Opinion: Condorcet 101, or We Can Do Better Than AV

Attentive readers may have noticed I am not a fan of the alternative vote. I don’t think it is proportional – because it isn’t. However, it is not a bad system for selecting a candidate for a single vacancy. On this basis the Lib Dems use it extensively for internal elections when there is only one vacancy. However it is, to my mind, not the fairest such system.

No single vacancy system can be proportional. That is why the Lib Dems rightly push for Single Transferable Vote in every election they can. However, there will always be single vacancy elections: for mayors, for candidates, for presidents. There is a method, the Condorcet method, which offers a fairer system of voting than AV.

Suppose we have an election in a deeply divided society. 100 people love marmite, like peanut butter, and hate vegemite. 99 people love vegemite, like peanut butter, and hate marmite. 50 or so people love peanut butter, and are split 25/25 between marmite and vegemite. (This example is quite robust and can work with many different numbers).

Let’s have the election under AV:

100 people vote marmite 1, peanut butter 2, vegemite 3

99 people vote vegemite 1, peanut butter 2, marmite 3

25 people vote peanut butter 1, marmite 2, vegemite 3

25 people vote peanut butter 1, vegemite 2, marmite 3.

In round one the results are:

Marmite 100

Vegemite 99

Peanut butter 50

Peanut butter is then eliminated and we move onto round 2:

Marmite 125

Vegemite 124

And so marmite wins. But most people would have much preferred peanut butter to the winner. Indeed peanut butter would have been a result everyone would have been happy with. This is what the Condorcet method does – it looks for the result that most people would be happy with.

Condorcet looks at every possible combination of two candidates; and looks at who voters prefer from each combination:

X Marmite Vegemite Peanut Butter
Marmite X 124 voters prefer vegemite to marmite 149 voters prefer peanut butter to marmite
Vegemite 125 voters prefer marmite to vegemite X 150 voters prefer peanut butter to vegemite
Peanut Butter 100 voters prefer marmite to peanut butter 99 voters prefer vegemite to peanut butter X

We then consider these as a number of separate battles:

125 voters prefer marmite to vegemite whereas 124 prefer vegemite to marmite – so marmite beats vegemite

149 voters prefer peanut butter to marmite whereas 100 prefer marmite to peanut butter – so peanut butter beats marmite

150 voters prefer peanut butter to vegemite whereas 99 prefer vegemite to peanut butter – so peanut butter beats vegemite.

So peanut butter has won every one of its battles and is the winner (occasionally no single candidate wins all of its battles – in which case various methods can be used to select a winner. The most common, Schluze’s method, considers the number of individual vote battles each candidate wins).

As well as always producing the most acceptable candidate, Condorcet has a number of other advantages: it is very simple (voting is the same as AV, or even a bit more flexible: any statement of preference can be counted as a Condorcet vote), it has a long history and a proud liberal tradition (like so much liberal thought it comes from the French Revolution – specifically from my hero Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet), it benefits from the very latest in psephological research (the Schluze method was only invented in 1997), it has been tried and tested in the real world (many companies use it to elect their board of directors), and results can be calculated quickly, transparently, and efficiently at no cost (Open STV is my favourite of the many free software packages available which can calculate Condorcet.).

Most of all though: Condorcet means that we always get the least bad candidate. We only need to look at the London Mayoral Elections to know that AV has a problem*. In both 2004 and 2008 it seemed that most Londoners would have preferred the Lib Dem candidate to either Ken (or Steven) or Boris (or Ken). Ken and Boris were the marmite and vegemite: nobody really liked either of them, but most people hated one of them enough for the other to win under AV. Tactical voting was part of the problem (and under Condorcet tactical voting would have had much less of an impact), as was the Lib Dems failure to explain how the system worked – and their subsequent receiving of thousands of utterly useless second preferences (under Condorcet every preference is useful). However, in the main this was due to a fundamental quality of AV itself.

