# Talk:Condorcet method

There's a good website on Condorcet's method. I forget the link.

One important point is to mention Arrow's Theorem. There is a weaker verison of Arrow's conditions that the Condorcet method does satisfy.

Probably referring to http://electionmethods.org . There's a redefinition of Independence from Irrelevant Alternatives Criteria whereby "Irrelevant" is redefined. Basically, under the weaker version, candidates locked in a circular tie aren't considered "irrelevant". Condorcet can meet that criteria because it's only the tie-breaker that gets you in trouble, not the core method.
This weaker criterion is called Local Independence of Irrelevant Alternatives.

A WikiProject is being developed at Wikipedia:WikiProject Voting Systems for further work on this and other voting system related pages.

 Contents

## Condorcet vs. IRV (core support)

On the other hand, the Condorcet winner could be a candidate with very weak core support, raising questions about that winner's legitimacy.

What is this "core support" that the Condorcet winner might lack? This needs to be explained or I'm going delete or majorly rework this comment. -- AdamRaizen 21:01, 2003 Aug 20 (UTC)

I didn't make this comment and I wouldn't make this argument. But I believe the arguments goes something like this: suppose you have preferences as follows:

47% A > B > C
46% C > B > A
4% B > A > C
3% B > C > A


In IRV, it would be clear that very few people actually support B as a real choice, only as a fallback. Therefore, B would be eliminated, and one of the two candidates with "core" (first-place) support would win. Even clearer, we could use a payoff matrix:

    A  B  C
47% 8  2  1
46% 1  2  8
4% 2  8  1
3% 1  8  2


DanKeshet 21:11, Aug 20, 2003 (UTC)

There's a matter of perspective involved here. IRV places excessive emphasis on the first place ranking candidates. They are strong opinions. Last place on an IRV ballot is almost certainly irrelevant. By contrast, Condorcet ranks are all equally considered, so a first-place rank is not a "strong opinion"—just a preference. Am I making this clear? —Daelin 12:52, 24 Oct 2004 (UTC)

This potential lack of core support for a winner can also hold true for IRV. As such, it is not a valid arguement for selecting IRV over certain condorcet methods.

An example of this would be:

07% FarRight>Right>LuckyRight>ModerateRight>ModerateLeft
02% Right>FarRight>LuckyRight>ModerateRight>ModerateLeft
04% Right>LuckyRight>FarRight>ModerateRight>ModerateLeft
07% LuckyRight>ModerateRight>Right>ModerateLeft
15% ModerateRight>LuckyRight>ModerateLeft>Right
16% ModerateLeft>ModerateRight>LuckyRight>Left
15% ModerateLeft>Left>ModerateRight>FarLeft>LuckyRight
13% Left>ModerateLeft>FarLeft
11% Left>FarLeft>ModerateLeft
10% FarLeft>Left>ModerateLeft

In this case, IRV elected LuckyRight even those one can only claim at best a 35% support for right leaning views among the voting population. Nearly every other voting system will elect Moderate Left. As such, the comment:

On the other hand, the Condorcet winner could be a candidate with very weak core support, raising questions about that winner's legitimacy.

should be removed until such a time as someone can prove at least that IRV would suffer from this less often.

