Bring Back Condorcet

Denis Mollison

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.


  • 23 April 2017 at 7:44am
    David Sharp says:
    Denis Mollison writes:
    "if Fillon recovers a little more, we could see a second round between the electorate’s third and fourth choices."
    This is incomprehensible: if Fillon faces Le Pen in the second round, that can only mean that those two candidates came out ahead of the others in the first round. Denis Mollison appears here to prefer the results of an Ipsos poll to those expressed by the electorate.

    "...worryingly, Fillon is the candidate predicted to have the narrowest margin against Le Pen."
    This is for a good reason: an awful lot of people in France (I am one of them) are fed up of having the media tell us that we must vote tactically, even in the first round. The demonisation of Le Pen is at the root of this. The implication being that she must be stopped at all costs, including that of voting for a candidate, such as Macron, who will pursue the neo-liberal policies of Hollande, or for for another who appears to believe Margaret Thatcher is still a model to be followed.

    In other words, everyone is busy replaying World War II, just as the initial approach to that conflict involved replaying World War I. But the world has changed, radically in many ways.

    I have the privilege of voting in France, and my view is that unless Mélenchon makes it to the second round, I will cast a blank ballot on May 7th.
    NB: Among his many reforms, Mélenchon promises to give full status to blank ballots. A stance which is also defended by another interesting candidate, François Asselineau, "le candidat du Frexit".

    • 23 April 2017 at 12:53pm
      martyn94 says: @ David Sharp
      What exactly does "full status" for blank votes mean? They are already identified separately from spoiled ballots and abstention. It is surely a matter of judgment whether you regard them as principled or merely squeamish, not a matter of status.

      None of the media I read or see or hear have told me to vote tactically even in the first round. Some may regard the choice as a pis aller, but making the best of a bad job is not the same as voting tactically.

      You may want to take your bat home (as we say in France) if M Mélenchon doesn't get through. But the question would remain: do you want the best of a bad job, or the worst? It's hardly a new dilemma in political life, nor one got up by the media.

    • 23 April 2017 at 1:18pm
      martyn94 says: @ David Sharp
      What on earth does "full status" to blank ballots actually mean? French electoral returns already enumerate blank and spoiled ballots separately, and identify the rate of abstention. Are we meant to think it specially admirable to almost vote and then bail out, or just squeamish?

      To fervently support M Mélenchon, and then regard M Asselineau as "interesting", seems merely frivolous, unless you mean it in the Chinese sense.

      None of the media I read have told me that I have to vote tactically, even in the first round. If I read the Figaro or Valeurs Actuelles regularly, I imagine they would tell me to vote for M Fillon out of conviction. Otherwise it's more of a pis aller, but making the best of a bad job is not the same as voting tactically

    • 23 April 2017 at 2:31pm
      David Sharp says: @ martyn94
      Since a law dated February 2014, blank ballots have been counted distinctly from spoiled ballots in French elections. To cast a blank ballot, the voter has to either put an empty envelope, or one containing a blank sheet of paper, into the box. However blank ballots are not provided in polling stations, and there is little or no publicity concerning this option.
      Above all, blank ballots are not counted as "votes expressed", which considerably limits their effectiveness.
      Imagine for example if the second round came down to Fillon versus Le Pen, but that instead of only two voting slips, we were presented with three, one of them blank. If there were more blank ballots than for either of the two candidates, or if the number of blank ballots prevented both the candidates from reaching 50%, the election would be considered null and void and have to be held again.
      That would be the result of Asselineau's proposal; Mélenchon's is not so precise.
      As regards the pressure to vote tactically in France, I have the impression that we don't live in the same country! Quite a lot of people I know disagree with most of Macron's programme, and most of them agree with either Mélenchon or Hamon, but they intend to vote for Macron in the first round simply because they've been convinced that he's the only one capable of beating Le Pen in the second.
      And no, my interest in Asselineau is anything but frivolous, although it is your right to consider it so.
      This is because I do not think any real progress is possible under the iron heel of the European Union, and I have considerable doubts about the possibility of reforming that institution from within.