I’m not suggesting Lib Dems drop the referendum on AV and push for Condorcet instead. The right system of voting for the House of Commons is Single Transferrable Vote and any further muddying of that water is not going to help anyone. However, I’d like to see Lib Dems accept that AV is not the best method of filling a single vacancy – and start to push for Condorcet in mayoral elections, and start to use it in their own internal elections. After all, how many times have we seen internal elections where, after two strong factions put up candidates, everybody seemed a little disappointed that the third candidate didn’t come through the middle?

*This is in part due to the fact that mayoral elections in the UK are fought under the weird Sri Lankan based “two preference” system: it is likely that under full AV Susan Kramer would have won in 2000. However, the difference between two preference and AV in ‘04 and ‘08 was likely minimal.

Fred Carver is a former Liberal Democrat councillor in the London Borough of Camden. He blogs on world elections and politics at Who Rules Where.

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34 Comments

  • Shame it’s not on the ballot paper, Fred. This is an entirely academic argument, especially when you concede the waters need no further muddying and that STV is the goal.

  • “Condorcet means that we always get the least bad candidate.”

    This is exactly why proportional systems are often disliked.

    I am in favour of fairer votes (like Roy Jenkins and Simon Hughes, I think AV plus may be preferable to STV for parliament) but with Condorcet you end up with the most bland candidate who hasn’t got any real policies so nobody disagrees with them. It would be an incentive for even less policy discussion and for candidates to just tell everyone what they want to hear without making any tough decisions.

  • That’s quite interesting. It seems to prefer candidates who are everyone’s second choice and no-one’s first which makes me wonder if a wider electorate beyond psephologists would accept it. Your choice of phrase “least bad candidate” seems apt. This method would choose the least unpopular candidate rather than the most popular. In that regard at least, I think it suits the British outlook on elections very well.

  • You have to be able to do paper counts in elections for MPs. Counting agents can observe the placement of every ballot paper, and can see the piles of ballots stacking up. Illegitimate ttempts to significantly alter the outcome are very likely to be detected.

    Electronic counting offers zero transparency, because only computer experts can be involved in auditing results. So, the question is, how does one arrange a count of paper ballots?

  • What a ridiculously silly idea.
    Not only does it, as has been mentioned, encourage blandness, but it creates a system wherein second preferences are as good as firsts. As I’m sure you realise, people join political parties to see them win, not to see another party lose.
    The traditional argument against fptp is that is runs a two party system. This would create a”3rd party” system.
    STV or bust

  • Ben makes a very good point (I also favour AV+ over STV btw).
    Also a big advantage of AV is that it’s simple.
    Not just the voting but the way the result is obtained. I think this is important for people to feel involved.. if they don’t understand how their vote is counted, they’re likely to either distrust the result or not bother to participate.

  • In your example, only 20% of the people want peanut butter, indeed it’s the third-most popular option in a three-horse race!

    That may all be well and good if you’re doing the sandwiches for the church picnic so nobody’s eating marmite (yuk), but it’s a bloody abysmal way of picking MPs and ultimately a Government.

  • Surely the logic of your argument on Shulze-Condorcet means that you must support CPO-STV rather than any of the variants currently used in practice or advocated by the Liberal Democrats?

  • Oh, and…

    “it is likely that under full AV Susan Kramer would have won in 2000.”

    Really? She got less than 12% of first preferences, Ken got 39%. You’re saying that Ken couldn’t have got more than one in six transfers from other candidates?

    Given that the “official” Labour candidate Frank Dobson came third with 13% of the vote, and most of his transfers would have gone to Ken over Susan, I doubt that she would have got in to the run off, even on the assumption that she would have got enough from the minor candidates to leapfrog from fourth in to third.

  • When are you expecting a referendum on this then – 50 years, 100 years?

  • I think where I fundamentally disagree with the people who dislike the system is that I don’t think least dislikeable equals most bland. Nobody likes bland – bland is offensive to many people. I would always rate a bland candidate very low on a ballot paper, as would many others, I actually think bland people would struggle under Condorcet. However what Condorcet does do is remove the tyranny of the plurality and make you work hard to prove yourself to all the voters – not just your loyal tribe. It removes tribalism and it favours inclusiveness. It also makes it much harder to win if you are from the extremes, but that is no bad thing. Democracy works best when you take the people with you.

