Talk:Condorcet criterion

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Elections and Referendums (Rated Start-class)
WikiProject icon This article is within the scope of WikiProject Elections and Referendums, an ongoing effort to improve the quality of, expand upon and create new articles relating to elections, electoral reform and other aspects of democratic decision-making. For more information, visit our project page.
Start-Class article Start  This article has been rated as Start-Class on the quality scale.
WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Low Importance
 Field: Applied mathematics

What's the origin of the name Condorcet? Ben Finn 14:13, 10 December 2005 (UTC)

The link to "minmax" goes to the wrong article.

First past the post[edit]

The following statements are taken from this article:

"The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate."

"Non-ranking methods such as plurality and approval cannot comply with the Condorcet criterion because they do not allow each voter to fully specify their preferences."

In a FPTP/plurality system, the voter specifies their preference for one candidate. The FPTP winner therefore has more votes than each other candidate in turn.

Therefore, on face value, FPTP does have condorcet winners - the second above statement is false. If it is assumed that there will always be an element of tactical voting and we therefore cannot see who the voter really would have voted for absent tactics, then this article should state this. The second statement above, however, states that FPTP does not allow each voter to fully specify their preference - and at face value this statement is false: there is one candidate to be elected, and the elector is allowed to vote for one candidate.

This article needs a re-write so that it says what is means to say, but at the moment it is a nonsense.

A further question arises, separate from the above points, in that if one is allowed to say that FPTP is not condorcet due to the tactical voting issue, then no voting system can be condorcet. Even if a specifies from 1 to 10 their order of preference of a candidate list with 10 people, then that voter still may be voting tactically. Therefore there can never be a strict logical criterion of condorcety, although it is of course possible to devise such a criterion is one introduces subjective areas of greyness in the definition.

Thoughts ?--jrleighton 04:23, 6 January 2006 (UTC)

I believe this article originally comes from's wording. This wording refers to sincere preferences (not voted preferences) in order to ensure that FPP and Approval fail. Usually, I think, it is better to not discuss sincere preferences, and simply try to analyze all methods as though they are rank ballot methods. For FPP this is easy. For other methods (for instance, a Condorcet method on a three-slot ballot) some more complicated reasoning has to be introduced. KVenzke 23:58, 7 January 2006 (UTC)
I have partially addressed this issue in the Plurality subsection of the article. See also the Approval subsection. —Preceding unsigned comment added by (talk) 14:00, 16 May 2010 (UTC)

Majority alternative[edit]

In the article Majority alternative (see this version) the following text appeared:

the choice of the majority alternative is not one version of the rule of majority among others. Its special importance is revealed, when voters are allowed to build coalitions with binding voting strategies in order to get the best possible result for them. For this situation one can prove the following theorem:
In any kind of voting system, which gives equal weight to individual preferences, an existing majority alternative will win, if all voters act and cooperate rationally.
Because most of the studies in collective choice theory assume "sincere" voting and do not analyse an election as a cooperative game with sophisticated voting strategies, this important feature of the majority alternative could not be detected by them.
The theorem stated above can be easily proved.
If for instance it is not the majority alternative m but some other alternative x, which is chosen by the voting system, then those individuals preferring m to x could have established a winning majority coalition on the basis of m, what would have been better for each member of the coalition.
One consequence of great practical importance is, that it is not necessary to elaborate complicated voting systems in order to choose an existing majority alternative. One may even use simple plurality voting for that aim, if there are no constraints for information and cooperation.

This text was unsourced, except possibly for the works listed in "Further reading" (Black, D.: The Theory of Committees and Elections, Cambridge 1958; Farquarson, R.: Theory of Voting. Oxford 1969; and Sen, A.K.: Collective Choice and Social Welfare. San Francisco 1970.) and it is unclear to what extent in may be Original Research. It is also unclear to what extent voters in real-world elections have the tools to form broad coalitions and engage in the kind of negotiations implied above -- it is clear that agreements to participate in a coalition are generally not enforceable, and are, in at least some jurisdictions, illegal.

If it can be attributed to a reliable source this text should be incorporated (in some form) into this article. Anyone knowing of such a source is requested to provide it here. DES (talk) 21:01, 22 June 2007 (UTC)

Perhaps, this is a reliable source: Wesche, E.: Die "unsichtbare Hand" in der Demokratie. Zur normativen Rechtfertigung von Abstimmungsverfahren. (The "invisible hand" in Democracy. About the normative justification of voting systems) in: Göhler, G. (Hg.): Politische Theorie. Klett-Cotta Verlag Stuttgart 1978.