    • 23 April 2017 at 3:24pm
      martyn94 says: @ David Sharp
      I don't think that blank ballots are meant to be an "option": they are just something that people do which are duly recorded. The fact that votes that have not been cast are not counted as "votes expressed" does not seem so unreasonable to me.

      But of course any absurdity is OK, from the extreme right to the extreme left (via wherever M Asselineau can be situated), if it gets us out from under the "iron heel". I suppose I should have guessed.

      You have a strange idea of "pressure": doing the least-worst thing because you believe it is the best thing to do (whether rightly or wrongly) , and that it is better to do something rather than nothing. Is exactly not acting under pressure.

    • 23 April 2017 at 7:44pm
      denismollison says: @ David Sharp
      " they intend to vote for Macron in the first round simply because they’ve been convinced that he’s the only one capable of beating Le Pen in the second"

      How were they convinced? The poll I quoted showed clearly that any of the 3 others would beat Le Pen in the second round.

      One of my reasons for writing is concern at the way the existing 2-round system puffs up the Front National's chances. Look at how Le Pen's father only picked up 1% more votes in the second round. I'd bet that Hamon would have beaten Marine Le Pen in a second round.

  • 23 April 2017 at 11:15am
    denismollison says:

    I am sorry you misunderstood me, especially as I think we are on the same side here.

    What I am saying is that the voters' true preferences are better seen in the head-to-head comparisons of the polls. In contrast to the first round, I don't see any obvious reason why those polled should express anything but their true preference for the second round.

    These head to head comparisons suggest that the electorates' preference order is Macron > Melenchon > Fillon > Le Pen. That is the sense in which Fillon and Le Pen are the voters' third and fourth choices. That it is quite possible they might come first and second in the first round is an indictment of the voting system.

    A key advantage of Condorcet's system is that there is no advantage in tactical voting: you simply express your true order of preference, and you should end up with a president who is preferred to each of the other candidates in a head to head contest. I note that Melenchon wants to revise the constitution: if he succeeds, I hope he will consider this better system for future presidential elections.

    • 23 April 2017 at 1:41pm
      David Sharp says: @ denismollison
      I probably did misunderstand your message; I admit I was unaware of the Condorcet proposal, although I am aware of the various systems of proportional representation which are probably derived from it.
      My comments nevertheless relate to the election as it is currently being fought.

    • 23 April 2017 at 7:46pm
      denismollison says: @ David Sharp
      But the whole point of my blog was to explain why the present system is not just unfair, but dangerously unfair in that it helps extremists like Le Pen.

  • 23 April 2017 at 4:50pm
    Graucho says:
    You could always have the 'I'm a politician get me out of here system'. Each round you vote for the one the hate the most and they get eliminated. The least disliked then wins.

