Talk:Condorcet method/Archive 1

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.

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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)

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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, $53/105>50\%$) 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)

OK, here is your roasting:

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] 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 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], 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] 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)

In theory there are some ways of voting tactically, depending on the tie breaking method. In practice it would need a superhuman knowledge of how others were likely to vote. However, tactical voting with FPTP is almost the norm. All third parties have to faced with the question "If I vote for you won't I just be letting the other lot in." IRO/AV has the same problem. Say the 2000 election was by IRO. If there had been a likelyhood of Nadar overtaking Gore in 2000 then that might well have given the election to Bush. Hence voters who wanted Nadar might have abandoned him because they expected many Gore voters to switch to Bush to keep Nadar out. It is allways possible that a candidate in Nadar's position, ie percieved to be too extreeme to be the condorcet winner, could in fact be the condorcet winner. It seems to me this article is over accademic and doesn't really look at how it might work in practice. Dejvid 14:42, 12 Feb 2005 (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, 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 ${\frac {n^{2}-n}{2}}$ plurality ballots, where $n$ 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)

By the way, I think "ideal democratic winner" is coined by Russ Paielli. No one else uses that term. KVenzke 23:53, July 28, 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:

	1	2	3	4	5
1	X	0	0	2	1
2	4	X	2	4	3
3	4	2	X	3	4
4	2	0	1	X	1
5	3	1	0	3	X

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)

Potential for tactical voting

Dear Fahrenheit451, you wrote: "Condorcet methods are vulnerable to burying. That is, voters can help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot." Can you prove that the Condorcet criterion and invulnerability to burying are incompatible? Markus Schulze 13 July 2005

I thought that was generally understood. Long ago, I wrote a post to the EM list that posited this fairly loosely as a theory:

"Unfortunately, I think that all Condorcet efficient methods give some strategic incentives for further downranking later preferences in order to help earlier preferences. That is, take any ranked ballot voting method that satisfies universal domain, anonymity, Pareto, non-dictatorship. If it is a method where a group of voters reversing the order of options ranked after some candidate B can’t change the result to B under any circumstances, this implies that those rankings can’t be looked at while B is still in consideration. That is, B must be eliminated before they are looked at. If this voting method eliminates candidates before all the rankings are looked at, then it will not be able to avoid eliminating a Condorcet winner."

I was under the impression that more concise and firm proofs had both preceded and followed my statement, although at the moment I can't remember exactly where to find them. I will post them if I remember. Anyway, I'm not aware of a Condorcet-efficient method that is invulnerable to burying; are you? --Hermitage 07:23, 14 July 2005 (UTC)

Dear Hermitage, I don't know where to find such proofs, either. How does Fahrenheit451 justify his claim that the Condorcet criterion and invulnerability to burying were incompatible? Does he know where to find such a proof? Markus Schulze 14 July 2005

I don't know if he does, but even in the absence of a proof, I suggest that it is a safe assumption to make, for the time being. The article can always be changed if a burying-proof Condorcet method is found. However, I strongly doubt that this will happen. I'm actually rather surprised that you would have doubts on this point; it is something that I have been taking for granted for over 18 months. --Hermitage 09:20, 14 July 2005 (UTC)

More Condorcet Completion Rules

are listed on http://accuratedemocracy.com/c_other.htm 80.185.152.212 11:19, 24 July 2005 (UTC)

I wouldn't be opposed to the creation of a page for Black, Dodgson, or Kemeny. I don't think that Coombs is Condorcet efficient. --Hermitage 00:06, 25 July 2005 (UTC)

Defeat strength and the Plurality criterion

Now that there is an article for Woodall's Plurality criterion, it seems to me that it would be appropriate to mention that some methods using WV satisfy Plurality, but methods using margins don't. I'd like to say the same thing about SDSC, but that's probably more controversial. KVenzke 20:34, August 10, 2005 (UTC)

Yup, I'd rather see W's PC in the article than SDSC. I think that W's PC is probably more well-defined. --Hermitage 11:13, 13 August 2005 (UTC)

I added W's PC to a new paragraph on Defeat Strength. Now, having added that, I do not think that the margins vs winning votes discussion is "open for debate", as I wrote. Some methods use them, but they are analytically and logically inferior. I'm leaving it for the moment, but I could rewrite the paragraph at nearly half the words if I removed that assertion. I want comment on this, as an earlier assertion that "margins lose information" was once removed, with an implication that it was "POV". --—Daelin 13:00, 2 October 2005 (UTC)

The concept of disenfranchised votes is salient, but the presentation either is incomplete or more likely misses the point. Disenfranchisement of votes can justify the use of margins.