I don't know of any other source for the respective theorem nor was there any refutation.

In any case the given proof is simple. The theorem can be falsified by any counterexample. Eberhard Wesche 17:59, 25 June 2007 (UTC)

Some remarks about the existing article „Condorcet criterion“.

The synonym to “majority alternative” is “Condorcet winner” not “Condorcet criterion”. Therefore it is difficult to merge both articles.

The term “majority candidate” was already used by Duncan Black.

It is written: “The Condorcet criterion for a voting system is that it chooses the Condorcet winner when one exists.”

How does the voting system “choose” the outcome? This is not explained. I guess it is assumed that each voter votes strictly according to his preferences.

This assumption is rarely fulfilled. Nobody wants to waste his vote by voting for an alternative with no chance to be the winner.

In any case voting “sincerely” is not the only possible model of voting behaviour. This the reader should know whenever a "criterion" is introduced.

If one assumes full information and unrestricted agreements of how to vote, an existing Condorcet winner will be the outcome even with plurality voting, which does not fulfill the Condorcet criterion.Eberhard Wesche 18:57, 25 June 2007 (UTC)

Majority-rule element[edit]

The definition of "Condorcet criterion" should make it clear that a Condorcet winner obtains a majority of votes against every other candidate. Condorcet methods thus belong to the class of majority voting rules. For instance, the current definition does not exclude the notion that a Condorcet winner must obtain, say, unanimous agreement against every other candidate.--Jsorens 15:50, 28 September 2007 (UTC)

I don't strongly object to your latest wording but I objected to the previous wording, which made it sound like a Condorcet winner can only be found in a "majority-rule election." I must say I do not know what a "majority voting rule" is. Can you clarify?
That said, I still think the wording can be improved. It isn't really a "majority" that is essential to the definition, but the fact that the CW is preferred to another given candidate by more voters than prefer this other candidate. KVenzke 15:57, 28 September 2007 (UTC)
"...the fact that the CW is preferred to another given candidate by more voters than prefer this other candidate." But isn't that precisely what a majority is? A Condorcet winner obtains a majority of votes in every head-to-head contest with other candidates. The qualification, of course, is that if voters are allowed to submit indifference relations (ties), a Condorcet winner might not have an absolute majority of votes in every head-to-head contest. Perhaps the most accurate wording would then be "...Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred by more voters to each of those candidates than voters who prefer each other candidate to the Condorcet winner." However, that is a fairly awkward wording.--Jsorens 17:36, 28 September 2007 (UTC)
Or "...Condorcet winner of an election is the candidate who, when compared with any other candidate, is preferred to them by more voters than prefer the other candidate"? I guess it probably is important to get it right and clear, and less important to not sound awkward. KVenzke 17:51, 28 September 2007 (UTC)
Oh, that looks good. Slight suggested amendment: "...Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred to him or her by more voters than prefer the other candidate."--Jsorens 18:02, 28 September 2007 (UTC)

No criticisms?[edit]

Given the prominent place this page has in Template:Electoral systems, shouldn't this page have something on the criticisms (and strengths) of the Condorcet criterion? Peter Ballard (talk) 11:49, 27 December 2007 (UTC)

Well, I'm not sure there is any reliable source on such. However, we could open a controversies section. In such, it's enough, I'd claim, that there is notable *argument* on a point, and the arguments should be attributed. Notability is a bit tricky to define here. However, outside of the article itself, I could certainly write about a defect of the Condorcet criterion. It is similar to the defect in the majority criterion; that is, preference strength is not considered, any preference, no matter how small, can create a Condorcet winner. The example I give is the pizza election. Three friends, election methods aficionados, want to choose a pizza; for some reason they can only buy one variety. Is it Pepperoni, Mushroom, or Anchovy? Two of the friends have a very slight preference for Pepperoni, but Mushroom is almost as good, they really don't care much. Turns out that everyone dislikes Anchovy. But one has a religious problem with the pork in pepperoni. What is the best election outcome, and what election methods will reveal it? Any majority criterion or Condorcet criterion satisfying method must choose Pepperoni. Range voting with sincere votes will choose Mushroom, as will Approval voting likewise. The debate over these methods is pretty silly except in contentious environments, where it is expected that there may be significant strategic voting. For example, the Pepperoni voters could decide not to vote for Mushroom. But, in fact, this contradicts the assumption that they really don't care much. Essentially, what is controversial is the behavior of methods that consider preference strength under conditions of strategic voting. Not with sincere votes. However, this is Original Research, probably. There may be something published about Approval on this point; Range is pretty new in the field of election methods.