  • 24 April 2017 at 6:06am
    guido franzinetti says:
    1. There is no such thing as a perfectly fair electoral system, other than perfect proportionality. Austria, Italy and Israel have had systems which were as close as possible to perfect Proportional Representation (PR). But even these systems had their caveats (in 1972, Italian leftists lost 1m votes because of the threshold requirements). Perfect PR would require a threshold of one vote. It is quite simply a utopian assumption
    2. Therefore any electoral system can be described as ‘unfair’. What critics mean is ‘this electoral system does not favour the kind of political alignment I would like’. I have never encountered critics saying ‘We won, but the system was unfair’.
    3. The point is that electoral systems and political alignments (i.e. parties) are simultaneous equations: they cannot be understood separately. System A (say, a first-past-the-post system) produces a political alignment which reflects the system, and vice-versa. So it is actually impossible for the electoral system to be substantially changed, except in two circumstances: (i) a post-war setting; (ii) a (near) post-civil war setting (e.g., France in 1958; there was an attempted coup in 1961). This is because any substantial change to an electoral system (as opposed to mere tinkering with it) involves ‘turkeys voting for Christmas’, which for some reason rarely happens.
    4. Many Italians are convinced that their electoral system was substantially changed in the 1990s. They never read the fine print: in the Mattarella reform 25% of the electoral system was preserved for (imperfect) PR. This was enough to preserve the basis political structure (and parties). Berlusconi was never able to impose a first-past-the-post system, because his allies never allowed him to do it. Nor did they allow him to create a French-style system. It was not in their interest. So Italy continues to long for a return to PR, which may well happen one day. (Of course it will be an imperfect PR, but there is no other form of PR.)
    5. So Macron will be set against Marine Le Pen, and he will probably win, unless Fillon voters and Mélenchon abstain in sufficient numbers, or actually vote Le Pen (not impossible). He will find himself in a position similar to that of Hollande, who won simply because Marine Le Pen considered a Hollande victory preferable to a Sarkozy victory (she was right, from her point of view). Hollande squandered his victory because he seemed to forget that he had won by default; he had NOT won on the basis of a leftist majority. Macron might win, but, again, only by default, as enough leftist voters would consider him preferable to Le Pen. But Macron will also have to remember that he would win (if he does win, that is) by default, not because he has a Centrist majority on his side. He is likely to get a majority (or sorts) in the forthcoming parliamentary elections, but that will not be enough.
    6. There is a lot of talk of a ‘populist’ in US and European politics. It is, quite simply, nonsense. Every single ‘wave’ is filtered by a different electoral system, and therefore (see above) by a different political system and alignment. So the results will be different in each case: Trump won because of the US system, Wilders lost because of the Dutch system, Le Pen will (probably) lose because of the French system, etc. The ONLY exception to this rule was David Cameron’s defeat: but in that case, he lost because he operated OUTSIDE the British (UK) electoral system, by staging a referendum which was NOT required. Sometimes you can be too clever by half. In the rest of the world, populists will certainly influence the political agenda, but so far they have won only in the US and in the UK.

  • 24 April 2017 at 6:47am
    Laurie Strachan says:
    Australia already has a system of preferential voting not dissimilar in intent from the Condorcet model. When you vote you are given a ballot paper with the names of all the candidates on it. Next to each name is a small box in which you don’t just enter a tick but a number. The candidate you most want to represent you is numbered 1 and so on down to the one you least want in there. When the ballots are counted the preferences are distributed starting with the candidate with the smallest number of primary votes (1s) and moving up until you have the one who has won most votes, whether primaries or preferences passed on up the chain. So, you can hedge your bets and maybe vote for a minor party candidate, say a Green, but give your next preference to, say Labor, just in case your original man/woman doesn’t make it and you don’t want a Liberal or National to win, and so on.
    The system works well in the lower house where there are surprisingly few minor parties and thus basically stable government but in the Senate, which is elected on proportional representation, six senators per state, there has been a huge growth of small, often single-issue parties, mainly from the smaller states – in Tasmania you can in on a handful of primary votes and a bundle of preferences gained through deals with the other minnows. So the Senate ballot paper is a huge document that you have to fold over and over to handle. Still it works in its way and makes the government of the day think more carefully about its policies.
    The other really sensible things about Australian democracy are:
    1. Voting, or at least attending a polling booth and entering a ballot paper, is compulsory.
    2. Elections are always held on a Saturday when nearly everyone can get to a polling station – and there are plenty of them, usually the local schools. In fact they’re almost a social occasion. Even the pollies get in on this with photo-opportunities of them snacking on a treat from the almost compulsory sausage sizzle. No one has to queue round the block in order to exercise their democratic right.
    Sadly none of this has led to us getting a government that will behave with a little compassion to asylum seekers who are treated worse than criminals in the offshore gulags of Nauru and Papua New Guinea, Australia’s greatest shame.