Ericgorr 15:12, 9 Feb 2004 (UTC)
Well, for a start, 16% of ML voters in that case are evidently right-leaning. But that's not the point. Whether in happens in IRV or not, it certainly happens in Condorcet(though not in FPTP, so it's an argument for that, I suppose).
Also, one criticism of Condorcet I've heard from IRV supporters is that it's possible for a candidate to win without having gotten one single first-choice vote, wheras in IRV you're required to have at least a not-last-place showing of first-choice votes. This may be the strongest definition of "core support" possible, unless someone can come up with something more precise. PenguiN42 17:24, Oct 26, 2004 (UTC)
I think this is a difference of opinion over the significance of a first-place rank. Neither system provides a good mechanism for distinguishing the magnitude of preference. IRV, however, places a great deal of emphasis on the first-place rank, while Condorcet places equal emphasis on all ranks. IRV's expression of magnitude is intractably poorer than systems designed to represent magnitude.—Daelin 17:09, 28 Oct 2004 (UTC)
Two responses: 1) This is a discussion of IRV vs Condorcet, not IRV vs some other non-condorcet system which addresses the concerns that IRV supporters have about condorcet. 2) I don't think "magnitude" really captures the idea here. The concern is more along the lines of "Who should win: everyone's 2nd favorite or the majority of the people's 1st choice?" This isn't an issue of people *expressing* the magnitude of their preferences, it's an issue of *interpreting* the overall preferences of the voting public. PenguiN42 23:12, Nov 3, 2004 (UTC)
I just counted up an election with 48 voting (A,B,C) and 52 voting (C,B,A). C won quite clearly. You can see that only 48% voted B over C. Now, if I change the election to add three (B,C,A) ballots then C still wins. If I add two more (B,C,A) ballots then B wins with 53 votes prefering B to C. (Also, [itex]53/105 > 50%[itex]) In other words, B has a majority over C. It doesn't matter that B was second place on most ballots. Now, IRV would declare C the winner still, despite a majority of ballots voting against C.
The problem of "core support" is an assumption that the first place candidate is a very strong preference. What if you don't really like your first place candidate but you just barely prefer him over the second place, both of which you want over the third? You don't really care. Yet, your vote counts among this "core support". Condorcet counts majority pairwise preferences. IOW, "core support" is an illusion based on a false assumption about the significance of first place. An assumed magnitude. The result of this election is obvious: A majority prefer B to A (52+5=57 votes), and a majority prefer B to C (48+5=53 votes). "Core support" is a matter of interpreting a greater-than-one value for first-place choices. You have to assume first place is more important than just beating everyone else on the ballot.
—Daelin 23:45, 25 Nov 2004 (UTC)
I agree with Daelin. "Core support" is a red herring. Hermitage 22:49, 9 Jun 2005 (UTC)

## Condorcet Objections

I added some objections to Condorcet being used in "serious" elections. Before I get roasted as a Condorcet basher, let me put in the record that I would love for Condorcet to be the way we vote. But I've been an agent, a poll clerk, and a deputy returning officer in enough elections and watched enough debacle in the US with its blackbox machines to have decided, regretfully, that the Condorcet ideal is very unlikely to be implemented in a way most electors could ever trust. Whether they were stupid/paranoid electors, or thinking electors. As flawed as our (Nova Scotia) methods are, it's very hard to jigger them without someone seeing it. Kwantus (2003 Aug 30)

in the procedure. (Even assuming the code is publically available, as in Australia but not in the USA, there is no way to prove to an elector that a results computer has been loaded with that code, nor that the machine is operating correctly even assuming its design is perfect.)

That's an issue independent of the voting system.
Not if the system is so complex as to make mechanical counting tempting. The way we do an election is open at every stage and simple enough no mechanical aid beyond a simple calculator is necessary. I grant that our elections are non-Condorcet ... but I believe elector trust in a nonCondorcet system is better than rampant distrust in a Condorcet system.
The transparency of the complex Australian IRV count is less often questioned than that of the heavily automated USA plurality elections. BTW the use of IRV in Australia refutes your argument, since it seems to be aimed more at the complexity of ranked methods in general than anything particular to Condorcet.
You missed the point. The distinction I'm after is that Australia puts the code for its voting machines on a website for public inspection whereas in the USA that code is a trade secret which the public is expressly FORBIDDEN to inspect.([1] (http://www.votefraud.org/Archive/Write/greatest.htm) That "trade secrets" have supremacy over the public's need/right to trust their democratic process is a splendid example of the fascism - business before people - in the US. Kwantus 23:15, 15 Sep 2003 (UTC)) The former system certainly engenders more voter faith than the latter; regardless, in neither case can a skeptical elector or even a poll official satisfy himself that the machine is running the proper code.
I think what's less questioned in Australia is the technology -- the American machinery is pretty blatantly riggable. But the confidence in the Australian system is still misplaced (unless they revert to a paper backup in disputed cases -- i don't know).