I've found this in a number of areas in the field of voting systems: there may be a method which has been around, even for centuries, and yet nobody studies it and the election criteria are designed as if the method does not exist. Approval was used for five hundred years in Venice to choose the Doge, it was used for quite a few centuries to choose Popes. A great deal is written about the supposed inherent contradictions in representative democracy as if the institution of the proxy did not exist, and so on.

The Condorcet Criterion satisfies a very important intuition, and the problem with it is only related to single-ballot election methods where there is insufficient mutual knowledge. With fully-informed voters, there is no problem with the Pizza election, for the majority will, assuming it cares about the society of friends, change its opinion and the vote will be unanimous. Plurality works fine! Indeed, democratic process is founded on binary votes, Yes/No, majority necessary for a decision to be made. Standard democratic process used for election by ordinary motion is Condorcet-compliant, in the hands of informed members. It is, in fact, obvious. But can we find any reliable source for that? I'd be fascinated to know, for this fact is my own original research, I read it nowhere. We can, if we want, *create* reliable source, it's not difficult if anyone cares (and if the thesis is accepted by the process, that is, it does pass peer review. Consider Usenet, Mr. Ballard, or a mailing list of election methods people, add only a membership and voting process, plus a "publisher" who uses that for the editorial process. Google the "Election Methods Interest Group" for one possible path that could lead to this. --Abd (talk) 02:44, 31 December 2007 (UTC)

Note my comment "Given the prominent place this page has in Template:Electoral systems". The way that template is organised, it gives the impression that the Condorcet criterion is the most important of all criteria of election systems. So this article needs to be enhanced to demonstrate its importance - i.e. Reliable Sources asserting its importance, as well as Reliable Sources against it. If that can't be done, then the Condorcet criterion isn't very important, so Condorcet criterion must be removed from pride of place in Template:Electoral systems. Peter Ballard (talk) 06:47, 31 December 2007 (UTC)
Good points - SHould discussion better be in template's talk page? Template talk:Electoral systems, or request duplicated there at least. Tom Ruen (talk) 07:13, 31 December 2007 (UTC)
I've just been reading and re-reading Woodall. There are a couple of major criteria, the Majority criterion (which Woodall defines differently than many have claimed, Plurality voting fails, the Condorcet Criterion, the Monotonicity criterion..... definitely the Condorcet Criterion satisfies a deep intuition: the winner of an election should not be a candidate who, based on the cast ballots, would lose against another candidate. Indeed, in my opinion, this loss is only reasonable when a method (Approval, Range, Borda -- which does it rather badly) starts to consider preference strength, and it is, even then, a serious compromise with basic democratic principles, and the very reason given by some people when opposing such methods . --Abd (talk) 22:42, 31 December 2007 (UTC)
Notice that the Condorcet category is a sub-category within "single-member" elections, and within this constraint it qualifies as the most important criteria. The other issues brought up here, such as the fact that compromises are often desirable (such as friends choosing a pizza), involve situations for which single-member (single-choice) voting are not appropriate. Specifically such voting events are not independent of past and future events (where an informal form of vote-trading may be involved) or are not independent of other elections (such as electing members of parliament where PR issues are very relevant). For isolated ("single-member") voting situations, the fact that all voters prefer the winning choice over each other choice (in pairwise comparisons) is extremely important, and therefore qualifies as an appropriate category. Of course there are valid criticisms against choosing a single-member voting method in the many situations for which this choice is not appropriate. Yet when a single-member method is chosen, the Condorcet criteria is the most important criteria. VoteFair (talk) 17:54, 1 January 2008 (UTC)
Certainly I agree with the prominence of this criterion, and, with fully-informed voters, it is, in fact, the most significant of them; though voting, say, under Robert's Rules, would never accept the Condorcet criterion as sufficient, the Majority criterion must, under those conditions, be satisfied or no election is accepted. However, given that a plurality winner must be accepted, the Condorcet criterion is golden. Why "with fully-informed voters?" Fully-informed voters will modify their preferences according to their perception of what is needed for overall satisfaction -- or, alternatively, to vote to maximize their own personal preference. However, again, given the lack of such knowledge, methods which can consider preference strength can effectively give weight, in applying the Condorcet criterion, to strength of preference, and it would be through arguments like this that it can be argued that Range voting satisfies the criterion, though most would, at least at present, disagree. The pizza election is a single-winner election, so it's not so easily dismissed. In fact, small numbers of people will discuss the outcome and generally will seek to maximize consent (Approval or Range voting being the single-ballot equivalent, but clearly inferior to full discussion). When push comes to shove, though, and if there is clear understanding of the situation by the electorate, Range likely reduces to Approval and Approval reduces to Plurality, and, indeed, Plurality reduces to a Yes/No question on a motion to elect (or amendments to the same), avoiding all the election paradoxes except the most stubborn of Condorcet cycles, and those are known to be themselves paradoxical when analyzed according to issue space position. I.e., not likely in real life. --Abd (talk) 20:50, 1 January 2008 (UTC)
If the Condorcet criterion is the most important criterion, WP:Reliable Sources should be added to the article to prove it. Currently the article is very a poor one for such a prominent position in Template talk:Electoral systems. Peter Ballard (talk) 02:08, 2 January 2008 (UTC)

