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A Condorcet method is an election system where voters rate their candidates in order of preference. As an example, for candidates A B and C, a valid vote can be [A > B > C], [C > B > A], [B > A > C] etc.

The vote then leads to chained preference problem which can be solved through several methods. In the above example, we have B > A > C (first two votes sums in A = B = C). Some of the votes are impossible to solve "perfectly", as known as Condorcet paradox, simply described as cyclic preferences. Each particular Condorcet method offer a different answer to this problem, but no matter what method chosen, if it respects Condorcet criteria it offers much advantages over classical votes:

  • Since it rates all the candidates in a single turn, a single vote can be cast to elect a winner.
  • This encourages being a good compromise candidate. For example, in a triangular scenario, the middle man can win without majority of first intention votes.
  • This does not harm diversity of proposals. If two candidates A1 and A2 have similar opinion group, their supporter can elect A1 > A2 > B > C and A2 > A1 > B > C. If the opinion group is the majority, A1 or A2 can be elected without majority of first intention votes.
  • It can be used as an exclusion vote, voting "against" some candidate or group
  • It simply is a more powerful expression vote, allowing more analysis and involving more the voter in the outcome

Despite this, I know no large scale implementation of any Condorcet method. Although some of them are complex and require (small) computing for resolution, this really shouldn't be a problem.

What other factors are against the Condorcet method in real world elections?

Nat
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Diane M
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    Australia uses preferential voting. They use different systems, but many are quite similar to Condorcet. – Philipp Jan 09 '16 at 17:42
  • @Phillipp For representative house, it looks pretty different. «The number of first preference votes are counted first. If no candidate secures an absolute majority (more than half) of first preference votes, then the candidate with the fewest votes is excluded from the count.» This is closer to a classic vote than it looks like. In a real Condorcet election, you can win without any first intention vote. – Diane M Jan 09 '16 at 17:48
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    It isn't clear to me what this question is asking. Some elections are conducted using systems meeting the condorcet criterion; does that answer the question? – Publius Jan 09 '16 at 23:34
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    @Avi I am asking about what are barriers against Condorcet method implementation. It is an old discovery, it solves practical problems that are well known in current voting systems, so I am asking myself why it has so little support. It is used in a few projects such as free software organisations but doesn't see daylight in actual politics debates. – Diane M Jan 10 '16 at 14:28
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    @ArthurHavlicek I still need a little more specificity. Are you asking why it's politically unpopular, or are you asking if there are any practical barriers to implementation? If your question is the former, what kind of evidence would you accept? People don't generally give specific reasons for not supporting concepts they likely haven't heard of. – Publius Jan 11 '16 at 02:44
  • @Avi My question was more about political support, although practical barriers are not completely off topic I suppose. Just wanted to hear a point of view from people who have more political culture than me about the implication of introducing a new voting system. – Diane M Jan 17 '16 at 21:56
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    @ArthurHavlicek "Just want[ing] to hear a point of view" from other people isn't really what StackExchange is for. You shouldn't ask questions with open-ended answers here. – Publius Jan 17 '16 at 21:58
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    Condorcet isn't even good criteria for a voting system. Why does it make more sense that the winner should be the one who would win in tournament-style voting rounds? Its specific to absurdity. Limiting yourself to the condorcet criterion prevents you from choosing better voting systems like Range voting. – B T Dec 25 '16 at 23:55
  • @BT True, though in practice, they produce the same outcome >80% of the time. – endolith Apr 09 '20 at 04:17
  • @endolith, I'm curious to know how you came to the 80% number. Is there any sources you can point to that support that idea? – B T Apr 15 '20 at 07:26
  • @BT I'm thinking of things like Merrill 1984 "A Comparison of Efficiency of Multicandidate Electoral Systems" and Pivato 2015 "Condorcet meets Bentham" – endolith Apr 15 '20 at 14:12
  • "Condorcet isn't even good criteria for a voting system. Why does it make more sense that the winner should be the one who would win in tournament-style voting rounds?" Boy that's the stupidist thing I read today, @BT. It's like saying "Up is Down" or "Wrong is Right" or "Black is White". – robert bristow-johnson Dec 20 '22 at 05:46
  • @robertbristow-johnson I regret to inform you that you can't use your brain. Imagine a 3 candidate election where 100% of people like candidate A, 51% like candidate B slightly more than A and hate candidate C, and the other 49% like candidate C slightly more than A and hate candidate B. In this case B would win even tho almost half the electorate hates B. With score voting the candidate everyone likes would win: A. This basically describes american politics. Choose the 2nd worst candidate to win. You defending this idiocy is sad to watch. – B T Dec 21 '22 at 21:37
  • The thing is that if our votes count equally (and I am not ceding the value of my vote to anyone), then it doesn't matter if I enthusiastically prefer A and you prefer B only tepidly. Your vote for B counts no less than my vote for A, nor should it if we are equal citizens with equal rights and equal franchise. – robert bristow-johnson Dec 22 '22 at 19:11
  • Cardinal voting or score voting (including Approval Voting) forces people to vote tactically whenever there are 3 or more candidates. Each voter has to think tactically whether it's in their best political interest how high to score, or whether to Approve their second-favorite choice. With the ranked ballot, there is no tactical voting unless the Condorcet winner is not elected (or, in the extremely rare case that there is no Condorcet winner). – robert bristow-johnson Dec 22 '22 at 19:15
  • *//"With score voting the candidate everyone likes would win: A. This basically describes american politics. Choose the 2nd worst candidate to win. You defending this idiocy is sad to watch"//* And that is bullshit offered with zero evidence to support it. – robert bristow-johnson Dec 22 '22 at 19:16

