Talk:Majority choice approval

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Majority Choice Approval doesn't satisfy the Participation criterion. Example:

51 A(favored),C(accepted),B(disapproved) 49 C(favored),B(accepted),A(disapproved)

Here, the MCA winner is candidate A.

However, when I add 3 B(favored),A(accepted),C(disapproved) voters then the MCA winner is candidate C. Markus Schulze

Couldn't that oddity be fixed by changing the 50% threshold of voters to a 50% threshold of people with voting rights? Well, getting 50% would be a very tough challenge then.217.227.3.166 18:53, 17 Dec 2004 (UTC)

I guess that would fix the participation criterion but in no way the consistency criterion. (Finally I get that there is a difference between those.) If winning by being 'accepted' instead of 'favored' has some side effects like less pay or a ban from running again that information would likely be revealed before the votes are counted. 84.144.91.50 20:43, 25 May 2005 (UTC)

Please do not merge the Majority Choice Approval article into either the Approval Voting or Range voting articles.

It is sufficiently different from both of those systems that it deserves its own article. With its 3 levels of choices and distinctive way of counting favored-vs-accepted candidates, the MCA system is qualitatively different from both Approval and Range voting. - Rich

Contents 1 Comments on Participation Criterion 2 VfD 3 What a Mess 4 Historical links 5 Revisions 6 Intro 7 Reply 8 Patriot Party 9 MMC 10 Reversal symmetry 11 Majority criterion

[edit] Comments on Participation Criterion

If we apply the "non-point" implementation of MCA to the example provided above, then MCA does not satisfy the Participation criterion. However if we apply the point system for counting MCA votes, then I think it does. Here is that same example:

Before:

Candidate	Favor	Accept	Dislike	Sum
A	51	-	49	102
B	-	49	51	49
C	49	51	-	149

Candidate C wins with the most points - and candidate A's chances are hurt by the high disapproval.

If we add in 3 more votes, we get:

Candidate	Favor	Accept	Dislike	Sum
A	51	3	49	105
B	3	49	51	55
C	49	51	3	149

Candidate C still wins even though the additional votes supported A and B over C. - Rich

[edit] VfD

On April 12, 2005, this article was nominated for deletion. The result was keep (no consensus). See Wikipedia:Votes for deletion/Majority Choice Approval for a record of the discussion. Mindspillage (spill yours?) 20:20, 25 Apr 2005 (UTC)

A second VFD (now AFD) debate, archived here also ended with a "keep" result. Sjakkalle (Check!) 07:16, 7 March 2006 (UTC)

[edit] What a Mess

The method devised by Forest Simmons and called "MCA" was called that because if one candidate has top-slot ratings on more than half the votes, that candidate wins. Where did this "point" version come from? Is every three-slot method a variant of MCA now?

The article says, unconditionally, "MCA does not satisfy the Majority criterion." If you're going to say MCA satisfies clone independence then I don't see how you can argue that Forest's method doesn't always elect a majority favorite.

The article also says MCA satisfies SDSC; neither version does or can. I'll fix that immediately in fact.

It seems to me that all the information on the "point" version needs to be removed, possibly relocated to an article devoted to the average rating voting method.

Kevin Venzke stepjak@yahoo.fr

Thanks for points those problems out. Because mca is a form of range voting, it does not satisfy the majority criterion, but does satisfy the consistency criterion. It also does satisfy independence of clones, as does range voting. --Fahrenheit451 23:47, 18 May 2005 (UTC)

Fahrenheit, MCA is not a form of range voting. Only the strange point version of it here is a form of range voting. References to it should be removed and I volunteer to do it myself. MCA does satisfy majority and fails consistency. It is a matter of debate whether limited slot methods (such as Approval and MCA) satisfy clone independence. --User:KVenzke

You just added the statement "MCA satisfies the Majority criterion, but some point methods do not." Now this is misleading. MCA only satisfies Majority when you do not use the erroneous point interpretation. "Pure" point methods never satisfy Majority. User:KVenzke

I am still cleaning things up, thanks. --Fahrenheit451 00:57, 19 May 2005 (UTC)

Thanks for those links. I strongly suggest you leave the point value stuff there if only to differentiate MCA from any point value attempted implementation. Anyone who may try that should be forewarned, it won't work the same.--Fahrenheit451 01:24, 19 May 2005 (UTC)

I don't think I have understood you. It seems to me that the article gives the impression (half the time) that MCA is a form of range voting when actually it's a form of Bucklin voting. It seems to me that the best solution is to move all of the point version interpretation to a separate section, pointing out that actually MCA is not that, and if the reader wants to know about the point version, they can just read the range voting article. What's your opinion on that? KVenzke 01:33, 19 May 2005 (UTC)

O.K. You are correct. Please let me remove the point value stuff and I will put a warning that mca is not a numerical voting method.--Fahrenheit451 14:27, 19 May 2005 (UTC)

[edit] Historical links

I added two links and corrected the year of MCA's first proposal. Hopefully this will make clear that MCA is not a blanket term for all three-slot methods. User:KVenzke

[edit] Revisions

I cleaned up the intro part. I think it's quite nice now. I removed two statements that I feel I should explain:

1. An altenative designation can be: 'Support', 'uncertain or indifferent', and 'oppose', where 'support' only signifies approval, reducing the possibility of insincere voting that can occur with some other voting methods.