(unindent) Sure. However, I've got other fish to fry. I made one change, but it's an example that anyone can verify, so it does not require sourcing. Nevertheless, if Mr. Ballard thinks any information in the article requires sourcing, he's welcome to add a citation needed tag, and anyone, including him, could do the research. The article currently, with an exception that I removed, consists, as far as I noticed, of well-known facts. What is needs most of all is not sources, but analysis of the significance of the criterion, which *will* require sources, to be sure. They certainly exist, it is merely work to find them, then edit the article to show the analysis, and cite the sources. Be our guest, Mr. Ballard. --Abd (talk) 04:17, 2 January 2008 (UTC)

Llull winner[edit]

Given that Llull winner redirects here, I'm assuming that a Llull winner is a candidate who wins according to the Condorcet criterion, but can someone confirm this for me, and if so, mention this in the article? Thanks. Jason A. Recliner (talk) 14:01, 14 August 2008 (UTC)

It goes to Condorcet method which explains it. RJFJR (talk) 15:27, 30 July 2011 (UTC)

Help request[edit]

Pictogram resolved.svg
This help request has been answered. If you need more help, please place a new {{help me}} request on this page followed by your questions, or contact the responding user(s) directly on their user talk page.

Should Condorcet criteria apply to three or more candidates? The article says two-candidate. If there are only two condidate, why bother with Condorcet? aai'm not trying to start a new topic. Only get a clarification of the original. If I try to preview, I get timed out. I have a vandalism charge showing on one attempt. DickBoyd 2/21/12

  • The bot flagged your edit as vandalism, because you essentially deleted the entire article and replaced it with a question. There are several issues with this article. Primarily, it lacks significant reliable sources. Entire sections are unsupported with citations. Rather than asking the community which criteria apply to the method, I would recommend doing some research on the subject to verify accuracy of any assumptions. Unfortunately, your question cannot be answered by the community providing opinions outside of reliable sourcing, since this would be recognized as original research. All articles require verifiability. If you have questions, please feel free to contact me. Best regards, Cind.amuse (Cindy) 11:36, 22 February 2012 (UTC)

Condorcet vs Arrow and other criteria[edit]

I think it is unfortunate that the Condorcet method is conflated with its various circular tiebreakers.

In other words, think of elections where there actually are Condorcet Winners. I believe that these elections are not in violation of IIAC or Arrow's Impossibility Theorem.

From what I remember of my studies, only the elections with no Condorcet Winners, and which seek to award a winner anyway, are the ones that fall afoul of these criteria. I am less sure about the other three mentioned criteria, but the same might be true in those cases as well.

The problem is that the only Condorcet methods that are discussed in these wikipedia pages are the ones that seek to award a winner even when there is no Condorcet Winner. If you think of every Condorcet method as a section of logic that finds a Smith set (I believe all are Smith-efficient), and then a "tiebreaker" section of logic that awards the winner from the Smith set, the distinction is not made that it is the tiebreaker methods that are problematic, and not the principle of finding a Condorcet winner. By definition, tiebreaker methods do not always find a Condorcet winner, because in those cases, the Condorcet winner does not exist.

