17 | by S.P. The Economist explains WHEN French voters head to the polls on Sunday April 23rd, for the first round of their two-stage presidential election, it will be the most closely fought race in their country’s modern history. In total 11 candidates—not even a record—are chasing just two places in the second-round final, to be held on May 7th. Almost every past French presidential election has featured a run- off between candidates from the two mainstream parties: the Socialists and the Republicans. This time, polls suggest that any one of four candidates might make it into the second round, and two of those are from the Eurosceptic, protectionist extremes: Marine Le Pen, on the far right, and Jean-Luc Mélenchon, on the far left. The polls are tight, voters are unusually undecided, and the stakes uncomfortably high: this is an election that could remake Europe, or destroy it. Tensions were heightened on Thursday night by a shooting on the Champs-Élysées, a terrorist attack claimed by Islamic State, which killed one policeman. Some of the candidates’ events for Friday, the last day for campaigning, were called off. Other presidential elections have also been volatile in the final stages. In 1995, two months before voting, Edouard Balladur, a centre-right candidate, was ahead of Jacques Chirac, a Gaullist, in first-round polling; but in the end it was Mr Chirac who made it to the run-off, where he beat Lionel Jospin, a Socialist. A far greater shock was the 2002 election, which polls suggested would once again feature Mr Chirac against Mr Jospin. Instead it was Jean-Marie Le Pen, of the far-right National Front (FN), who stunned France and qualified, only to lose to Mr Chirac. The difference this time is that only four to five points separate the four front-running candidates: Emmanuel Macron, a centrist independent, Ms Le Pen, daughter of the FN’s founder; François Fillon, of the conservative Republicans; and Mr Mélenchon. This makes the outcome particularly uncertain, for two reasons. One is turn-out, which is historically high at French presidential votes, at about 80%. Polls suggest that this time it might be closer to 70%, with high abstention possible in the formerly Socialist-voting banlieues , or outer-city housing estates. This could favour the candidates with the most solid and determined voter base, notably Ms Le Pen (84% of whose voters say they are sure of their vote) and Mr Fillon (81%). The other is the number of undecided voters. Fully 28% say that they could yet change their mind. Last-minute decision-making is not unusual, but pollsters say that this time it may not reflect the general trends. Some voters may do so for tactical reasons to keep out the extremes. Mr Mélenchon and Mr Macron look the most vulnerable, with only 70% and 74% of their voters saying they are sure of their choice. So what to expect on Sunday? The possibility that Ms Le Pen reaches the run-off remains high, although that of her winning in the second round is not, because voters tend to gang up at the ballot box to keep her out. No poll has suggested that she could beat any of the other three candidates. The chances that she might meet Mr Mélenchon, in a run- off between two extremes, have spooked markets, and would be dire for France, but are unlikely. Mr Fillon could yet benefit from a return of shy voters, put off by the scandals clinging to him but even more so by the alternatives on offer. Perhaps the most radical thought is this: that polls in the closing days are simply right, and that the 39-year old Mr Macron, a candidate with no electoral experience, is indeed the most likely to go through to the second round, at which point he would become the favourite for the presidency.