"Invalid votes" as sign of voting fraud in Turkey's 30 March Elections? I doubt so.

Erik Meyersson has a recent blog post  that has received quite a lot of attention, especially in Turkey, which looks at the "invalid ballots" at the ballot box level and argues that the correlation between the AKP votes and invalid votes across the ballot boxes in major metropolitan areas points to a systematic voting fraud in Turkey's 30 March elections. I argue that Meyersson's post is (i) uninformed about the definition of "invalid ballots" in the Turkish context, (ii) fails to make a comparison with the previous elections, especially the previous local elections in 2009, (iii) fails to take into account one major cause for the invalid ballots that was the direct result of decreasing the number of ballot boxes from 3 to 2 in this election, and finally, (iv) violates the basic assumption of statistics that all factors other than the one under consideration or comparison must be random (the ceteris paribus condition in Economics).

I shall discuss each of these points below.

(i) "Invalid ballots" in the Turkish election system

Again, I think a basic understanding of what constitutes "invalid votes" in the Turkish election system is a necessary prerequisite for this type of analysis. I have written a blog post explaining what the entries on the "Ballot Result Report" (Sandık Sonuç Tutanağı) mean:
http://iradeimilliye.blogspot.com.tr/2014/04/an-explanation-of-entries-on-election.html

You will see that there are 5 components to the invalid votes, denoted from (10) to (14), the sum of which gives the total number of invalid votes. Those components are:

(10) The number of invalid envelopes
(11) The number of empty envelopes which contained no ballots at all.
(12) The number of envelopes [that contained some ballots for other elections, that is, county mayor and/or county council] that did not have a ballot for the mayor election for the metropolitan area.
(13) The number of ballots that were counted as invalid.
(14) The number of ballots that were not taken into consideration.

I must also note that casting an invalid vote is a basic political right. As there are five different components of the invalid votes count, there are conceivably five different ways of deliberately marking your vote invalid:

(1) If you deliberately put a sign on the envelope that you place your ballot in, that envelope is counted as invalid (as in entry no. (10) above). Even if your ballot is perfect, any sign on the ballot envelope or any other problem related to the envelope will result in that envelope taken out of consideration. It will not even be opened.
(2) If you take the ballots you have been given with you, keep them as souvenirs or simply destroy them, and cast your envelope as empty, that envelope is counted as invalid (as in entry no (11) above) (As a further incentive, if you put those ballots into fire somewhere else, take photos/videos of those burnt ballots and post them to social media, you can even blame the government for voting fraud.)
(3) If you simply take the ballot for the metropolitan mayor away, but cast your votes for the other two ballots, this will only make your vote for the metropolitan mayor as invalid. Your other two votes will still be counted as valid (as in entry no (12) above)
(4) If you place the "Yes" seal on more than one candidate, if you mark your ballot in any other way (such as writing "thief" under the name of the ruling party's candidate, or "impotent" under another candidate's name), your ballot will be counted as invalid (as in entry no (13) above).
(5) Any other way that will take your ballot out of consideration.For details on this one, I need to check the Higher Election Council's memos.

Hence, when considering invalid votes, there are three possible explanations, which are not taken into account by Erik Meyersson:

(a) Those that are cast deliberately as invalid,
(b) Those that are mistakenly cast as invalid (I have witnessed several examples of this)
(c) Those that are declared or made invalid as part of a systematic election fraud.

One commenter to Meyersson's post, Yakup Ozsoy, stated that in Konya and Kayseri, where AKP won the election by a landslide, "people probably did not bother arguing about votes being valid or not. In other cities, however, it was worth the effort to nullify the vote." His comment concerns the process of counting ballots after the closing of the ballot boxes. How about people not bothering to vote at all, or to cast an invalid vote? In Konya, AKP received close to 70% of all votes in 2011. If someone, who could well have cast an invalid vote if he/she lived in Ankara or Istanbul, would he be more likely to do so in Konya, or would he be inclined to vote for an opposition party?

On the other hand, we know that Ankara, Istanbul and Izmir were all scenes of energetic protests during the Gezi events in June 2013. The Gezi protests were not simply protests organized by CHP, MHP or other political parties. True, they were mostly directed against the ruling party and its leader, Erdogan, but there was some criticism directed against the opposition parties as well. In Ankara, an MP from CHP, Aylin Nazliaka, ran a campaign to become CHP's mayoral candidate for Ankara. Certainly, Gezi protesters did not embrace Mansur Yavas, the former MHP candidate, and Mustafa Sarigul, famous for his corruption, in Ankara and Istanbul, respectively. Thus, it is quite possible that many Gezi protesters in these three largest Turkish cities, who were not satisfied with the opposition parties' mayoral candidates, decided to cast their votes as invalid.