Another is division of labour; counting cannot be distributed to the workers in individual polls

I don't see why not.
Because the time to communicate the count to the returning office would be large fraction of or even more than the time it'd take the RO to count the ballots itself. (Unless you use digital methods, which cannot be inspected.)

. In Nova Scotia, a poll usually handles about 400 electors, and in a recent election there were 7 candidates in one riding. That means there 5040 ways of marking a full-ranking ballot. The ballot of every elector in a poll, indeed a dozen polls, could be unique. (Even assuming a few favourite candidates, there's a lot of wiggleroom.) The present method of counting ballots in the poll and telephoning the tallies to the returning office cannot be adapted; the polls in such a riding could easily have dozens of numbers to call in, requiring.

Exactly 49 numbers. Managable by phone I would have thought.
--pm67nz
hmm...y'okay, I guess the pairwise counts are enough (tho 49 is still a long list to transfer accurately verbally). But if you want to audit to the number of ballots cast, you then have to insist all ballots are marked with a full ranking else the pairwise counts won't share their total. <suddenly i'm not sure they would even then, i'll have to cipher> (There's nothing deeply wrong about such insistence but there'd be lots of electors who'd mark their ballot in the old way…follow instructions? ha!—and either that can be accomodated…there's a quite reasonable interpretation of a mark-yer-X-type ballot—at the expense of being able to check the pairwise totals against each other, or it can be a lot of rejected ballots.)
<PS: actually i guess you can make that work for only those two kinds of ballots—no trying to handle partial orderings. Otherwise you lose the cross-checking, and converting about 400 7-candidate ballots into 42 or 49 numbers is hairy enough you want the cross-checking.>

## What Condorcet Can Do

I think it may be worth noting that a Condorcet Method can support some very natural selections. You have ordered preference of course (A xor B). You can also specify no preference between two candidates, except that they're less or more prefered than others: ( 1. A, 2. B or C, 3. D )

The article also says that "'(usually, candidates not placed on the ballot at all are considered to be less preferred than all those that are and equally preferred compared to each other)'". This should be expanded on to include what a Condorcet Method can do but which this statement says is usually not done: stating no opinion. CIVS (http://www5.cs.cornell.edu/~andru/civs/) permits this. A "No Opinion" candidate does not beat nor is beaten by any other candidate. So, that's four possibilities: Win (preferred: 1v0), Lose (less preferred: 0v1), Don't care (no preference: 0v0), and No Opinion (Col X and Row X are zero).

I would also like confirmation for the "don't care" values. Most descriptions of Condorcet's Method I've read say you build the pairwise matrix by indicating if a candidate is preferred to another, so no preference would be 0v0. It could, however, be 1v1 without affecting that pairwise election. However, this could affect certain ambiguity resolutions. Daelin 2004-04-30 12:17-0500

## Condorcet's susceptibility to tactical voting?

I'd just like to start a discussion to clarify exactly under what circumstances Condorcet is susceptible to tactical voting. This article had previously stated that Condorcet was *not* susceptible [2] (http://en.wikipedia.org/w/wiki.phtml?title=Condorcet_method&diff=6875117&oldid=6873928), which I am pretty sure is untrue, as I once claimed that on the Election Methods email list and was lambasted for it. Then an edit directly after mine [3] (http://en.wikipedia.org/w/wiki.phtml?title=Condorcet_method&diff=0&oldid=6875117) clarified by saying that it's only susceptible when it "includes a tie-breaking mechanism." What does this mean, exactly? Only when it includes a mechanism to deal with a situation where a pairwise comparison between two choices results in a tie? See, I was under the impression that the strategy concern in Condorcet was more serious than that -- that even without the tie-breaking mechanism, the strategy of "burying" your strongest opponent by ranking them lower on the list than your true preference could create an ambiguous/circular result, which, depending on the method used to resolve the ambiguity, could cause your candidate to have a better chance of winning. In fact it was argued to me on the election methods list that it doesn't matter which method you use to resolve the ambiguity -- any method would be a strategy concern in some circumstances. Finally, if the above editor in saying "tie-breaking mechanism" actually meant an ambiguity/circularity resolving mechanism, then I think that should be clarified in the article. PenguiN42 17:17, Oct 26, 2004 (UTC)