To resolve a circular ambiguity, a defeat only has to be reversed, not totally ignored. Reversing a defeat only requires disenfranchising margin + 1 of the winning votes, not all of them. Consider a circular ambiguity that can be resolved by selecting a 100 to 99 defeat or a 97 to 5 defeat. The winning votes measure of strength casts the choice as a selection of which defeat to ignore -- whether to disenfranchise 100 or 97 votes, choosing the latter. But the margin measure of strength casts the choice as a selection of which defeat to reverse -- whether to disenfranchise 2 or 93 votes, choosing the former.

Because the winning votes measure of strength sees the issue in terms of totally ignoring a defeat, it artificially inflates the count of disenfranchised votes and so can result in an excessive disenfranchisement. Of the two, only the margins measure of strength will stepwise minimize the number of votes that actually have to be disenfranchised. From this perspective, the preference for margins is more than just a popular intuition. If disenfranchisement favors margins, maybe the debate is still open.

Particularly with the above in mind, the currently worded argument in favor of winning votes, "Because cycle resolution involves ... may be very large—or not," offers statements that apply equally to winning votes and margins and does not explicitly make a case for one or the other.

I'd suggest the passage be at least modified, perhaps as part of a rewrite, to correctly compare and contrast how the disenfranchisement criteria applies to winning votes and to margins. DCary 08:30, 7 October 2005 (UTC)

Proposing a rewrite

I'm planning on proposing a rewrite and restructure of the article, using Single Transferable Vote as a skelton. Because of the current "structure", I'm not sure it's worth the effort to do incremental revisions. I think the volume of the article can be cut significantly without reducing information or clarity. Actually, I think it would increase clarity. I'm fishing for opinions on this act, and how I should go about it. (eg, shall I post it on the discussion page before commiting it?) --—Daelin 13:11, 2 October 2005 (UTC)

This is one of the more usefully informative voting article, to me anyways, just please preserve all the information. JeffBurdges 16:13, 27 November 2005 (UTC)

I support this; I stumbled across this article and found it difficulty to read. This is compounded by all of the related articles containing very similar information (i.e. condorcet winner, condorcet criterion, Condorcet Approval Instant Runoff Voting, and probably others I've left out.) They could easily be consolidated into a more concise article that would bring all of the information together. As it stands there is a bit of overlap between them and it's confusing to follow. Peyna 03:57, 30 November 2005 (UTC)

Multi-winner

What is generally considered the best "Condorcet like" method for ellecting multiple representatives? If you need fewer winners than the Smith set provides, I guess you can use Schulze to trim it down until you get all ties or reach the desired number, and maybe use STV to go further if necissary. But what if you need more representatives than the Smith set provides? Seems like the computations of STV should be employed in a Condorcet-like way, no? JeffBurdges 16:13, 27 November 2005 (UTC)

If you want a majoritarian multiple-winner method that reduces to Condorcet, all you have to do is use a Condorcet method to generate a ranking, and take the top N candidates from that ranking. Ranked pairs gives you the ranking for free, and so do other methods like Minimax, but you can also repeatedly run a Smith-compliant method like Schulze and take out the winner.

If you want a proportional method like STV that reduces to Condorcet, though, it gets a lot harder. There's CPO-STV, but it's mostly hypothetical because it's really difficult to implement. I don't think one that's computationally simple has ever been proposed. rspeer 01:25, 1 December 2005 (UTC)

I'm not sure what the ideal n-winner Condorcet criterion would be, but it seems like it should imply that "If the smith/ set has at most n members, then the smith set wins." Here would be one simple proposal:

1. Compute the Smith set
2. If there are at most n members of the smith set; then elect them, reduce the votes of people who supported them, ala STV, and repeat from 1.
3. If there are more than n members of the smith set; then start dropping weakest defeat, ala Schulze, and go to 1.

Maybe I should be using the Schwartz set there?

Ideally, you'd want a multi-winner version of local independence from irrelevant alternatives (Local IIA) which also implied your multi-winner Condorcet criterion. Maybe the following:

1. If a set of candidates X wins an election, and a new alternative y is added, X will win the election if y is not in any minimal unbeaten set with at least n members.

Or something like that. I should just think about it. Oh, the pdf on the CPO-STV page is a dead link. JeffBurdges 23:33, 1 December 2005 (UTC)

If you don't want a proportional method, just elect the top N candidates in whatever ranking the used Condorcet method produces. This will elect all Smith members if there's room for them. KVenzke 05:50, 2 December 2005 (UTC)

I have just uploaded a paper about a proportional version of the Schulze method. (To understand the used terminology, you also have to read this paper.) Comments are welcome! Markus Schulze 15:55, 21 March 2006 (UTC)

Wikipedia:Articles for deletion/Condorcet Instant Runoff Voting

Hey, if Instant Runoff Voting can be integrated into a Condorcet format somehow, can this please be added, per the merge vote at the discussion above? I'm not an expert on the subject, although I do find it fascinating.

