How people elect parliaments
What would have been the result if the French had chosen their president yesterday by a single round of preferential voting?
Preferential voting is use to elect parliaments in Australia, and to elect the presidents of Éire and Sri Lanka.
Known as ‘instant runoff voting’ in the United States, or the ‘alternative vote’ in Britain and Canada, single-round preferential voting is similar in some ways to the two-round runoff system.
The main technical difference is than in the two-round runoff system, only the candidates who place first or second on the first ballot get a chance of winning.
The main practical difference is that voters only need to go to the polls once, and fill out a ballot by marking ranked preferences for each candidate.
So in French polling booths yesterday, the voters would have marked the candidates with numbers from 1 to 11 in order of their preferred choice of president.
The ballot counting would then proceed by tallying all the “1”s – the so-called ‘first preferences’.
Assuming for this hypothetical that the first preferences matched the real election results (which is actually a significant assumption), no candidate would have came anywhere near winning 50% of the vote. The leader Emmanuel Macron is only on 23.9%.
So the candidate who placed 11th yesterday – right-wing Jacques Cheminade – would be eliminated, and the 64,157 ballots* where he was ranked first would be re-examined and transferred to the tally of the candidate the voters had marked “2”.
(*The numbers used in this post are from the Interior Ministry website, which stated that 96% of votes were counted at the time the screenshot below was taken. The term “Exprimes” is French for the share of the formal vote, shown in the last column.)
French election results at around 2:30am CEST in Paris
The tallys for the remaining ten candidates would then be re-totalled. Still no-one would be close to 50% of the remaining votes, so the next lowest candidate – the Workers Struggle candidate Nathalie Arthauld – would be eliminated, and the 229,235 ballots for her (plus any just transferred from Cheminade’s set) would also be transferred to others.
In fact, if the rules allowed for it, all five of the bottom-placed minor candidates could be eliminated at once, since the total of all their five tallies is lower than the 1,671,400 first preferences tallied for 6th-placed Nicholas Dupont-Aignan, a minor right-wing candidate who polled a quite respectable 4.75% of the total.
In fact, the same is even true of the bottom seven candidates, including also the Socialists’ 5th-placed Benoît Hamon. Their total tallies are less than that of 4th-placed Jean-Luc Mélenchon, originally on 6.8 million votes.
So there is no doubt who the final four candidates are – Macron, Marine Le Pen, François Fillon and Mélenchon.
Under an instant runoff preferential system, the ballots initially supporting all the lowest seven candidates would therefore be transferred to one of these four.
But some of these ballots might transfer to no-one at all. In Australia full preferencing (ie: marking all the candidates) is in many cases a strict condition of valid voting. But more tolerant preferencing systems do not demand this, and it might be that this election used ‘voluntary preferencing’. If so about 10%-20% of these ballots, possibly more, might end up in an ‘exhausted ballots’ pile.
In any case, the two most significant exclusions would be those of Dupont-Aignan, a right-wing candidate, where ballots would likely flow strongest to Fillon, and from the Socialist Hamon, from whose 2.2 million ballots Macron would likely do best, with a reasonable number also going to Mélenchon.
All up, and making some assumptions based on the political profile of the supporters of the eliminated candidates, the re-tallying of votes after seven eliminations would have looked something like this:
Note that on this estimate an important change of order has occurred; Fillon has very narrowly overtaken Le Pen for second place, largely reflected the gains from Dupont-Aignan.
But Macron, still leading clearly, is not yet close to 50% of the remaining total of votes.
Mélenchon would thus be eliminated next in fourth place. We can be fairly confident in our estimates leading to this point, the gap to Le Pen being an estimated 350,000 or so votes.
Where would the ballots of the supporters of the radical left candidate Mélenchon go next? One obvious answer is to Macron, the least right-wing of the remaining three candidates.
But there might also be a solid share of ballots going across to Le Pen, since the supporters of these two candidates have in common a desire to disrupt the political establishment.
Certainly, relatively few Mélenchon preferences would flow to the conservative establishment candidate Fillon’s column.
So Le Pen would likely overtake Fillon once again, to get back to second place in the tally among the last three candidates.
But in any case, among the final three candidates Macron is likely to be holding a lead of around 1.5 million votes, possibly more. But still not 50% of the total.
It’s hard to say which of Le Pen or Fillon would thus become the last to be eliminated. If it is Fillon who goes out, the ballots of his supporters – and by now a variety of other ballots added to his column in earlier transfers – would most likely prefer Macron in significantly greater numbers to Le Pen. That would help blow out Macron’s lead even further, finally making him the decisive winner.
But there is, strangely, one final twist. If it were to be Le Pen who ultimately placed third, the opinions of the voters who cast the millions of ballots in her column might well favour Fillon quite significantly over Macron.
It is plausible that this could be enough to help Fillon close the 1.5 million vote gap with Macron.
So it is conceivable – unlikely, yet conceivable – that François Fillon could actually have won this election had yesterday’s voting been preferential.
Conservative presidential candidate of Les Republicans party, François Fillon
All of which goes to show how much voting rules matter.
Macron would be president under a simple plurality rule, and he is almost certainly going to become president under the two-round runoff system.
But with preferential voting using sequential elimination, the order of elimination can often become crucial in tight races, yielding irritating results. The elimination order reflects little in the way of deliberate voter choice, and can therefore leave observers wondering how some election results might well have gone otherwise.
The problem is nor preferencing per se, but rather the ubiquitous rule for the sequential elimination of candidates during the counting process.
In any case, the fact remains that in France yesterday around 47% of the votes cast went to right-wing candidates, while 28% were cast for left-wing candidates. The minor centrist Jean Lassalle held 1%.
Macron won 24%, and he is classified as a centrist candidate, but his supporters are a complex mix of centre, left, right and unclassifiable opinions.
Macron is most likely the Condorcet candidate – the one preferred to all others in one-on-one comparisons – but he is not certainly so. And the preferential voting system, had it been used, might well have exposed that the Condorcet winner was really Fillon (although the preferential system would not have guaranteed revealing this; had Fillon eventually placed third it would have remained concealed.)
In truth a large number of voters who might have ranked Macron fairly highly were among those who placed Fillon first, and their flow of support to Macron manifests only if and when Fillon is eliminated from the contest – either under the two-round runoff method or the instant one.
A final contest between Macron and Fillon might well have been very close.
Which raises the question – have French voters been denied the final contest they most deserved – one between Emmanuel Macron and François Fillon – rather than the runoff that will actually be held between Macron and Le Pen?
Fillon’s campaign was an utter disaster, but he was just beginning to recover slightly at the end.
Might he have been the unlucky third-placed Condorcet winner, as Socialist Lionel Jospin was in 2002?
We can only estimate that point, and on balance, probably he was not – the data does seem to favour Macron. It is always best to fight such contests from the political centre, where Macron was very well placed.
But we will never know for sure.