Sorry I didn't have a chance to respond to this earlier. Yes, that is definitely what I meant by "tie-breaking mechanism". It seemed to me that the previous version required some kind of clarification. "Any voting system which chooses the Condorcet Winner when it exists is known as a Condorcet method" and it seems to me that within this narrow goal, Condorcet is impervious to tactical voting. Well, almost: people might be able to vote strategically to prevent there from being a Condorcet winner, but it is impossible for tactical voting to result in a different person becoming the Condorcet winner. Once you add "an ambiguity/circularity resolving mechanism", that is a whole other kettle of fish. If this can be expressed more clearly than in my version, that would be great. - Nat Krause 15:52, 5 Nov 2004 (UTC)
Ah ok, that's what I suspected. Just making sure I wasn't completely off-base :) ... I clarified the wording in that section, at the expense of making it even longer. PenguiN42 17:28, Nov 8, 2004 (UTC)

## Merge Note

Ashley Y made two changes, one radically changing the second paragraph, the second a note to merge with Condorcet criterion. I am reverting these changes because the first is a) wrong, b) poorly written. I am reverting the second because it is a bad suggestion and that article is on clean-up.

• The Condorcet criterion is a principle applied in voting theory, and should not be shoe-horned into an article about another topic related to the same progenitor.
• A Condorcet Method can be explained without mentioning the Condorcet Criterion. This change made understanding of the Condorcet Criterion a pre-requistite to understand the paragraph.

Now, it should be mentioned that Condorcet proposed the method he did because it fit his criteria. This is historical information, not functional, so it should not be in the opening section of this article. Stating the obvious, comment is welcome. I make the revert now primarily because the new grammar is barely readable and untranslatable. ——Daelin 01:57, 14 Nov 2004 (UTC)

I'm not sure that I agree, Daelin. Ashley's changes don't seem all that inaccessible to *me* -- they provide a bit more information, defining all their terms, and are subordinate to the lead graf to begin with. And they do make it clear, which the current approach does not, that there can be more than one method that is a Condorcet Method. I believe some more discussion is called for on this change. Baylink 19:10, 14 Nov 2004 (UTC)
Right. The point is that there isn't a single "Condorcet method", only methods that happen to conform to the Condorcet criterion, and one should not consider them a single "voting system". —Ashley Y 02:20, 2004 Nov 15 (UTC)
There is a specific method which can clearly be called Condorcet's Method, which is the method Condorcet proposed (which was previously invented). Ignoring cyclical ambiguities, there is then a category of methods which are mathematically equivalent. These are the methods which "choose the Condorcet winner" or "conform to the Condorcet criterion". The bulk of this article is devoted to the later, as they deal with the cyclic ambiguities. This summarizes the issue, correct?
I still do not think Condorcet criterion should be merged. I add to my reasons structural inconsistancy with the other voting method "criterion" such as the Monotonicity criterion, which are not encapsulated in related articles. Brief discussion is warranted, as the two subjects are more closely related than most methods are to specific criterion. However, an in-depth discussion of the criterion would be a significant detour from this article's subject. Perhaps we should beef up the relationship? ——Daelin 21:52, 15 Nov 2004 (UTC)
If there's a specific method that can clearly be called Condorcet's Method, it isn't mentioned in the article. Instead the article talks about a number of voting systems that happen to conform to the Condorcet criterion.—Ashley Y 03:34, 2004 Nov 16 (UTC)
I suggest that the article "Condorcet method" should be merged with the article "Condorcet criterion". Most of the confusion in the public is caused by the fact that many people mistakenly believe that the term "Condorcet" refers to a method and not to a criterion.
For example: In the Voting Systems Study of the League of Women Voters of Minnesota (http://www.lwvmn.org/LWVMNAlternativeVotingStudyReport.pdf), the League discussed five methods: Plurality, Approval, Borda, Condorcet, and IRV. They reject Condorcet because it "does not always produce a winner" (page 5). If they had considered a concrete Condorcet method (e.g. CSSD) and had treated Condorcet rather as a criterion than as a method then their conclusion wouldn't have been feasible. Markus Schulze 22 Nov 2004
I agree. —Ashley Y 02:18, 2004 Nov 23 (UTC)

