(Note: This post may be updated)

My previous post documented a peculiar relationship between the share of invalid ballots and higher voting share of the ruling AKP government in last week’s local elections in Turkey. In both Ankara and Istanbul, this relationship was robust to across-district, even across-voting-station, differences. Thus even within a single voting station, like a primary school etc, invalid ballots appear to drive up the vote share for the AKP. Moreover, the relationship appeared to particularly bias votes toward the AKP in areas that tend to have more support for the opposition.

By now, that post has received considerable attention (see here, here, here and here), raising the question of whether these elections included non-trivial degrees of voting fraud. I’ve from the start been deliberately careful in not labeling this as fraud, partly due to the preliminary nature of the analysis, and partly because statistical anomalies remain so only until they receive adequate explanations.

As additional data has come in, thru the CHP-STS data collection system, and thanks to Twitter user @erenyanik for sending the data my way early on, I’ve had some time to replicate this analysis for additional cities.

Mostly for the sake of presentation, I’ve selected nine cities to look into at first. The first three of these are races between the ruling AKP and the largest secular opposition party CHP: Ankara, Istanbul, and Izmir. The second three are races between the AKP and the second-largest opposition party, the nationalist-conservative MHP: Adana, Manisa, and Mersin. The last three represent races that can be regarded as safe races for the AKP (although with MHP as the runner-up): Gaziantep, Kayseri, and Konya.

The choice of these three triplets is to see how the relationship holds up in races where there is substantial competition between AKP and the two opposition parties (CHP and MHP), as well as in races that can be considered relatively safe for the AKP.

My reasoning is the following.

The explanation for why invalid ballots appear to bias votes towards the AKP could be due to voting irregularities. Without knowing exactly how this would occur, one very simple way would be if there was a system to more intensively declare invalid opposition ballots than AKP ballots.

An obvious question mark in the analysis is to what extent any correlation represents systematic mistakes, not systematic fraud. Suppose the AKP has a higher support among the illiterate who are more likely to make mistakes when voting. In this case, we would not be surprised if there was a correlation between invalid ballots and AKP support. An explanation would be that those more likely vote for the AKP are also those more likely to make voting mistakes and have their ballots declared invalid. Given the large difference across districts in the large cities in Ankara and Istanbul, one can easily imagine this as a plausible explanation for the simple unconditional correlations.

It is here that the fixed effects used in the previous analysis becomes crucial, i.e. including fixed effects (FEs) to regressions of vote shares on invalid ballots control for all factors that vary across the FEs. Adding FEs for districts (Ilce) means we’re only looking at variation across ballot boxes within districts, whereas adding FEs for voting station means only looking at variation across ballot boxes within voting stations.

When doing this, although voters going to the same station to vote may still differ along several characteristics, it is much more difficult to argue that this systematically affect their likelihood of making mistakes in voting. The strength of the FEs is thus not that they control for everything, but that they reduce these differences to the point where it is less likely that the remaining differences represent an competing explanation for the correlation.

Furthermore, to the extent that this represent fraud, one would expect the relationship between AKP’s vote share and invalid ballots to be stronger in races with significant competition and less likely in races where the AKP was safe. (For the obvious reason that there is little return to engaging in fraud in races where you’re expected to win without fraud.)

Showing this for both Ankara and Istanbul was illustrating of this, but it would be useful to look at other cities where the correlation between voters’ preferences and socioeconomic characteristics may not necessarily be the same. For example, whereas in the previous two cities, the relatively richer may tend to lean more toward the opposition CHP. But in other cities, like Adana, Mersin, or Manisa, where the opposition party is the MHP, this is not necessarily the case. Investigating relationships in cities other than Ankara and Istanbul thus allows a kind of robustness test as the latent correlation between the omitted variables (education, income etc) and the invalid share of ballots, is likely to be different.

On to the analysis.

At first I plot the AKP vote share against the invalid share of ballots at the ballot box-level separately for each city. As a simple adjustment for omitted variables at this point, for each variable in an observation I subtract the district mean of the variable. The slope is thus equivalent to the coefficient of regressing AKP vote share on invalid share of ballots with district fixed effects. The below graph thus plots this district-demeaned correlation between AKP vote share in invalid share of ballots (see here for higher res image)

The figure shows clear positive correlations between AKP’s vote share and the invalid share of ballots particularly for the first two columns. These are also cities where political competition between parties is also relatively high. In the third column, for Gaziantep, Kayseri, and Konya – races that tend to vote for the AKP no matter what – the relationship is significantly weaker.

This supports earlier findings and shows it is not specific to Ankara and Istanbul. A more detailed analysis of different parties and using voting station (instead of district) FEs can be done by regressing, for each city, each vote-getting partie’s vote share on the invalid share of ballots controlling for voting station FEs.

The below figure reports the regression coefficients for each city and party (see here for higher-res image), this time with fixed effects for voting stations:

This figure shows a rather striking and consistent phenomenon. In especially the two first columns where the AKP faces stiff competition from CHP and MHP, invalid ballots appear to bias votes toward the AKP and away from its main competitors. In the safe races, in the third column, the correlations are both smaller and less statistically significant overall (with some exceptions).

All together, these last results further supports the hypothesis that Turkey’s most recent elections may have been implemented with substantial irregularities. Until a valid explanation for these results is presented that does not include voter fraud it is difficult to imagine what else could be going on.