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There are lots of arguments which could be made against a voting system, like being too complicated to understand for the average voter or requiring so much work to fill out that many voters will start filling in preferences arbitrary.

But the most likely barrier to changes of voting systems is that in most legislations, those people who could change the systems got into their positions through the existing system. Changing the system would very likely make it less likely that they (or people with similar agendas) get re-elected, so they won't be very motivated to do this.

Philipp
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I think Ireland has single transferable vote, which probably comes closest to Condorcet method.

Take a look at Arrow's Impossibility Theorem; in group choice you cannot guarantee a Condorcet winner exists given three or more choices while at the same time satisfying certain criteria (unrestricted domain, non-dictatorship, Pareto efficiency, independence of irrelevant alternatives) with the implication that all ranked voting systems have their own benefits and drawbacks.

See http://www.d.umn.edu/math/Technical%20Reports/Technical%20Reports%202007-/TR%202011/TR_2011_4.pdf

To circumvent some of Arrow's criteria you'd have to implement cardinal utility voting (instead of ordinal).

endolith
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erocoar
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  • I already knew about some of the drawbacks. No system is perfect, and this imperfection is fine by me. I disagree about cardinal voting though: many ordinal voting systems satisfy a subset of the criteria, such as Schulze method which is known to have very little weaknesses. – Diane M Jan 09 '16 at 19:31
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    STV isn't a Condorcet election system; in fact, it meets the Later No Harm criterion, which is exclusive with the Condorcet criterion. – Publius Jan 09 '16 at 23:33
  • You are right. My bad, should have said ranked voting system :) – erocoar Jan 10 '16 at 00:19
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    @erocoar A ranked voting system isn't necessarily a condorcet one, nor is it "close" to one in some way. – Publius Jan 11 '16 at 10:31
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    There definitely can be a Condorcet winner, for any number of choices; it is even likely that one exists when a group is choosing from a reasonable number of candidates. You just can't guarantee the existence of a Condorcet winner when there are three or more choices. – ohspite Nov 09 '16 at 11:11
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Score Voting and Approval Voting are much simpler, and better according to an objective economic measure of expected utility, called Bayesian Regret. http://scorevoting.net/CondorcetExec.html

And these methods may be better Condorcet methods than real Condorcet methods. http://ScoreVoting.net/AppCW.html

Though I suspect that the primary reason Condorcet has seen so little traction is simply its complexity, and the fact that social choice theory is extremely under-appreciated by the general public.