  • 24 April 2017 at 6:59am
    David Sharp says:
    @Martyn94 wrote:
    "None of the media I read have told me that I have to vote tactically, even in the first round.../... making the best of a bad job is not the same as voting tactically"
    I don't know if you have access to the excellent media criticism site "Arrêts sur Images", but if you do they have a pretty convincing article showing how several of the top newspapers called on readers to vote not for their convictions, but to stop Le Pen.
    On Saturday Libération, for example, had photos of Le Pen and Fillon on its front page, with a huge title: "Anybody but them".
    As for "making the best of a bad job", in my view it is exactly the same as voting tactically.

  • 24 April 2017 at 9:56am
    martyn94 says:
    I guess that the psephologists will enlighten us in the weeks to come, but I very much take guido's point: the "convictions" that you are tempted to express are very much determined by the system you are voting under. In France you have the luxury of voting your "heart" in the first round, and your "head" in the second. Unless things go wrong.

    Which of the two votes are more "tactical" is anyone's guess. I imagine that some of M Mélenchon's voters are privately relieved: they have made their point without having to live with it (unlike many of the poor saps who nominated Mr Corbyn).

  • 24 April 2017 at 4:50pm
    denismollison says:
    Guido and Laurie: you are both straying onto the topic of electing a set of representatives, a topic I'm very interested in but reluctant to stray onto here, as my blog was concentrated on how to elect a single representative such as a president. Let me just say (1) that I recommend David Hill's 1988 paper in J Roy Statist Soc A,`Some Aspects of Elections--To Fill One Seat or Many' (, and (2) the Australian Senate system is a debased form of STV (it has recently been improved somewhat).

    Returning to the French presidential 2-round system, I agree very much with Guido that turkeys are reluctant to vote for Christmas, but that doesn't explain why the non-FN majority don't change a system that makes the FN appear more important than it is. It's not as though FN success benefits any particular other party: it eliminated the left in 2002, and the right in 2017.

    • 24 April 2017 at 5:41pm
      David Sharp says: @ denismollison
      You wonder "why the non-FN majority don’t change a system that makes the FN appear more important than it is."
      One part of the explanation for this is political.
      It will not have escaped your notice that although the Front National gets huge attention by seeking to win the presidency, its presence in the French Parliament is tiny: one member of the National Assembly and two in the Senate.
      Unfortunately, the introduction of proportional representation has often been seen in France as a political manoeuvre. This was notably the case in the 1986 parliamentary elections, when PR brought in by Mitterrand allowed the party to win 35 seats. This was widely interpreted as a cynical move allowing Mitterrand to split the right wing vote.
      Although French presidents have been able to tinker with the rules for parliamentary elections, it is far more difficult to change those for the presidency, which of course endows massive power on its holder.
      This is behind the call by Mélenchon, and several other candidates, for a 6th Republic, with new rules and an end to the "presidential monarchy" we now have.

    • 25 April 2017 at 7:59pm
      guido franzinetti says: @ David Sharp
      I think David Sharp provides already an answer (although one could add that Mitterrand's change of the electoral system for the National Assembly was actually short-lived: a 1985 reform, revoked in 1986).

      The main point I wanted to make is that tinkering with an electoral system is one thing (e.g., Mitterand’s reform); changing the nature of the electoral system is quite another matter. The latter automatically creates a coalition of the ‘unwilling’ (from all sides). At the height of the Cold War, in 1953, Italian Christian Democrats tried to push through an electoral reform, and they failed.

      Voting for the president in France is not so different from voting for parliament. In both cases, there are two ballots, which favour fragmentation on the first ballot and regrouping on the second. This does condition the kind of political spectrum on offer.

  • 25 April 2017 at 4:52pm
    Stu Bry says:
    "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."

    Of the three only Sabahi could be considered an Arab Spring candidate and he has since lost credibility by participating in the sham 2014 Presidential election. Fotouh is an Islamist and Moussa was a Mubarak stooge who is now an Al Sisi stooge.

    Despite likely massive electoral fraud the two Islamist candidates polled 42% combined in the first round.

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