Many methods can be combined in various ways with Condorcet. I can't see any reason to mention IRV specifically. KVenzke 04:23, 6 December 2005 (UTC)

Defeat strength explanations

The choice between margins and winning votes is open for debate. Because all Condorcet methods always choose the strong Condorcet winner when one exists, the difference between methods only appears when cyclic ambiguity resolution is required. The argument for using winning votes follows from this: Because cycle resolution involves disenfranchising a selection of votes, then the selection should disenfranchise the fewest possible number of votes. When margins are used, the difference between the number of two candidates' votes may be small, but the number of votes may be very large—or not. Only methods employing winning votes satisfy Woodall's plurality criterion. A counterargument is that equal preferences (either implicitly or explicitly declared) should not be given more or less "weight" by the election system compared to strict preferences. Since the difference in assessment can simply be bypassed by resolving equal preferences randomly, one could argue that voters with sincere equal preferences at the bottom of their ranking are unfairly being pressured to randomize them in fear of "punishment" by the system. In other words, the use of winning votes is open to the criticism that it encourages random voting even without knowing anything about other voters (something itself captured by Blake Cretney's pro-margins sincere expectation criterion).

From an intuitive point of view, margins as a measure of defeat strength tend to appeal more.

I think this can be improved. For one thing, there are other arguments in favor of winning votes. If I had to explain in principle why to prefer winning votes, it would be because it seems more consistent with majority rule: It tries to respect the preferences of an actual majority (more than half of the voters) before considering the others. There is of course reduced strategy when a majority can gets it way merely by being a majority. Winning votes also creates less favorite betrayal incentive (explained why here).

The notion of not giving "weight" to equal preferences makes no sense to me as written.

The segment beginning "Since the difference..." doesn't follow: Since the difference in assessment can simply be bypassed by resolving equal preferences randomly, one could argue that voters with sincere equal preferences at the bottom of their ranking are unfairly being pressured to randomize them in fear of "punishment" by the system.

I can't find where Cretney defined the "sincere expectation criterion," which makes me think it shouldn't be mentioned here. I can only find a message by Chris Benham reporting that it requires that there should be no strategy better than sincere voting in the zero-info case. It's true that winning votes has zero-info strategy while margins doesn't. KVenzke 05:50, 8 January 2006 (UTC)

Sorry for saying it, but you could have easily found it, as it was the fourth result given by Google [4]. Anyway, my edit was just a start at trying to counterbalance the pro-winning votes side, as the margins side also has more arguments, in this case more than just the appeal to intuivity. NPOV and all that. Blake Cretney even has a whole page devoted to it [5], which can help in explaining and thus elaborating above text. -- Dissident (Talk) 15:41, 8 January 2006 (UTC)

I did Google it, but didn't find it. I have read Cretney's article, but when I went to his site I couldn't find a link to it. I don't mind NPOV but I don't think the argument given against WV (in this article) is very accurate. In the zero-info case, WV probably gives incentive to randomly rank among the least liked candidates. But it gives incentive to compress strict rankings at the top into an equal preference. The only reason margins doesn't give incentive to rank randomly is because its mechanism for handling equal rankings is effectively the same as voting randomly. Advice to rank randomly in (non-zero-info) WV elections doesn't seem like good advice to me. Cretney gives the impression that this will uniformly hurt (and not help) the bottom candidates, but this isn't guaranteed. It can backfire and elect one of those candidates. KVenzke 04:08, 9 January 2006 (UTC)

You might want to take a look at Talk:sincere expectation criterion, where I have a more technical discussion with Markus Schulze about this. -- Dissident (Talk) 23:12, 13 February 2006 (UTC)

Blake Cretney criticizes that, when MinMax(pairwise opposition) is being used, then ranking an additional candidate sometimes helps but never hurts an already ranked candidate. In other words, MinMax(pairwise opposition) satisfies later-no-harm and violates later-no-help.

However, MinMax(pairwise opposition) isn't a Condorcet method in the proper sense because it doesn't satisfy the Condorcet criterion. Therefore, Blake Cretney's criticism cannot be interpreted as a criticism of some types of Condorcet methods.

Furthermore, the Condorcet criterion and later-no-harm are incompatible. Therefore, Blake Cretney's criticism cannot be generalized from MinMax(pairwise opposition) to Condorcet methods.