Two comments here. First, under MCA it would be exceedingly unwise to assign the middle slot to a candidate about whom you were "uncertain or indifferent." Second, I don't know what is meant by "support," only, signifying approval. The resulting method seems undefined to me. I don't know what was meant by this "reducing the possibility of insincere voting."

As compared with Approval voting where one is only allowed to approve or disapprove. There are cases where uncertain is a real outcome, but not expressed in the voting method.--Fahrenheit451 22:04, 19 May 2005 (UTC)

I don't understand what your first sentence is a response to. Also, I don't understand what your second sentence means. KVenzke

2. This system elects a candidate who is favored by a majority, and rejects all candidates in case none gains majority approval (favored or accepted status).

Joe Weinstein suggested that Demorep's idea (to elect no one) could be copied into MCA, but as far as I know this idea is only really liked by Demorep (who probably hasn't even heard of MCA).

KVenzke 21:16, May 19, 2005 (UTC)

That is the notion of none of the above - NOTA, which has been around for a couple decades.--Fahrenheit451 22:04, 19 May 2005 (UTC)

I was attempting to explain why someone might have believed that NOTA is an inherent part of MCA. One could get that impression by reading Joe Weinstein's message. KVenzke

[edit] Intro

Fahrenheit, I am critical of the change from

Thus MCA is a variant of Bucklin voting, different in that the voter may only rank two places, but may vote any number of candidates in those places. MCA can also be considered a three-slot version of median rating.

to

Thus, MCA is a variant of Bucklin voting, different in that the voter may only rate two places, but may vote any number of candidates in those places.

A variant of MCA could include the third Disapproval slot as significant if a voter choses this for all choices for a seat or referendum item. In this case the ballot entry is viewed as None of the Above or NOTA.

1. You changed "rank" to "rate" in the first sentence. The point was to explain in what way MCA differs from Bucklin, and in Bucklin one does rank. But this is a small point.

To be exact, MCA classifies. It certainly does Not rank, which means to compare all choices pairwise or in sequence. Rate means assign a score to, but this is not quite accurate in MCA.--Fahrenheit451 20:45, 22 May 2005 (UTC)

I don't object to how you have changed it. But it still seems that you don't understand my point: I was not trying to say that one "ranks" in MCA. I was trying to explain how one would alter Bucklin to arrive at MCA. KVenzke 02:23, May 23, 2005 (UTC)

1. I don't understand why you removed the reference to "median rating." Do you think I should not try to link to an article that doesn't exist yet? Even if I don't, it is fairly obvious what "median rating" means (try searching for the term), and MCA is one version of it. That is factual and useful information.

I was a math major in college and have no idea what "median rating" means. Wikipedia should not force a reader to do a websearch. If you want to use the term, then write the article.--Fahrenheit451 20:45, 22 May 2005 (UTC)

Actually, median rating is a esoteric, never-used voting method and a comparison to MCA would be quite useless. Perhaps would confuse the reader like a badly written text on abstract algebra. Please keep it out of this article.--Fahrenheit451 20:54, 22 May 2005 (UTC)

I think you must have tried too hard to understand what I wrote. You have no idea what "median rating" is? You obviously know what "rating" means, so it would have to be median that you didn't get.

Considering that MCA is median rating, insofar as MCA never elects a candidate who does not have the highest median rating, this is arguably information that belongs in the first paragraph. KVenzke 02:23, May 23, 2005 (UTC)

1. Your NOTA note does not even describe what I removed from the article, and was referring to above. In fact, all it says is that "if a voter disapproves all the options then you could view this as NOTA." This statement is trivial. If you want me to restore what I deleted then I will do that.

You edit on that is o.k.--Fahrenheit451 20:45, 22 May 2005 (UTC)

KVenzke 18:04, May 22, 2005 (UTC)

I clarified the language I had used, put back the "nobody wins" option, and also had a stab at the new "drawback" you added. You wrote:

MCA also shares a vulnerability with Approval voting: In highly contested elections, a super-majority of partisan voters could only vote for their Favored candidate and not choose any Accepted candidates. In such a case, MCA would tend to revert to Plurality voting. [...]

This is more specific than necessary; actually, if a super-majority gets their favorite candidate then we shouldn't be too upset. The problem is if the winner's supporters are not a majority, and only win because other voters don't feel safe in adding compromises to their ballot.

