistent with widespread voting manipulation, not proof of it, both in terms of the change in the distribution of last as well as adjacent digits,” Meyersson concludes the paper with.

“Sunday’s landslide victory by the AKP represents a remarkable comeback for a government that according to the overwhelming majority of polling companies looked set to repeat its June loss. Many are now pointing fingers at these pollsters (and analysts overall) asking how they could have been so wrong. But what if they weren’t?”