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Would My Vote in the Referendum Have Mattered?

Two weeks or so ago, there was a referendum in Turkey. A referendum so significant in its items, that it could literally turn the country into a one-man dictatorship. I did not vote in it because it was too expensive to travel to the consulate in Rotterdam and get registered as a voter. I simply did not believe in the power of my vote enough to spare thirty or so euros—primarily because of its statistical insignificance.

…and as you may know, the referendum passed with an ‘Evet’ (Yes) vote, effectively making the parliament meaningless and introducing an executive presidency. You may find it odd, but I do not feel guilty.

Set aside the probability theory and predictive analytics, as someone from a country with a past as troubled as Turkey, I cannot get myself to believe in the power of the people. I knew, deep down since the referendum date was announced, that the leading party would do absolutely anything in its power to get the proposed constitutional changes through—yet I still had some hope that the results would be such that the secular and democratic Turkey saw another day. Seems not.

My girlfriend studies political science in Germany, and she deeply believes that it is every citizen’s duty to vote, whatever the odds, and cites various social and political uprisings as evidence for the power of the people. After the referendum, she was not furious at me for not voting because it was expensive, but she was furious at me because I did not trust the idea that my vote would have changed something. I thought that maybe I was being very irrational and dramatic, dismissing the idea that democratic choices can really empower people. To rationalise what I thought was irrational, I got down to reading articles and journal papers…

Initially, in a very straightforward manner, I tried googling ‘does your vote matter’ and the variations thereof, which led me to a lot of articles talking about what my girlfriend was telling me; your duty to vote, signalling your position, voting for independents is not a waste of ink… I agree, those are all very important, under certain circumstances—although not exactly applicable when you country becomes a dictatorship whether you want it or not.

Most of the investigative analysis I found online were focused heavily on the United States’ presidential elections. Because the US political system is effectively a two-party system—due to Duverger’s law, and the fact that the two polarised parties are in such positions that they can integrate the agenda items of the smaller parties—the papers were concerning the electoral college, and how certain states were ‘settled’ on a specific party.

This sort of research is not directly applicable to Turkey, because even though most provinces can be classified as ‘Evet’ or ‘Hayır’ (No), their votes count individually, instead of being lumped into one party or the other as it is the case in with the electoral college. Fruitless as my search was in trying to put my beliefs into numbers, I started digging through the university’s journal database, and found quite a few useful papers on the matter.

The Turkish elections are notorious for having very high turnouts. The referendum had a turnout of 85.32%, the November 2015 general election had 85.18%, the June 2015 general election, which produced a hung parliament, had 83.92%, the 2011 one had 83.16%, and so on. The turnout basically never goes below 80%, and mostly hovers at about 85%. This is incredibly high according to the data from the Institute for Democracy and Electoral Assistance, which puts most European countries in the 40-70% range. It is said that high turnout is very important for the functioning of a democracy, or in this case, the overthrowing thereof.

The question of why these people did not vote is rather ambiguous in the case of Turkey. There are a lot of conflicting studies in the US that disagree on the reason why people do not vote, and the primary disagreement is based on satisfaction or dissatisfaction in the status quo. Certain studies note that non-voters are often dissatisfied in the way the government works, and others argue that a significantly low turnout may mean an overall satisfaction. These results are not particularly applicable, because Turkey is a country that, again, has very high turnouts.

One reason to think that the non-voters could be ‘Hayır’-leaning is the likelihood that they were discouraged, like me. Although people may be afraid to express their opinions, given the attempts at actively suppressing ‘Hayır’ campaigns and the mass-purge after the coup, being discouraged from voting is likely not a significant problem. After all, the most important thing to note is the fact that Turkey, since 2001, has been voting in favour of the same party, with consistent turnouts. If we were to assume that the non-voters would be a ‘Hayır’ majority, they would have been pushed to vote to express their dissatisfaction. ‘Evet’ voters are already the group that is effectively in charge of the country, so they are not as roused to vote as the ‘Hayır’ demographic.

A study I found by Highton and Wolfinger, titled The Political Implications of Higher Turnout, was focusing solely on the voter characteristics of non-voters, and try to extrapolate from thereon. They found out that, by using a simulated population constructed with a political view survey, the difference in the outcome would have been very little in general if the entire population voted. They also found that ‘those at the top end of the income scale turn out in far larger numbers than those at the bottom end,’ which is rather unsurprising.

Although the study focused heavily on the United States, it would not surprise me if Turkey had similar characteristics in the non-voter population. Most developed provinces of Turkey, such as İstanbul, İzmir, and Ankara, have all voted ‘Hayır.’ Looking at the provinces who voted ‘Hayır’ in majority, I found out that they contributed to 69.71% of the GDP in 2014, as only 32 out of 81 provinces of Turkey. Seeing also that these provinces have turnouts higher than the overall, it would have been more difficult for them to contribute to a greater shift.

In the referendum, out of 49,799,163 votes counted, only 48,934,116 were valid. Of those valid, 25,157,025 were ‘Evet’ and 23,777,091 were ‘Hayır.’ This gives us a 51.41% to 48.59% ‘Evet’-‘Hayır’ ratio. These results are not finalised, but they are good enough to move on.

So, over the 58,366,647 eligible voters, I will be analysing the amount of votes required to turn the balance to 50-50 and 51-49 splits, where the first one is the bare minimum to tilt the outcome, and the second one is to move the result beyond a reasonable doubt, and perform these analyses over 100%, 95% and 90% turnouts; in order to figure out how the vote could have been turned into a ‘Hayır.’

The formula to solve for the necessary ratio of ‘Hayır’ in the remaining valid votes for any given turnout here is:

(23,777,091 + (P × T − 48,934,116) × H) / (P × T) > {0.5, 0.51}, where:

P is the eligible voters, T is the turnout, as a member of {1, 0.95, 0.9}, H is the percentage of voters who voted ‘Hayır.’

The idea is that, the sum of all ‘Hayır’ votes in the results and all ‘Hayır’ votes in the remaining votes over all votes should be higher than 50% or 51%. This is a simple linear equation where P and T are already defined, so it is solved for H. In parenthesis are the nominal number of people for the respective ratio.

As you can see, the ratios from the people who did not vote are exceptionally high. Even at the best case scenario, where only 57.3% of the people have to vote 'Hayır' to take the vote to 50% in a full turnout, is impossible to achieve. I performed the statistical test for proportion difference between two populations for the value in this, to receive p-values that are consistently lower than about 10-1000. For scale, 1080 is the estimated number of atoms in the universe. You can still argue that there can be variations in the group who did not vote, but referring back to my previous points, I doubt that you can ever achieve such ratios: The difference between 48.59% and 57.31% alone is almost nine percent, and that is the best possible case. There is not even the slightest guarantee that the people who did not vote would have voted for a higher percentage of 'Hayır' than 'Evet.'

I guess I should conclude by making sure it is understood that I am not telling you not to vote. There are elections and referendums in which a single vote can really change things. However, the way democracies function make it such that sometimes you just do not win. It may be the best way we have to decide on things, but that does not at all mean that you cannot be unhappy with the results. We saw that happen in the latest US presidential, where the unexpected Trump victory against all public polls, caused a massive outcry from the Democrat voters.

Realising that feeling myself is truly bitter, and so is having to deal with the consequences of this referendum. Statistically, however, I am not surprised. At least now I know the answer to my question; it would not have mattered even if I had gone and voted.


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