user4012
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Clay Shentrup
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    The paper you point out is biased. Score voting boils down to approval voting, and strategic approval voting have numerous cases (https://en.wikipedia.org/wiki/Approval_voting#Strategy_with_cardinal_utilities) where the vote only goes to favourite candidate. Condorcet method(s) are much more robust to this. You have a point with your last paragraph though. – Diane M Jan 10 '16 at 14:17
  • Welcome to StackExchange. FYI, you don't need to sign your posts. – The Pompitous of Love Jan 12 '16 at 16:18
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    @ArthurHavlicek

    Score/Approval Voting outperform Condorcet with any mixture of strategic or honest voters. http://ScoreVoting.net/BayRegsFig.html

    And under plausible models of voter strategy, they may actually be better Condorcet methods than real Condorcet methods. http://ScoreVoting.net/AppCW.html

    It is certainly not true that 100% of Score Voting users will tactically vote in an Approval style. E.g. see this contentious straw poll we conducted. http://scorevoting.net/RLCstrawPoll2015.html

    And yes, if your favorite candidate is strong, you may want to bullet vote. That's not a "problem".

     – Clay Shentrup Jan 16 '16 at 19:09
  • I was willing to go in a debate with you, but I think no good would come of it. My last words on this: AV and SV fail majority criterion, that they sacrifice for greater utility "performance" as you say. In my humble opinion, which one is best is more philosophical than political, and I prefer my side, so please lets close this off topic discussion. – Diane M Jan 17 '16 at 21:38
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    @ArthurHavlicek Failing majority criterion is a good thing. A single-winner voting system should select the candidate who is most representative of the population as a whole, not just of half of it. Majority criterion leads to unbalanced winners, perpetual two-party domination, and political polarization. – endolith Dec 03 '16 at 14:13
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    @ArthurHavlicek Also it's totally false that "Score voting boils down to approval voting" or bullet voting. – endolith Jun 15 '17 at 03:52
  • @endolith Tbh it's an old question I no longer really care about, I changed point of view a lot by then, but I still think you are absolutely disrespectful about different opinions and wrongly believe any objective answer about "best method" truely exist. Range voting has merits, condorcet have others, and I could simply call that I prefer Condorcet just for the sake of disagreeing. For all I can see, none of your sources offer more valid scientific point of view. Which is to be expected, because science is rational and happiness isn't. Please quit trying to convince me or my readers. – Diane M Jun 17 '17 at 15:36
  • @endolith also when you link something for source support, it's best to make sure it truely supports what you claim. It happens to not contradict what you quoted, which makes me think you tried to manipulate facts, which angers me to a high point. – Diane M Jun 17 '17 at 15:40
  • @ArthurHavlicek Please read the link in my previous comment: 'Certain people criticize score voting as “just like taking approval voting and trying to dupe the naive into casting weak votes,” which is “unfair.” The point is, on average, people are quite possibly better off using score voting than using approval, if you consider how often people may use approval voting sub-optimally.' – endolith Jun 18 '17 at 03:41
  • @endolith Has done a great job here. – Clay Shentrup Feb 04 '20 at 20:08
  • Score voting satisfies the majority criterion if every voter is tactical and has enough information though. If an absolute majority of voters favour one specific candidate, they can always force their preference by bullet voting. More generally, the Condorcet winner is always one of the stable Nash equilbria for cardinal methods, if most voters identify the two candidates most likely to win and set their approval threshold inbetween the two. – saolof Oct 26 '20 at 17:04
  • Also, it's worth mentioning that the "condorcet" method analyzed in the scorevoting.net link uses nanson-baldwin, which basically defaults to borda counting if it can't find a winner. The link basically intentionally picks the theoretically worst method to use if you want to measure vulnerability to tactical voting, while Schulze, Smith/IRV, or Smith/Approval are all very difficult to manipulate. – saolof Oct 26 '20 at 17:12
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The argument that it is too complex is bogus. Put the candidates in order of your preference. The results will be reviewed by comparing each candidate against every other candidate individually. The one candidate that beats all other candidates in these head to head contests is the winner.