I realize that the point of elections are to award a winner, but I think there is utility in pointing out that these criterion problems might only be relevant for the elections where there is no Condorcet Winner. — Preceding unsigned comment added by Tunesmith (talkcontribs) 05:07, 29 May 2012 (UTC)

Arrow's Theorem says that no voting system can satisfy all its four/five criteria at the same time. One of the criteria is the Universality (or unrestricted domain), that says, that there have to be a winner in every case. So, the "plain" Condorcet method, which elects the Condorcet winner, if there is one and does not elect anyone, otherwise, violates the universality criterion. Thus, "plain" Condorcet is affected by Arrow's theorem directly by definition. --Arno Nymus (talk) 11:11, 29 May 2012 (UTC)
Thanks and an excellent point. I believe that distinction is lost on many who read the wikipedia articles, though. Because it means that it is possible that for elections where one candidate would beat any other candidate head-to-head, the Condorcet method is "perfect". The Universality Criterion is silly when applied to elections where a population feels genuine ambivalence. I think there is room for making this point in the Condorcet-specific articles. In elections where a candidate beats all others head-to-head, the Condorcet method may not run afoul of Arrow's theorem, while other methods do. — Preceding unsigned comment added by Tunesmith (talkcontribs) 07:42, 13 June 2012 (UTC)
Not having any result for a relatively big number of possible outcomes is definitely a drawback. The method can't be used for any election that needs a result in any case. I think, that would be a reason to say that the method is - at least - not "perfect". --Arno Nymus (talk) 16:35, 13 June 2012 (UTC)
Can you point to a source that indicates that contests without Condorcet Winners are common ("relatively big number")? If that could be identified, it would be a good way for me to flesh out that section of the article without necessarily changing the implications/conclusions. And just as a thought experiment, I suppose it is always possible to have a multi-round election (like the Louisiana runoff) where the second round is just for the candidates in the Smith/Schwartz set. At worst it would delay the non-ideal tiebreakers. Tunesmith (talk) 19:30, 18 November 2012 (UTC)

About the compatiblity with the consistency criterion[edit]


I tried to edit this article and correct the false statement arguing that the Condorcet criterion is not compatible with the consistency criterion, quoting the works from H.P. Young and A. Levenglick in their paper "A Consistent Extension of Condorcet's Election Principle" (1978). The corrections have been canceled, arguing the definition of the consistency criterion is different in their work than the usual admitted definition.

As to avoid an "editing war", I'm posting here to discuss the matter.

On Wikipedia, the consistency criterion is defined as follows : "A voting system is consistent if, when the electorate is divided arbitrarily into two (or more) parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative."

Quoting H.P. Young and A. Levenglick, the definition of the consistency criterion : "If two committees meeting separately arrive at the same consensus ordering, then meeting together this should still be their consensus".

Aside from the fact that H.P. Young and A. Levenglick only consider exactly two parts of the electorate in their definition, which has no impact on it as it is arguably trivial to prove it can be generalized, there is no difference in the definition of the consistency criterion. In the same paper, they also showed the Condorcet's criterion and the consistency criterion are compatible, as they even showed a unique method checks three properties, including these last two.

Maybe I'm wrong, but I'd like to know how, then. Thanks. (talk) 15:18, 17 March 2014 (UTC)

Blacklisted Links Found on the Main Page[edit]

Cyberbot II has detected that page contains external links that have either been globally or locally blacklisted. Links tend to be blacklisted because they have a history of being spammed, or are highly innappropriate for Wikipedia. This, however, doesn't necessarily mean it's spam, or not a good link. If the link is a good link, you may wish to request whitelisting by going to the request page for whitelisting. If you feel the link being caught by the blacklist is a false positive, or no longer needed on the blacklist, you may request the regex be removed or altered at the blacklist request page. If the link is blacklisted globally and you feel the above applies you may request to whitelist it using the before mentioned request page, or request its removal, or alteration, at the request page on meta. When requesting whitelisting, be sure to supply the link to be whitelisted and wrap the link in nowiki tags. The whitelisting process can take its time so once a request has been filled out, you may set the invisible parameter on the tag to true. Please be aware that the bot will replace removed tags, and will remove misplaced tags regularly.

Below is a list of links that were found on the main page:

    Triggered by \bhalshs\.archives-ouvertes\.fr on the global blacklist

If you would like me to provide more information on the talk page, contact User:Cyberpower678 and ask him to program me with more info.