    It also doesn’t make it impossible to win if you are from the extremes but it means that to do so, it is not enough to just gather together a loyal group of fanatics (as have often won elections from the extremes under FPTP) – you have to actually win the argument. Many people would consider me an extreme liberal and I’m not scared of Concordet because I think liberalism stands more chance in a fair system which requires you to win the argument than an unfair system. I believe Allende could have won the Chilean elections of 1970 under Condorcet with his extreme views because he won the argument. However Condorcet might have stopped someone like Milošević or Duvallier (or Hitler) winning with from the extremes with the support of only a section of the population.

    You can do a hand count of a Condorcet election. There are a number of different systems. One is that as the officers view each ballot they mark in what it means in terms of pairwise defeats on a big chart (similar to the ones used in the final stages of three-up councillor election). Another slower version is to do manual counts of each candidate vs each other candidate in turn. The maths only ever gets complicated on the very rare occasions when one candidate hasn’t beaten all the other candidates (this only happens when you get a result that most people prefer A to B, but also most prefer B to C, but also most people prefer C to A). This doesn’t happen very often in natural elections. When it does happen the RO can take the agents through the maths of it step by step.

    However I don’t think we need to be scared of electronic counting. You can scrutinize the entry of the data just as closely as you can manual counts and the software code can be full examined (parties can run the results on their own software too to confirm the result)).

    I do support CPO-STV. But any STV at all is better than any non STV – and actually the practical differences between STV systems are surprisingly small. Things like the size of constituency have a far bigger impact (I favour big constituencies)

  • 2 brief comments whist I’m here

    @Nick you may be right, there is no way of knowing. However the number of second prefs Susan got was phenomenal. I looked at the mats once and thought I saw that transfers 7th to 4th gave her enough to get into 3rd, transfers 3rd to second was enough to get her into 2nd and transfers from 2nd was enough to win. Susan ran quite a left campaign and many Dobbo fans might have preferred her to Ken but more importantly almost all of them would have preferred her to Norris, which is what she needed to get into 2nd. Similarly most of the 7th to 4th candidates were left.

    @Andy actually I think there’s nothing to stop local parties adopting it tomorrow.

  • Stuart Mitchell 29th Oct '10 - 2:11pm

    Your example is completely unrealistic because it assumes that all voters will rank every single candidate. How would it cope with the fact that many voters will select only one candidate? Such votes would have to be simply ignored when calculating the two-candidate run-off between any of the other candidates. Such a system would be horribly complicated, nigh on impossible for the average voter to understand, and like AV would make votes less equal, since some votes would be counted in more rounds than others.

    I started setting up a spreadsheet to model some of the possible effects but after five minutes of messing around decided I had better things to do. A system which required complex modelling of that sort totally fails the parsimony test, which I think is one of the most important requisites for any system. I agree that the system may work in certain kinds of organisation, but for electoral politics it looks hopeless.

  • “the number of second prefs Susan got was phenomenal.”

    Well, she got 28.5% – undoubtedly a good performance, but phenomenal might be pushing it a bit. And I really can’t see how it could’ve been enough to win, given that many of those second preference would have come from Ken, so would have counted for nothing in the final run off even had she made it.

    “many Dobbo fans might have preferred her to Ken but more importantly almost all of them would have preferred her to Norris, which is what she needed to get into 2nd.”

    No it isn’t. To get to 2nd, she would have needed not only Dobbo voters to prefer her to Norris but for sufficient numbers of them to prefer her to Ken. If they voted, say, 1 Dobbo 2 Ken 3 Kramer 4 Norris, their vote would go straight to Ken’s stack when Dobbo was eliminated and not help Kramer vs Norris at all.

    That’s because AV isn’t a Condorcet system, which was, erm, the whole point of your original post…

    “Similarly most of the 7th to 4th candidates were left.”

    Yes, but then that just reinforces the point – a lot of those transfers would have gone straight to Ken and been no use at all to Kramer even in getting her past Norris at the penultimate round.