Furthermore, as I point out in my blog post, some ballot result reports mistakenly included the number of unused ballots under column no. (14) above. An unused ballot cannot be an invalid ballot, because an invalid ballot is by definition a ballot that has been cast by someone and placed into the ballot box. This is a misunderstanding due to the legal language of the report that was apparently missed by some of the ballot box committee members. Hence, the data that Erik Meyersson uses contains figures for some ballot boxes that simply does not correspond to the reality. I don't know what percentage of the ballot boxes exhibit this problem, neither do I know how they are distributed across localities. But what is certain is that they obfuscate Meyersson's conclusions.

(ii) Comparison with 2009 local elections

Meyersson speculates the invalid ballots in this election is a sign that voting fraud has been committed, but he fails to check if the number of invalid ballots conforms with the situation in previous elections.

Let me first provide the invalid ballots for the 30 metropolitan areas in this election:

2014 Metro	Cast Ballots	Valid Ballots	Invalid Ballots	Invalid, %
ADANA	1.277.115	1.227.801	49.314	3,86%
ANKARA	3.274.380	3.164.555	109.825	3,35%
ANTALYA	1.358.582	1.315.452	43.130	3,17%
AYDIN	684.636	653.789	30.847	4,51%
BALIKESİR	809.458	783.155	26.303	3,25%
BURSA	1.794.353	1.720.587	73.766	4,11%
DENİZLİ	643.433	611.845	31.588	4,91%
DİYARBAKIR	762.646	723.072	39.574	5,19%
ERZURUM	409.135	395.935	13.200	3,23%
ESKİŞEHİR	544.999	524.725	20.274	3,72%
GAZİANTEP	909.620	881.824	27.796	3,06%
HATAY	864.238	839.523	24.715	2,86%
İSTANBUL	9.067.393	8.724.840	342.553	3,78%
İZMİR	2.751.913	2.657.447	94.466	3,43%
KAHRAMANMARAŞ	614.382	593.986	20.396	3,32%
KAYSERİ	799.899	767.715	32.184	4,02%
KOCAELİ	1.069.728	1.024.289	45.439	4,25%
KONYA	1.262.689	1.205.325	57.364	4,54%
MALATYA	492.694	483.166	9.528	1,93%
MANİSA	924.927	885.759	39.168	4,23%
MARDİN	330.317	321.601	8.716	2,64%
MERSİN	1.060.859	1.016.158	44.701	4,21%
MUĞLA	583.247	557.889	25.358	4,35%
ORDU	463.054	440.428	22.626	4,89%
SAKARYA	595.627	576.368	19.259	3,23%
SAMSUN	802.705	770.201	32.504	4,05%
ŞANLIURFA	828.156	802.059	26.097	3,15%
TEKİRDAĞ	573.443	550.441	23.002	4,01%
TRABZON	475.785	459.858	15.927	3,35%
VAN	451.065	439.154	11.911	2,64%
2014 30-Metro	36.480.478	35.118.947	1.361.531	3,73%

I have compiled the following table below, which provides the number of invalid ballots for the 2009 local elections, using the Higher Election Council figures.

2009 Metro	Cast Ballots	Valid Ballots	Invalid Ballots	2009 Invalid %	2014 Invalid  %	Delta
ADANA	835.470	802.522	32.948	3,94%	3,86%	0,08%
ANKARA	2.533.176	2.440.455	92.721	3,66%	3,35%	0,31%
ANTALYA	539.782	524.052	15.730	2,91%	3,17%	-0,26%
BURSA	1.122.453	1.074.707	47.746	4,25%	4,11%	0,14%
DİYARBAKIR	360.973	349.230	11.743	3,25%	5,19%	-1,94%
ERZURUM	183.443	178.380	5.063	2,76%	3,23%	-0,47%
ESKİŞEHİR	392.825	378.540	14.285	3,64%	3,72%	-0,08%
GAZİANTEP	594.367	569.897	24.470	4,12%	3,06%	1,06%
İSTANBUL	7.199.083	6.946.435	252.648	3,51%	3,78%	-0,27%
İZMİR	2.043.178	1.972.359	70.819	3,47%	3,43%	0,03%
KAYSERİ	494.668	477.233	17.435	3,52%	4,02%	-0,50%
KOCAELİ	891.735	857.940	33.795	3,79%	4,25%	-0,46%
KONYA	537.776	521.199	16.577	3,08%	4,54%	-1,46%
MERSİN	456.339	439.265	17.074	3,74%	4,21%	-0,47%
SAKARYA	362.515	351.875	10.640	2,94%	3,23%	-0,30%
SAMSUN	313.710	299.805	13.905	4,43%	4,05%	0,38%
2009-16 Metro	18.866.391	18.166.597	699.794	3,71%	3,73%

In 2009, there were 16 provinces in Turkey that were also metropolitan areas ("büyükşehir" in Turkish). Even for those 16 provinces, the metropolitan areas in those provinces did not encompass the whole province. In 2013, the law pertaining to the metropolitan areas was changed. The new law increased the number of provinces having metropolitan municipalities to 30, from 16. Furthermore, the metropolitan areas in all these 30 provinces were enlarged to cover the whole area of the province.

