BOND-MARKET nerves and narrowing polls have drawn fresh attention to the risk of a President Marine Le Pen in France this spring. Since the start of 2017, the leader of the nationalist Front National (FN) has consistently topped voting intentions for the first round of the presidential election, which takes place on April 23rd. No poll this year, though, has suggested that she might win the second-round run-off on May 7th. Under the country’s directly elected two-round presidency, she needs to win an absolute majority of votes cast. This sets the bar high—but, arithmetically, it could happen.

The last time Ms Le Pen stood for the presidency, in 2012, she secured 6.4m votes, or 18%. Turn-out in French presidential elections is consistently high, at about 80% of the 46m on the electoral register; some 75% cast an unspoilt ballot paper. Assuming that turn-out remained the same this year, she would therefore need the backing of just over 17.4m voters in the second round in order to win the presidency. This would require Ms Le Pen to nearly triple her vote from 2012. To see how tough this would be, consider current polls, which give Ms Le Pen about 26% in the first round, or some 9m votes. This would still leave her more than 8m votes short of a second-round majority. A more generous scenario is based on the 42% she scored at the second round of regional elections in 2015, when Ms Le Pen stood in what is now called Hauts-de-France. This region, with its rust belt and mining basin, is particularly favourable to the FN, and she has a local history of campaigning there; most other parts of France, bar the south, are less sympathetic. Were she—however improbably—to match this share of the vote countrywide in May, Ms Le Pen would win a massive 14.6m votes. This would still not, however, be enough to secure her an absolute majority, under traditional turn-out rates.

What if voters, however, uninspired by the alternative to Ms Le Pen—whether François Fillon (centre-right), Emmanuel Macron (centre), or Benoît Hamon (Socialist)—decided to stay at home en masse, rather than uniting behind her second-round opponent? In order to gain an absolute majority on the most conservative assumption (9m votes), turn-out would have to collapse to around 40%. If Ms Le Pen managed the higher figure (14.6m votes), turn-out would have to drop to 63%, or some 68% if spoiled ballot papers were included. Since the Fifth Republic was founded by Charles de Gaulle in 1958, this has never happened. Which makes a President Marine Le Pen unlikely—but not impossible.