The French presidential election will be held in 10 days from now, and it seems like a nail-biter. The first round, which seeks to determine which two candidates will be qualified for the final runoff^{1}, seems to have become essentially a four-way race. And we are not talking about a four separate, but similar politicians. We are talking about a pro-European centrist candidate (Emmanuel Macron), a neo-conservative who, after being charged for embezzlement of public funds, is now France’s most unpopular politician (François Fillon), a brash but eloquent candidate endorsed by the French Communist Party (Jean-Luc Mélenchon), and, of course, Marine Le Pen. According to the latest polls, all of them are, essentially, within 5 points of each other.

The French media is, understandably, covering the election relatively nervously. Even though every poll for the past few weeks has shown Macron and Le Pen with a somewhat comfortable lead over Fillon and Mélenchon, every one of the 6 potential match-ups is brought up by pundits. (This has a lot to do with a massive 15-year old election upset; I’ll come back to that a little later.) Most bonkers, however, is that this concern is actually probably *under*played. Just by taking a look at the general shape of election polls, it is pretty clear that something weird is going on, and that we may underestimate how truly unpredictable this first round is shaping to be.

The big red flag of these election polls is that they really, really don’t deviate from each other. It is a pretty easy thing to measure. Polls, because they take measurement on a sample, are inherently flawed; fortunately, that flaw is simple to estimate. For this post, I am assuming that the sampling error for one poll, for the first round, is around 2.7 points^{2}. This is the sampling error that one would expect when trying to evaluate percentages around 20 points, and with samples of 1000 people. This what we are talking about here: the four candidates’ numbers are currently in the range of 17 to 25 points; and almost every poll has a 1000-ish sample.

If that standard error due to sampling is 2.7 points, that means that we should find results within that interval something like 68% of the time.^{3}. This is what would happen if all the surveys were done with random sampling, and no tinkering on the back end. What happens if you line up the polls together and compare them?

The black dots here, represent the different polls. The black line is the moving average (computed with a local regression). The blue interval is this average +/- 1.35 points, which represents the sampling error. We should normally expect to see roughly a third of polls outside that interval. It is obviously not the case. Even more striking is the fact that polls get significantly closer 60 days before the election, after February 25th, at the moment where you can see a lot of movements in the numbers. For the past three months, basically, there has been virtually no outlier poll for any of the four major candidates. This should not happen in an ideal polling environment, and is quite concerning.

To get more dramatic, I used a chi-square test, which is used to determine if a dice is weighted. Here is what it yields:

- The odds that the fact that Macron’s scores were this consistent is a coincidence is 0.001%.
- The odds that the fact that Fillon’s scores were this consistent is a coincidence is 0.0003%.
- The odds that the fact that Mélenchon’s scores were this consistent is a coincidence is 0.0006%.
*The odds that the fact that Le Pen’s scores were this consistent is a coincidence is 0.00000000002%.*

There are potential two explanations to this. Firstly, French pollsters almost uniformly use a method called quota sampling. In other words, they seek for a certain balance with regard to their samples to achieve certain ratios that would be, in their mind, representative of the electorate. The consistency of the quotas used by pollsters could be the cause of the consistency of the polls; and, of course, this is a controversial polling method. It was discredited in the US in 1948, after it failed to predict Truman’s re-election. And this is probably a very bad election cycle to promote quota sampling. The 2017 election cycle has been defined by its volatility, as well as an unusually high number of undecided and a big question mark with regard to turnout. (That, in short, never really happened before^{4}.) In this disjunctive election cycle, it seems a little bit crazy to pretend that the quality of polls rely on a deep understanding of the electorate and its dynamics.

The second explanation, much less nice to pollsters, is what Americans would call herding. In other words, manipulating poll data, or hiding some results, to prevent outliers^{5}. I don’t know to which extent this is the case, because it would require a little bit more of analysis, but it definitely does seem likely. That polls seem more and more consistent during periods at the end of the campaign that displayed a lot of poll movements looks very suspicious to me. I just don’t buy that pollsters have a better grasp of the electorate now that they had four months ago, especially provided that the campaign has been essentially upended a few times since then.

I am all the more suspicious of French pollsters that they actually screwed up big time before. In 2002, all of them showed Prime Minister Jospin and President Chirac as confortable front-runners in the first round; they were virtually assured of being qualified to the second round. What happened, in fact, is that National Front’s Jean-Marie Le Pen came in second, ousting Jospin. (And with an almost 1 point difference!). This was, and still is, a national trauma, as the public did not see it coming. And guess how were pre-election Le Pen’s poll numbers? (The red dot is his actual, eventual score)

It seems like history is repeating itself 15 years later. What does that mean for Election Day? Essentially, fasten your seat bells. The uncertainty around this election is much, much higher than polls might let us think. A lot of second-round possibilities, even between the far-right and the far-left, are to be considered. And, for once, the political TV circus is actually justifiably hysterical.

(1) The French election votes according to the runoff voting system. First round candidates need 50% of the votes to win, or else the two top candidates face off in the second round to get these 50%. And for those who think that this system is a French peculiarity, you might want to think again: it’s actually the voting system used in next Tuesday’s special election in Georgia.

(2) This is also somewhat less than the average error that French polls have historically displayed 30 days before the election. If I were to use that metric, though, it would only strengthen my claims that French polls may be pretty low-quality, and too close to each other.

(3) The standard error is basically half the margin of error. If a pollster say “20%” to you, it really means that it is 95% confident that it will fall between 17.3 and 22.7 points (+/- 2.7 points). And 68% that it will fall between 18.65 and 21.35 (the range is 2.7 points large.)

(4) Turnout for French presidential elections tends to be in the 80%’s, which is obviously much higher than elections in the U.S.. This tends to reduce uncertainty with regard to the effect of turnout on elections.

(5) Much more through explanation of herding is given in this article, which served as a partial inspiration for this post.