Perhaps the merged page should be called "Condorcet Voting" or "Condorcet Election". Voting is so closely tied to elections that they are almost synonymous, but of course voting is necessary but not sufficient for elections since certainly counting is needed, so I might suggest "Condorcet Election" over the other. I didn't know about the Condorcet criterion until recently, but I had known about Condorcet voting, which is what I went looking for. The criterion can be applied to more types of voting than just Condorcet voting, but it seems to me that any criterion is subservient to elections. Perhaps more people would search for Condorcet in combination with "voting" or "election" than "criterion". I could endorse having a large main "Condorcet Election" page with a smaller page that discusses the details of the Condorcet criterion. Calling a main page Condorcet Method seems too generic. Should there be another page about "Condorcet Winner"? (I don't think so.) What does the criterion relate to? Elections. What does the method accomplish? Elections. Call it "Condorcet Election". Hu 03:16, 2004 Nov 23 (UTC)

Well, Condorcet's method is about counting. The ballot is just an ordered list, just like IRV and Borda. The difference is in how you aggregate the ballots. Elections involve more than the voting system. The method of Condorcet is to convert each ballot into a boolean matrix of 1s and 0s, and add them up. Condorcet gave two methods for considering a winner from the sum matrix. One doesn't consider a circular tie, the other nobody has really been able to divine his exact meaning. Both of the methods indicate that you discard the fewest number of votes possible (so you do not use margins). This, all together, is a method, albiet an incomplete one as it does not cover all cases.

It's a language problem, I suppose. It has become the practice to refer to any completion of Condorcet's method as a Condorcet method. Wikipedia could clarify it by changing the language. Should we? I think it should be done, but if we do it then it makes the articles less useful by misrepresenting jargon.

—Daelin 22:54, 25 Nov 2004 (UTC)

## Complex Ballots endanger Anonymity

Did it occur to anyone that complex ballots, like those used in Condorcet or IRV or Borda, give so many voting possibilities that you could bribe/blackmail someone into voting a certain way and be able to verify that vote?

A ballot for Range Voting/Approval/Majority Choice Approval could simply be cut into as many ballots as there are candidates.

A ballot for a Condorcet method could be replaced by ballots for every pairwise match. That would give every voter in a 5 candidate race 10 ballots and in a 10 candidate race 45 ballots! Oh, and individuals could vote in cyclic ambiguities.

I don't know a solution with IRV and Borda. 80.129.185.58 18:32, 8 Dec 2004 (UTC)

This is a question about the practicality of implementing preferential voting. AN answer is that it is not more suseptible to breaches of anonymity than other method, including [plurality]. The format of the ballot should have no effect on the level of anonymity afforded by the ballot. Specific implementation would have an effect: for instance, tieing a unique ID to each ballot and allowing people to check that ID online would allow what you describe. However, there's just as much call for that whatever the method.
There are not a massive amount of possibilities in Condorcet Methods. Your ballot is just an ordered list. 1, 2, 3, 4, I want them in this order. You don't need to see the matrix which is used to add your ballot to others. You don't check each box (which would allow you a cyclic ambiguity with yourself). Now, you COULD translate that ballot to [itex]\frac{n^2-n}{2}[itex] plurality ballots, where [itex]n[itex] is the number of preferences you specify. That doesn't affect the anonymity, however. —Daelin 16:02, 13 Dec 2004 (UTC)
Btw, not all Condorcet methods are calculable just from the pair-offs, though most of them are. Black and Smith/IRV are not. —Ashley Y 06:10, 2004 Dec 14 (UTC)
Black is calculable just from the pair-offs. Markus Schulze 17 Dec 2004

## What the hell?

Okay, this is downright fishy. All references to Condorcet's definition of "Ideal Democratic Winner" have been struck from wikipedia by someone in the 62.246.. class-B. This resolved to p62.246.140.83.tisdip.tiscali.de and may be accurate. The modifications I've noted follow:

Condorcet Criterion
62.246.160.248
http://en.wikipedia.org/w/index.php?title=Condorcet_Criterion&oldid=7253007

Condorcet method
62.246.140.83
http://en.wikipedia.org/w/index.php?title=Condorcet_method&curid=44446&diff=0&oldid=0

The rather qualitative "Ideal Democratic Winner" has been replaced each time with "Condorcet winner" or "Condorcet candidate." I think this change is POV-motivated. The term is defined by Condorcet and seem clearly indicated as such. This change seems subtle, yet note how the Condorcet articles have become self-referencing and basically a dead end in the wiki, and conceptually removed from the rest of the voting articles. It is not just a false dichotemy, but a false isolation.

—Daelin 17:49, 7 Jan 2005 (UTC)

I agree that the term "ideal democratic winner" is too vague, and insufficiently value-neutral. I haven't noticed a pattern of Condorcet links being removed from the rest of the voting articles, but I'll look out for that, and prevent it when I can. Hermitage 22:45, 9 Jun 2005 (UTC)

## Example

The example isn't very clear. More detailed explanation would be helpful. Maurreen 05:31, 1 May 2005 (UTC)

## In principle . . .

Why is it that the "basic procedure for casting ballots is" necessarily "identical to most preferential ballots"? Couldn't I, in principle, submit a ballot saying that I prefer A to B, B to C, and C to A? The system could handle that. Is it just that it makes no sense for an individual to have those preferences? Sorry if I sound confused, because I am—voting theory confuses me quite badly. —Simetrical (talk) 03:26, 4 May 2005 (UTC)

• Generally it's because the ballot is designed to not allow you to do that - you vote in an ordered list, rather than with a circle. Preferential ballots use ranked, ordinal lists of preferences. This is a reasonable assumption for most individuals, and correllates very nicely with ordinal theories of utility. Scott Ritchie 09:26, 24 May 2005 (UTC)

## IRV as ambiguity resolution

Maybe I'm just confused, but how does IRV resolve ambiguity? Let's take a vote where you have the votes:

• 2 > 4 > 3 > 5 > 1
• 2 > 3 > 5 > 4 > 1
• 3 > 2 > 1 > 5 > 4
• 3 > 5 > 2 > 1 > 4

That gives you a grid like so:

12345
1 X0021
2 4X243
3 42X34
4 201X1
5 3103X

Now, there's a tie between 2 and 3. Try breaking it with IRV among the Smith set, and your four votes are:

• 2 > 3
• 2 > 3
• 3 > 2
• 3 > 2

Doesn't solve much, does it? IRV ties as well. Am I missing something? —Simetrical (talk) 06:03, 8 May 2005 (UTC)

One of the fundamental assumptions in most voting systems is that true ties are very, very unlikely in an election with many voters. I'd have to check the math, but I think that an exact tie is equally likely in IRV as with the plurality system.

## Ramon Llull

The first sentence currently reads as follows: "Any election method conforming to the Condorcet criterion is known as a Condorcet method. The name comes from a deviser, the 18th century mathematician and philosopher Marquis de Condorcet, although the method was previously devised by Ramon Llull in the 13th century."

I think that this opening gives Condorcet too little credit, and Ramon Llull too much credit. As far as I know, Ramon Llull's procedure used iterative voting rather than ranked ballots. In my opinion, the use of ranked ballots to simulate pairwise elections (rather than just holding actual pairwise elections) is an essential part of Condorcet's method.

I will remove the Llull reference for now. If there is evidence that Llull used ranked ballots, then I apologize for my mistake. I don't mind having some info about Llull in the article, but I would prefer it to be in a separate section later in the article, and I would prefer that it describes precisely how Llull's voting procedures worked.

I suppose that it can be argued that any method passing a preference version of the Condorcet criterion is a Condorcet method. However, this page as written describes methods based on ranked ballots rather than iterative voting. If we define Condorcet methods in part as methods that use ranked balloting, then Llull's method, and the commonly used legislative procedure of voting on amendments (which also passes a preference version of the CC), do not qualify as Condorcet methods. Hermitage 22:37, 9 Jun 2005 (UTC)

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