Going into the first round of the French presidential election, four candidates have polling figures between 19 and 23 per cent. The shooting of a policeman in Paris on Thursday night won’t do any harm to Marine Le Pen’s chances of making it to the second round. In 2002, her father narrowly beat the Socialist candidate, Lionel Jospin, into third place (16.9 to 16.1 per cent), setting up a second round contest with Jacques Chirac that he lost by the record margin of 18 to 82 per cent. Since the 13 other candidates, who between them took 47 per cent of the vote in the first round, were more left than right-wing, it is quite possible that Jospin would have won the second round if only he had got that far. Almost certainly, several of the 13 would have beaten Le Pen.

Most countries – the United States is a notable exception – regard it as unacceptably undemocratic to elect a president with less than 50 per cent of the vote. Having a second round between the two top candidates, as in France and about forty other countries, ensures that the final winner does have an absolute majority. But that is far from guaranteeing that we end up with the candidate who has most support among the electorate.

The definitive work on this problem of electoral choice was written by Nicolas de Caritat, Marquis of Condorcet, in 1785. Condorcet is one of the most attractive figures of the Enlightenment: as well as a brilliant mathematician he was an early supporter of women’s rights and opponent of slavery. He proposed that voters should give their order of preference, and the winner should be the candidate who is preferred against every other candidate in a head to head comparison. Condorcet recognised that there may be no winner under this system – it is possible for A to be preferred to B, B to C, and C to A – but this occurs very seldom in real elections, and there are several tie-breaking rules available if it does.

An Ipsos poll last week provides strong evidence of the likely Condorcet winner in tomorrow’s election. Respondents were asked how they would vote in the six possible head-to-head contests between the four leading candidates. The result is striking: Macron beat Mélenchon by 14 per cent, Mélenchon beat Fillon by 16 per cent, and Fillon beat Le Pen by 10 per cent; the other comparisons followed the same order. What is notable is how large the differences are: it looks as though the second round should be clear-cut whoever reaches it.

Less satisfactorily, if Fillon recovers a little more, we could see a second round between the electorate’s third and fourth choices. And, worryingly, Fillon is the candidate predicted to have the narrowest margin against Le Pen.

This possibility recalls the Egyptian presidential election of 2012, which saw a run-off between Mohamed Morsi and Ahmed Shafik, who each got just under 25 per cent in the first round. The votes of what might be called the Arab Spring majority were split between three candidates, at least two of whom would probably have beaten either Morsi or Shafik in the second round. So the two-round system bears some responsibility for the post-2012 disaster in Egyptian politics.

In a civilisation dominated by complex technology it seems ridiculous to insist that electors can only mark an X in a box. But democracy is bedevilled by vested interests. Condorcet died in a revolutionary prison, jailed for complaining when the Montagnards rejected his proposed constitution and voting system in favour of something that suited their interests better.