    I come back to my earlier point – given Ken’s huge lead in first preferences, Kramer would’ve needed to be winning about five out of six transfers to beat him under AV, which really would have been phenomenal.

    I’m struggling to think of any serious example in real-world electoral politics in which someone has won an AV election with less than 12% on the first round, especially against a rival who’s nearly at the 40% mark.

  • Fred Carver 29th Oct '10 - 3:14pm

    So Ken might have got over the 50% granted. But if he didn’t, then your task in AV is simply to survive to the next round.

  • Fred Carver 29th Oct '10 - 4:01pm

    @AV2011.co.uk. Thanks. I don’t disagree. In fact I think I said:

    I’m not suggesting Lib Dems drop the referendum on AV and push for Condorcet instead. The right system of voting for the House of Commons is Single Transferrable Vote and any further muddying of that water is not going to help anyone. However, I’d like to see Lib Dems accept that AV is not the best method of filling a single vacancy – and start to push for Condorcet in mayoral elections, and start to use it in their own internal elections.

  • Also, out of curiousity I just looked up the supposedly left wing “other” candidates. Sure, the Greens picked up a couple of percent, but the others were the Christian People’s Alliance, BNP, UKIP, and Pro-Motorist And Small Shop candidates, who got about two thirds of the “other” vote between them. Somehow I doubt that Kramer would’ve got more of those transfers than Norris!

    “So Ken might have got over the 50% granted. But if he didn’t, then your task in AV is simply to survive to the next round.”

    I don’t think you survived the last round of this argument.

  • Aside from the completely rubbish system, which no one could persuasively argue for in a referendum, AV is clearly the best place to start for a move to STV. I don’t think anyone in any of the major parties would consider putting through this in a bill instead of the AV referendum bill.

  • @Fred

    sorry I didn’t see your btl post until I commented :P.

  • Fred Carver 29th Oct '10 - 8:21pm

    Two further articles that might be of interest to anyone with a Jstor login:

    Reitz, T., 2008 “Three-way Experimental Election Results: Strategic Voting, Coordinated Outcomes and Duverger’s Law” in Handbook of Experimental Economics Results , Vol 1, Available online at: http://bit.ly/ctYd0U

    The TLDR version: candidates from the left and right can win under Condorcet, they just need to get smarter.

    Colomer, J. M. , 2007, “Non-median and Condorcet-loser Presidents in Latin America: A Factor of Instability” Paper presented at the annual meeting of the American Political Science Association, Hyatt Regency Chicago and the Sheraton Chicago Hotel and Towers, Chicago, IL. Available online at: http://www.allacademic.com/meta/p209177_index.html

    The TLDR version: analysis of 200 odd elections in Latin America over the last 50 years shows that when the Condorcet winner wins their regime is smoother, more stable, more peaceful, more democratic and less likely to descend into dictatorship than when a non-Condorcet winner wins. The STLDR version: Condorcet leads to better people winning.

  • David Abrahams 29th Oct '10 - 9:31pm

    Hi Fred,

    Very interesting article. I’m aware that the Condorcet system has received considerable academic support:

    2 questions/ concerns:

    1) As you acknowledge in your article Condorcet doesn’t always produce a winner. You refer to Schluze’s method of resolving such situations, but don’t explain how that works. In terms of clarity/comprehensibility it seems a distinct disadvantage that a further ‘tie-breaker’ procedure is required in to resolve tight elections.

    2) Is Condorcet really practical in public elections? You don’t refer to any examples of it being used in a such a context, even though the system’s been around? Are there any examples?

    On a parochial note, I presume that the Lib Dems in Hampstead & Kilburn would have been clear winners if Condorcet had been used last May (I’m much less sure what the result would have been under AV). Obviously that’s a point in its favour as far as I am concerned…

    Finally, are you still planning to vote No to AV?