Markus Schulze 12:30, 14 February 2006 (UTC)

From what I understand, in 1998 what was called votes against then meant winning votes and not pairwise opposition (which I believe wasn't introduced till later), unless you think Mike Ossipoff was advocating a non-Condorcet method all the time. Not likely. Blake Cretney's sincere expectation criterion was meant as a strike against the really Condorcet-complying winning votes Condorcet methods. -- Dissident (Talk) 15:20, 14 February 2006 (UTC)

Votes against means pairwise opposition and not winning votes. See here! Markus Schulze 18:23, 14 February 2006 (UTC)

Obviously that doesn't prove anything apart from maybe that the terminology was settled upon in 2005. -- Dissident (Talk) 20:59, 14 February 2006 (UTC)

Obviously, this proves that either Blake Cretney didn't understand the difference between pairwise opposition and winning votes or that he didn't understand the strategic implications of winning votes. In any case, this proves that you cannot use Blake Cretney's website for your claim that the sincere expectation criterion was incompatible to the use of winning votes. Markus Schulze 22:00, 14 February 2006 (UTC)

From what I'd gathered, the difference didn't become prominent until much later, so I think it's reasonable to excuse both Blake Cretney and Mike Ossipoff in being sloppy with the terminology, especially as it isn't often completely agreed upon by the election-methods-list members as the case of the resolvability criterion clearly demonstrates. Anyway, apart from the terminology, Cretney implicitly shows an awareness of the difference between later-no-harm+not-later-no-help and his criterion, by saying in my primary source (emphasis mine):

Votes-Against fails this criterion because if your sincere preference is A > B=C, it is more likely to your advantage to rate A > B > C or A > C > B. It can back-fire, but the insincere vote is more likely to get you what you want, so unless you have detailed knowledge about how everyone else is voting, the insincere vote is better.

-- Dissident (Talk) 22:30, 14 February 2006 (UTC)

Similarly, IRV supporters usually argue that, when a Condorcet method is being used, then the voters will use bullet voting. It makes a big difference whether someone makes a prediction about how the voters will vote under a concrete election method or whether someone proves that a concrete election method violates a given criterion. Markus Schulze 00:21, 15 February 2006 (UTC)

I have the impression that you haven't looked at Talk:sincere expectation criterion since I made a new attempt at proving the noncompliance of Condorcet methods with winning votes (and not just pairwise opposition). -- Dissident (Talk) 01:28, 15 February 2006 (UTC)

Defeat strength

I strongly recommend that the defeat strength section should be moved from the Condorcet method article to the articles of the individual Condorcet methods. The consequences of the specific choice of the defeat strength measure simply depend too much on the used Condorcet method. Examples:

1. MinMax(pairwise opposition) satisfies later-no-harm. However, this is not true for Schulze(pairwise opposition) or Ranked Pairs(pairwise opposition).
2. When Ranked Pairs is being used, then pairwise opposition and winning votes are equivalent. However, this is not true for Schulze or MinMax.
3. Schulze(winning votes) satisfies Woodall's CDTT criterion. However, this is not true for Ranked Pairs(winning votes) or MinMax(winning votes).

Therefore, I suggest that the defeat strength measures should be discussed only in connection with a concrete Condorcet method. Markus Schulze 00:42, 5 March 2006 (UTC)

I disagree. Many Condorcet methods come with different variants depending on how defeat strength is assessed, so the concept itself is generic enough to talk about it on the equally generic Condorcet method article, as long as of course only universal statements are made here. Furthermore, no one is stopping you from expanding on it in the respective Condorcet methods. -- Dissident (Talk) 02:22, 5 March 2006 (UTC)

Nanson's method

Dear Iota, you have added 4 uses of Nanson's method. However, if I understand McLean's paper correctly, then 3 of these 4 uses are out of date. Markus Schulze 09:05, 21 March 2006 (UTC)

The website of the University of Adelaide says that its council is elected by proportional representation by the single transferable vote [6]. Therefore, it seems to me that all four examples for uses of Nanson's method are out of date. Markus Schulze 20:47, 21 March 2006 (UTC)

I have removed the examples for the use of Nanson's method. According to McLean's paper, the University of Melbourne abandoned Nanson's method in 1983. According to footnote no. 7 of his paper, also the Anglican diocese of Melbourne abandoned this method. According to the website of the University of Adelaide, its council is elected by proportional representation by the single transferable vote [7]. Markus Schulze 19:33, 22 March 2006 (UTC)

My bad. I was simply relying on the Nanson's method article. Tend to forget that Wikipedia can be unreliable sometimes. I've just corrected the out of date information in that article too. Iota 03:27, 23 March 2006 (UTC)