Emmanuel Macron, a centrist candidate, and Marine Le Pen, of the far-right-wing National Front, will advance to a runoff in the French presidential election after finishing in the top two positions in a first-round vote on Sunday. Macron is an overwhelming favorite to win the runoff on May 7. But we’re likely to hear two weeks of punditry that draws misleading comparisons between Le Pen, President Trump and Brexit — and that exaggerates Le Pen’s chances as a result.

Although vote counts are still being finalized, the first-round result should be a good one for pollsters, which correctly had Macron and Le Pen in the top two positions. In fact, the pre-election polls — which had shown Macron at 24 percent, Le Pen at 22 percent, the center-right François Fillon at 20 percent and the far-left-wing Jean-Luc Mélenchon at 19 percent — should come within a percentage point or two of the final result for each of the top four candidates.

The same polls show Macron in a dominant position in the runoff. He leads Le Pen by 26 percentage points in polls testing the two-way matchup, according to data compiled by G. Elliott Morris of The Crosstab.

And yet, observers of the race seem cautious about Macron’s chances. Betting markets give Le Pen a 13 percent chance — about 1 in 7. Ian Bremmer, a political scientist who runs The Eurasia Group, has given Le Pen a 40 percent chance, meanwhile. (Bremmer’s estimate wasn’t based on any sort of statistical model; he argues that the polls don’t reflect major elements of French politics.) And esteemed publications such as The Guardian are questioning whether the polls can be trusted at all, despite their accuracy on Sunday:

By contrast, polling-based models give Le Pen very little chance. Morris’s model, at The Crosstab, gives Le Pen a 3 percent chance of winning the runoff. And a model designed by The Economist puts Le Pen’s chances at less than 1 percent.

I worry about overconfident models — for a variety of reasons, statistical models can underestimate tail risks if they’re not designed carefully. In the U.S. election, models varied wildly in their estimates of Trump chances, from 29 percent in the FiveThirtyEight “polls-only” model to less than 1 percent according to the Princeton Electoral Consortium. A lot of those differences had to do with how these models analyzed the Electoral College, a complication that models predicting the French election don’t have to contend with. Still, I’m more comfortable with slightly more conservative estimates such as Morris’s than with The Economist’s.

But in my view, the conventional wisdom espoused by analysts such as Bremmer is more likely to be way more out to lunch. Before the U.S. election, Trump trailed Hillary Clinton by only about 2 percentage points in the average swing state. In the Brexit vote, the “Remain” campaign’s lead was at least as narrow: about 2 points according to a simple average of polls, or just 0.5 percentage points according to a more complex averaging method. So while Trump’s victory and Brexit were historic events in world history, they were utterly routine occurrences from a polling standpoint; 2- or 3-point polling errors are extremely common.

But while there were plenty of precedents for a polling error large enough to elect Trump, there aren’t all that many examples of a 26-point polling error, which is what Le Pen would need. Pundits and other political observers often have poor intuition when it comes to translating polls into probabilities, leading them to treat narrow, fragile leads the same as double-digit ones. Ironically, the same type of sloppy thinking that led people to underestimate the chances for the Trump and Brexit victories may lead them to overestimate Le Pen’s odds.

Of course, there are still two weeks to go until the runoff and it’s possible that Le Pen could narrow her deficit. But by the same token, Macron could expand his lead in the final weeks. Fillon, whose voters agree with Le Pen on some issues, has already endorsed Macron. So did Socialist candidate Benoît Hamon. And Le Pen faded down the stretch run of the first-round campaign, having regularly polled in the mid-to-high 20s in February and March before seeing her numbers decline to about 22 percent in the final polls and in the actual vote.

Some of the bullishness about Le Pen’s chances reflects the idea that there’s a lot of hidden support for Le Pen, perhaps among voters who say they are undecided. This is a version of the “shy Trump voter” theory of the American election, which says that people are afraid to tell pollsters that they support “politically incorrect” candidates. In the abstract, this theory could make some sense; pollsters have long worried about the effects of social desirability bias. A voter who held contemptuous views toward a racial minority group might not want to express those views in a phone call with a stranger conducting a poll, for instance.

However, there’s no evidence that candidates such as Le Pen systematically outperform their polls. Across dozens of European elections since 2012, in fact, nationalist and right-wing parties have been as likely to underperform their polls as to overperform them.

I’ve built a database that covers the performance of right-wing parties and candidates, such as Le Pen and the National Front, in European elections since 2012. (More specifically, the parties are those identified by the New York Times as being “right-wing”; they “range across a wide policy spectrum, from populist and nationalist to far-right neofascist.”) I found 47 elections during this period in which one of these parties competed and voters were regularly polled about it before the election. Some of these elections featured multiple right-wing parties or candidates, so there are a total of 66 data points.

On average, the right-wing parties were predicted to win 13.5 percent of the vote in polls conducted at the end of the campaign. And they wound up with an average of … 13.5 percent of the vote. Polls have been just as likely to overestimate nationalists as to underestimate them, in other words.

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For European elections with “right-wing” parties since 2012. Le Pen’s vote total reflects a preliminary estimate from Ipsos.

Sources: New York Times, Wikipedia,

The same has been true in France, where the National Front has variously underperformed and outperformed its polls. In five elections since 2012, the National Front has averaged 21 percent in polls and finished with 21 percent of the vote.

In European elections since Trump’s win, in fact, the trend has been for nationalist candidates to perform disappointingly. Geert Wilders’ Party for Freedom faded badly down the stretch run in the Dutch general election and then underperformed its polls on election day last month. Meanwhile, Austria’s Norbert Hofer, of the Freedom Party of Austria, considerably underperformed his polls in a presidential re-vote last December. Trump isn’t popular in Europe, and his victory may have done candidates who emulate his rhetoric no favors.

There’s still some uncertainty about the outcome, however. Although the polls haven’t systematically underestimated nationalist and right-wing parties, they also haven’t been all that accurate in pinning down their support, having come in both high and low in different elections. In cases since 2012 where the right-wing party polled at 25 percent or more, the polls missed the party’s actual support by an average of 3.6 percent of the vote. That translates to a true margin of error (or 95 percent confidence interval) of about plus or minus 9 percentage points. And because any vote that Le Pen gets is one that Macron won’t get, the margin of error for the gap between Le Pen and Macron is twice as large, or about 18 percentage points.

An 18-point margin of error is huge! But it still isn’t enough when you’re 26 points behind, as Le Pen is against Macron. If Le Pen can significantly narrow her deficit with Macron over the next two weeks, Macron’s supporters will have reason to worry. If she still trails by something like 26 points on election day, however, a Le Pen victory would be essentially unprecedented. She could beat her polls by as much as Trump and Brexit combined and still lose to Macron by almost 20 points.

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