  • David Abrahams 29th Oct '10 - 9:32pm

    Re previous comment, should have read:

    “even thoughtthe system’s been around for two hundred years”

  • Thanks David:

    1 I didn’t want to get bogged down in explaining Schluse’s method (AKA Schwartz sequential dropping)because it’s a little technical and it rarely comes up. Basically there’s almost always a Condorcet winner. There only isn’t if you get a rather unnatural circular result such as: most people prefer A to B, most prefer B to C, but also most people prefer C to A. When it does happen it normally only involves three candidates – although in extremely complicated elections it can involve more.

    I don’t think its a disadvantage that Condorcet is a two step process any more than it is a disadvantage that STV is two step. Like Condorcet, STV has a reactively straightforward first step (meeting the quotas) and a moderately complicated second step (transfers). In fact you could say Condorcet is simpler in this regard as STV almost always needs the second stage whereas Condorcet almost always doesn’t.

    As with STV, the second stage of Schluse’s method is a natural progression of the first stage. Firstly you identify the “smith set”. These are the candidates such as everyone inside the set is preferred to everyone outside. In other words you drop all the candidates who have no chance of winning and leave yourself with the small number (normally 3 if this stage is needed, sometimes more) who might still be preferred due to the sort of circular relationship described above.

    Then you draw out the circular relationship and the strength of the links in it (each link means “I beat you” and each number means the margin of the win). You get something like this:

    http://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Schulze_method_example6a.svg/217px-Schulze_method_example6a.svg.png.

    You then drop off the weakest links, one by one, until you are left with a linear relationship with a clear winner. So in this example you would drop the links with strength 16, 17, 18, and 19 and be left with C as the winner (in this diagram the arrows go from winner to loser)

    2 I really don’t see why not, but yes you are right, so far the most “public” election it has been used for are the open primaries of a few small European political parties. I was, in the first instance, just suggesting it for some Lib Dem internal elections so the Lib Dems wouldn’t be pioneers in this regard. and you know I’ve never been scared of the new anyway.

    3 I really don’t know which way to vote on AV. On the one hand academically I think AV is better than FPTP, but on the other the real life experience from Australia suggests it might not be, on the one hand I really want proper voting reform (STV) and I think a yes win might be a step in the right direction but on the other hand I fear a yes win might be the last word on voting reform for many decades.

  • Andrew Suffield 30th Oct '10 - 2:18pm

    (I support Condorcet methods wherever they occur; they are obviously the only thing which generates a fair result in a single-winner election, and most of the problems people have raised above are just observing that many single-winner elections can’t really be very fair and what you want is proportional representation)

    As you acknowledge in your article Condorcet doesn’t always produce a winner. You refer to Schluze’s method of resolving such situations, but don’t explain how that works. In terms of clarity/comprehensibility it seems a distinct disadvantage that a further ‘tie-breaker’ procedure is required in to resolve tight elections.

    The only important response to this is to point out that FPTP and AV don’t always produce a winner. I refer you to the following ballot:

    A: 100 votes
    B: 100 votes

    No winner. The Schulze method delivers a tie about as often.

  • Fred Carver 30th Oct '10 - 2:18pm

    Reading back I think I need to clarify on two further points, and add a point of fact:

    1 I’m not advocating this for general elections for all the reasons people have said. General elections should be fought under STV. However I am advocating that parties adopt it for their internal elections where there is one vacancy right now (election of party president, elections of local chair, elections of ppc until the system is changed, elections of party leader, elections of chair of council group, elections for London mayoral candidate) and in the future campaign for it to be introduced in direct mayoral elections and for other single vacancy elections (speaker of the house, leader of council groups where there aren’t directly elected mayors, President if we ever abolish the monarchy, directly elected police chiefs if we really have to have them etc..),

    2 @Adam Bell put his finger on it when he said “This system actively devalues first preferences in favour of consensus.” That is exactly why I support the system. I think we have to move away from the idea that first preferences have some magic right to special treatment, and realise that fundamentally democracy is a tool (of necessity an imperfect tool but nevertheless the best we have) which translates the opinions of the public into a series of choices. These choices are not as simple as yes/no and the opinions of the public are far more complicated than “I want him”. Condorcet captures that complexity and, to my mind, comes up with results that far closer fit the opinions of the voters. We might want clear majorities, simple systems etc…. but it’s not about what we want; its about designing a system which reflects, in its results, what the people want.