Remarkably, the percentage of invalid votes for the total of 16 metro areas in 2009, 3.71%, is just 0.02% short of the percentage of invalid votes for the total of 30 metro areas in 2014, namely 3.73%!

If we compare the figures for invalid ballots for each metro area, we see that the diffence between the percentages are less than 0.50% for most of them. In only 3 metro areas do we see the percentage of invalid ballots changing more than 1% between 2009 and 2014.

(iii) Less Ballot Boxes May Have Meant More Invalid Ballots

One result of the new metropolitan ares law that went into effect just before this election was that the so-called "Provincial General Assemblies" (İl Genel Meclisi) were abolished for the metropolitan areas. Previously, a metropolitan area did not cover the whole province, hence the only assembly that the whole province voted was these provincial general assemblies. With the new law, the Metropolitan Municipality Assembly, which consists of the union of all county assemblies in the province, covers the whole province, rendering the general assemblies unnecessary. In previous elections, a separate ballot box, and a separate set of ballots and ballot envelopes, were used for the general assembly elections. This meant voting in a metropolitan area was a 3 step-process. Voters would first be presented with the ballots for the mayoral elections and the corresponding envelope. They would cast their votes, place the envelope in the corresponding box, and then they would be given ballots for the provincial general assembly, return to the voting booth, and cast the envelope in the second box. Finally, they would be presented with an envelope for the local quarter (mahalle) elections. When there were three boxes and three rounds of voting, it was easy for the voters to comprehend that ballots of the mayoral elections (unified ballots, printed by the Higher Election Council) and ballots for local quarter elections (separate ballots provided by candidates themselves) would go into the corresponding envelopes. Now, in this elections, the elimination of the general provincial assemblies increased the probability that voters might think all ballots, including those for the local quarter elections, should go into a single envelope. This apparently increased the number of invalid ballots.

Meyersson's analysis does not take into account how this might have affected the invalid ballot count. On the other hand, looking at the tables I have provided above, it seems that even if decreasing the number of ballot boxes from 3 to 2 had an adverse effect on the invalid ballots, it certainly did not cause the invalid ballot percentage to shoot through the roof. So how to make sense of all this? This brings to my final argument against Meyersson's blog post.

(iv) The Ceteris Paribus condition is violated at all levels by Meyersson

The fundamental rule of scientific analysis gets different names in different disciplines but the idea is just the same. In physics and other natural sciences, we talk about "controlled experiments" where only one variable is changed and everything else is kept constant. In medicine, we talk about "evidence based medicine" which takes clinical trials as the basis, and the "double blinded clinical trials" are the backbone of golden standards. In economics, we talk about the Ceteris Paribus condition, that is, "Other things being equal." I am not a statistician, but I know that the most important point in statistics is to keep the sample domain random. Meyersson's analysis is based on the premise that the correlation between the AKP votes and invalid ballots at ballot box level is the control variable. He then compares the results between different metropolitan areas. He finds that in such places as Konya and Kayseri, the correlation between AKP votes and invalid ballots is weak, whereas in places such as Ankara and Istanbul, there is a strong(er) correlation. He argues that this points to voting fraud. The underlying assumption in Meyersson's analysis is that all other things are being equal when moving from the Konya, Kayseri etc datasets to Ankara, Istanbul, etc datasets. This is simply not true.

One important "thing" that may not be equal is the attendance rate. If we look at province-wide attendance rates, we see them to be remarkably close to each other, being around 90%. How about the attendance rates at ballot box level? Meyersson's analysis assumes attendance rates at individual ballot boxes does not have any effect on the relationship he posits between AKP votes and invalid ballots. I find this to be highly dubious.

I have already presented another point in the first section above. Some invalid ballots are cast that way deliberately, as a political expression, whereas others are simply due to voter errors. We simply cannot assume that the ratio of deliberately cast invalid ballots to mistakenly cast invalid ballots is constant. If Meyersson plotted AKP votes against, say, Saadet (SP) votes, or any other party's votes, he could well have come up with results similar to these results. 

Another way of controlling the variables would be to make a comparison between 2009 and 2014. The results of the 2009 election are available at ballot box level. I have provided tables above showing the invalid ballots for the metropolitan areas for both 2014 and 2009 elections. Looking at these tables, the invalid ballot rates for this election are consistent with the 2009 data.

Meyersson concludes his blog post by stating that "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." He argues that his results point to voting fraud, but he does not explain how such a fraud could have been committed. He says nothing about the fact that close to 1 million ballot box committee members have served in this election, including one member from CHP and another from MHP for the great majority of the boxes (excepting the areas with strong BDP presence). How could a voting fraud have been committed at a ballot box, when the whole process was carried out in the presence of the two major opposition party members, who then did not hesitate to affix their signatures to the official ballot box result reports? Meyersson's analysis cannot provide answers to these questions.