A major obstacle has been perceived complexity of obtaining the result. If the ballot papers are a conventional list then that is indeed a problem. This can be overcome by a bit of lateral thinking. The voter should be presented with a list of all the available combinations of orders of candidates. So if there are 4 then there will be 4! Combinations, ie 24. The voter then puts the option number on the ballot paper.

A spreadsheet can be pre prepared which will work out the number of votes cast in each of the individual pairings. The number of votes cast for each combination can be input to find the condorcet winner, if there is one. So vote counting takes no longer than at present. If no winner then revert to largest share of vote for runners up.

I have done a version of the spreadsheet for both 4 and 5 choice elections. The 5 choice gives 120 combinations of orders . It could be used to choose out of Labour , Tory, Lib-Dem, UKIP and Green, who governs.

David Cameron White
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    What about a seventeen choice election? As actually happened in the 2016 Republican primary in the US. And some people want to have a single election rather than a two stage election. There were upwards of thirty choices overall and that's without the extra encouragement of a ranked system. Even 17! is already trillions. Or 7! is thousands. I don't think that an ordered list is that complex, but it is more complex than making a single choice as plurality voting has people doing. – Brythan Feb 15 '17 at 16:43
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    Condorcet method are O(n^2 summable), not O(n!) summable like IRV. You only need to count pairwise preferences, i.e. each ranked ballot with c candidates is a list of c(c-1) votes for the distinct pairs of the form a>=b.

    So they are much easier to merge than IRV since you can just add the pairwise preference matrix from each polling station, though of course cardinal methods are linearly summable.

     – saolof Oct 26 '20 at 17:15
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The reason this voting method is not in effect in the US Political System as well as in most political voting systems, nor communal voting systems is because of a scenario you allude to in your question.

This encourage[s] being a good compromise candidate. For example, in a triangular scenario, the middle man can win without majority of first intention votes.

This does not incorporate the ideals of "voting" translating to the idea of "electing" based on majority. This will cause the majority to not be happy because the minority can actively cause major disrutiptions (far more than single vote systems) in the election process.

Allow me to illustrate by taking this non-political example. 30 dinner guests have to vote for the main dish out of 3 choices using the Condorcet method. The dishes are Burgers, Tacos, and Fish.

20 Dinner guests rank the dishes as 1. Burgers, 2. Tacos, 3. Fish

10 Dinner guests rank the dishes as 1. Fish, 2. Tacos, 3. Burgers

If you weight the votes in a "fair-ish" manner it will appear that the Tacos were the most wanted Dish between the dinner guests, which appears to be the bad trade in this deal because the majority of guests wanted Burgers.

So it's obvious to see in this example how this voting method means that the majority will rarely get what they most wanted. If you think that the majority should not have what they most want, then why have a vote anyways as the candidate most wanted will never win. Your system of voting will nearly always end with a result not wanted by most of the voters.

Taking it a step further into serious matters, this form of voting allows for malicious disruptions. Say that the 10 dinner guests knew what the other 20 dinner guests would be voting for, but did not care what to vote for as long as the 20 dinner guests did not get the dish they most wanted. In this system they can always ensure by voting the 2nd choice of the 20 dinner guests as their 1st choice.

It is for these reasons that the Condercet Method is not used. On paper the Condercet Method is great, but when applied to real life examples as well as seeing the potential consequences used in elections over serious issues it falls short by allowing the minority to disrupt and distort the election.

nanonano
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    That's not how Condorcet scoring works. Burgers would win in this case, 20-10 over Tacos and Fish. – Brythan Jan 16 '16 at 23:54
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    "which appears to be the bad trade in this deal because the majority of guests wanted Burgers." This is called tyranny of the majority, and is a bad thing. 1/3 of the population hates burgers, why should that be the winner? See this for a better food example: http://leastevil.blogspot.com/2012/03/tyranny-of-majority-weak-preferences.html "A majority, 2 out of 3, prefer pepperoni to all other options. Therefore, pepperoni must win. It's completely reasonable. And it means you're willing to send your friend home hungry." – endolith Dec 03 '16 at 14:17