From your friendly hard working bot.—cyberbot II NotifyOnline 15:24, 27 March 2014 (UTC)

Yes check.svg Resolved This issue has been resolved, and I have therefore removed the tag, if not already done. No further action is necessary.—cyberbot II NotifyOnline 07:15, 29 March 2014 (UTC)

Incoherent sentence in opening paragraph[edit]

I think this sentence is incoherent: "When voters identify candidates on a left-to-right axis and always prefer candidates closer to themselves, a Condorcet winner always exists." What does it mean to "prefer a candidate closer to [one]self"? Where is that defined? Is there an alternate expression of this idea that does not require the use of an undefined notion? — Preceding unsigned comment added by Wdowling (talkcontribs) 18:33, 4 August 2014 (UTC)

I think these two sentences are contradictory: "For a set of candidates, the Condorcet winner is always the same regardless of the voting system in question. A voting system satisfies the Condorcet criterion (English pronunciation: /kɒndɔːrˈseɪ/) if it always chooses the Condorcet winner when one exists." The latter sentence implies there are systems which do not satisfy the Condorcet criterion, while the first states there are no such systems. Philgoetz (talk) 22:43, 20 November 2016 (UTC)

Incoherent or incomplete sentence in the section on Range Voting.[edit]

In pluralistic head-to-head elections, you would get

Followed by nothing. — Preceding unsigned comment added by (talk) 09:34, 17 June 2016 (UTC)

Agreed. In fact, that is immediately followed by a second incompleteness:

"Range voting satisfies the Condorcet criterion as long as voters score candidates in the head-to-head elections as they do in the full election.[5] For example, let's say three voters vote for three candidates (A,B,C) as follows:

<missing details on how the voters vote>

The second candidate is the Condorcet winner ..."

I'd love to see this completed, because range voting strikes me as the perfect mechanism for maximizing the satisfaction of an electorate, and I am trying to understand the significance of the objections to it. — Preceding unsigned comment added by AmigoNico (talkcontribs) 02:48, 3 September 2016 (UTC)

AmigoNico (talk) 02:50, 3 September 2016 (UTC)

You're right that there's a problem with the page; here's an example of Range Voting's Condorcet failure. Suppose there's a two candidate election with candidates A and B, and voters rate candidates on a scale from 1 to 10. There are three voters and the ballots rate the candidates thusly: (A:6, B:1), (A:5, B: 2), (A:1, B:10). The total scores are A:12 and B:13, making B the winner even though a majority of voters strictly preferred A over B.

Range voting often looks very attractive in terms of the formal criteria it satisfies, but its ability to satisfy many of these criteria is complicated by various arguably unrealistic assumptions about voter behavior.

For example, range voting strongly incentivizes a form of tactical voting in which voters give a maximum possible rating to options they most prefer and the minimum possible ranking to other options. If this behavior is typical, then range voting degenerates into approval voting. SoapstoneTurtle (talk) 03:20, 3 September 2016 (UTC)

Relationship to IIA[edit]

The article states this: The Condorcet criterion implies the majority criterion; that is, any system that satisfies the former will satisfy the latter. Because of this, Arrow's impossibility theorem shows that any method which satisfies the Condorcet criterion will not satisfy independence of irrelevant alternatives.

In the first place, it's not at all obvious what the second statement about IIA has to do with the majority criterion.

In the second place (and this is the major point), I don't see how the Condorcet criterion conflicts with IIA. Arrow's Impossibility Theorem does not address the Condorcet criterion. In fact, IIA would seem to me to imply the Condorcet criterion rather than conflict with it, since starting with any two-candidate election in which the Condorcet winner trivially wins and then adding other candidates who cannot pairwise beat the winner should not change the winner under IIA. If I'm wrong about this, can some explanatory language or references be added to justify these assertions? SoapstoneTurtle (talk) 03:20, 3 September 2016 (UTC)

Well, as written the article is wrong because it ignores the possibility of a dictator. It also assumes unrestricted domain (which seems like a more reasonable assumption). I think it's clear what was meant though. Arrow's Impossibility Theorem does not address the Condorcet criterion but it does address the majority criterion, which is implied by the Condorcet criterion. Therefore Condorcet is incompatible with IIA (ignoring the other two "outs" of Arrow's Theorem). (talk) 06:08, 23 September 2016 (UTC)