    On a point of fact: Condorcet can handle incomplete ballots, indeed it does so far better than AV. It can also handle people voting for one or many candidates with an x, it can handle people ranking candidates as being equal. It can handle virtually any expression of opinion as a valid and useful ballot.

  • Andrew Suffield 30th Oct '10 - 2:30pm

    Surely the logic of your argument on Shulze-Condorcet means that you must support CPO-STV rather than any of the variants currently used in practice or advocated by the Liberal Democrats?

    Or Schulze-STV. But it’s actually less important than you’d expect. STV delivers proportional results in all cases where it is possible to do so, and is already fair in all those cases. The extended STV methods are addressing a fairly perverse and minor case. Consider: a constituency has 3 seats up for election, with four major candidates, and the electorate is roughly split as 25% for each of them. Now there’s obviously no “fair” result possible here: you can’t proportionately distribute 3 seats between 4 people. STV will more or less randomly pick three, which is not unreasonable; CPO-STV or Schulze-STV will resolve this case down to the last vote, and come up with a “fair” answer.

    But what’s really happened here is that we don’t have enough seats in the constituency. If you always have enough seats to deliver a proportional result, then STV will do the right thing. The extended methods are interesting, but for a Parliamentary election (where the number of seats or the size of constituencies can be adjusted to eliminate such problems) they aren’t actually necessary. The existing proposals for STV in the UK deliberately set the constituencies large enough to accomplish this. Interested readers may observe that if you set the constituency size to 1 seat, then the above argument degenerates into an explanation of why the Schulze method is better than AV.

    (Schulze-STV also has some interesting properties about resisting vote management, but those could be adopted later if this turned out to be an actual problem. In an election on the scale of the UK, vote management is unlikely to be practical)

  • Andrew Suffield 30th Oct '10 - 2:32pm

    However, it can throw up some odd results, especially if lots of people dont express full preferences (which would be the norm in public elections). For example, 4 people rank X above Y, and no other preferences. One person ranks Z above X and no other preferences. The Condorcet outcome is Z, X, Y – since it satisfies everyone’s preferences.

    That’s a setup error. All unranked options should be considered as equal and placed below all ranked options, so the first four people have implicitly voted XYZ.

  • Fred Carver 30th Oct '10 - 2:40pm

    I’ve totally agreed with everything Andrew Suffield has said. If it was up to me we’d have a general election on the basis of CRO-STV with Meek’s method, Tasmanian ballots, and big constituencies. But failing that I’d settle for any STV. Indeed I’d pretty much settle for AV+. I still think Condorcet is the best way of electing to a single vacancy, which was the point of the article.

    So now I’m going to play devil’s advocate. How about Condorcet for the Lords? Obviously it would be nice to have one proportionate chamber (although I’d rather it be the Commons) but Condorcet would make sure that we had a consensual House of Lords which could act as a check and balance on the Government.

  • Fred Carver 30th Oct '10 - 2:50pm

    @Nathan It strikes me that this is very much a party hack argument. Most people don’t join parties at all. Most people just vote. They vote in order to express their opinion – which is rarely one of blind devotion or bitter hatred. Traditional voting methods translated that opinion into a result in an incredibly reductive way. Condorcet views that opinion holistically and establishes the winner the public want.

    Most people I know in the real world feel quite good about 2 or 3 parties, and pretty negative about 2 or 3. They have nuanced views, they are not party loyal, they have results they would feel good about, they have results that would be acceptable to them, they have results that would be a grave disappointment to them and they have results which would make them want to burn things. It is not as simple as seeing your side win or lose unless you are as sad and devoted as you are and as I was. For most people it is just about having your views reflected in the result

  • Range voting (aka score voting) is way better than IRV/AV. Take a look at voter satisfaction scores of score voting vs instant runoff here: https://electology.org/sites/default/files/comparing_voting_methods_simplicity_group_satisfaction.png

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