No it is Not. You had better give some sort of example when such a thing can occur so the reader has a realistic understanding of the importance of this characteristic. This is not an abstract algebra text.--Fahrenheit451 20:50, 22 May 2005 (UTC)

What is "No it is Not" a response to? Are you saying that the problem of voters not wanting to approve additional candidates is only a problem in "contentious elections" in which voters insist on only voting for their favorite? The text I added made clear that the problem is more general than that. You could get Plurality-style results just from voter miscalculations. KVenzke 02:23, May 23, 2005 (UTC)

A response to your stating that my edit is more specific than necessary. I rewording that in the general sense but citing an example.--Fahrenheit451 14:41, 23 May 2005 (UTC)

I stated "super-majority of voters" in the context of partisans in that super-majority all voting exclusively for their favorites. We should be concerned about that behavior because then it devolves into Plurality voting. Then we do Not have majorities. --Fahrenheit451 20:45, 22 May 2005 (UTC)

My question (also on the Approval talk page) is why you use the term "super-majority." Typically "super-majority" is attached to a specific percentage, like 2/3rds. What's wrong with "majority" or "most"?

Because majority is not accurate, which could mean 51%. Super-majority is at least two-thirds. mca and av outcomes resemble plurality outcomes when there are single votes in a super-majority, not 51%.--Fahrenheit451 14:41, 23 May 2005 (UTC)

Also, the problem as you've stated it is a problem under any other election method as well, as long as it allows truncation. If everybody bullet-votes under Condorcet because everybody is "partisan," then we will get a Plurality result. But the problem is that Approval could return Plurality results even when nobody is especially "partisan." They just have to worry (with good justification) that approving compromises may keep their favorite candidate from winning.

You are correct about AV and Condorcet, but it is a drawback that should be identified.--Fahrenheit451 14:41, 23 May 2005 (UTC)

By analogy, the current text is a bit like "Rotten fish has a drawback in that it may taste bad when eaten with bad milk." When actually you don't need the bad milk for this problem.

You added the following paragraph:

MCA can get a potentially divisive candidate elected: As in the first part of the example below, 51% of voters favored A, while 49% disapproved of A, yet A wins, even though 49% favored C and 51% accepted C. A has a 51% approval rate, while C has a 100% approval rate. If candidate A did not compromise on polarizing issues once installed in office, considerable conflict could ensue.

This is very misleading; do you think other methods do not have this problem? This is not an article about majoritarianism. KVenzke 02:23, May 23, 2005 (UTC)

O.K. I will remove the last sentence, but the first should be taken into consideration by anyone who wants to use this method, and yes, there are other methods that have this same drawback; irv and plurality come to mind.--Fahrenheit451 14:41, 23 May 2005 (UTC)

Please comment on my changes. KVenzke 18:53, May 22, 2005 (UTC)

It looks to me that mca complies with the strong defensive strategy criterion. I recall that you stated it did not. Please show me why.--Fahrenheit451 01:14, 23 May 2005 (UTC)

SDSC says: If a majority prefers one particular candidate to another, then they should have a way of voting that will ensure that the other cannot win, without any member of that majority reversing a preference for one candidate over another or falsely voting two candidates equal.

When you have only three slots, then sometimes you will have to falsely vote two candidates equal. This is the entire difference between SDSC and WDSC. This is noted at Weak defensive strategy criterion. KVenzke 02:23, May 23, 2005 (UTC)

Thanks, now I understand.--Fahrenheit451 14:41, 23 May 2005 (UTC)

[edit] Reply

Fahrenheit, you wrote:
Because majority is not accurate, which could mean 51%. Super-majority is at least two-thirds. mca and av outcomes resemble plurality outcomes when there are single votes in a super-majority, not 51%.

Please explain this claim. Are you assuming there are just three candidates?

Who says "super-majority is at least two-thirds"? Three-fifths is less than two-thirds.

I changed super to large.--Fahrenheit451 16:41, 23 May 2005 (UTC)

This is what I mean when I say the scenario is too specific: Suppose 49% back A and nobody else. Suppose 51% are split roughly evenly into B>C>A and C>B>A camps. Under Approval voting especially, it is very likely that A will win this election, due to the BC voters not wanting to vote their favorite equal to their second choice.

This is a general problem of Approval and doesn't require a particularly "contentious" election. KVenzke 15:39, May 23, 2005 (UTC)

O.K. I will remove the contentious clause.--Fahrenheit451 16:41, 23 May 2005 (UTC)

I wrote:

This is very misleading; do you think other methods do not have this problem? This is not an article about majoritarianism. KVenzke

You responded:

O.K. I will remove the last sentence, but the first should be taken into consideration by anyone who wants to use this method, and yes, there are other methods that have this same drawback; irv and plurality come to mind.--Fahrenheit451

It should be taken into consideration (as should the possibility that it's preferable to have officials appointed rather than elected), but not here: This "drawback" is experienced by every method that satisfies the Majority criterion. It should go there, or under voting system.

By analogy, you wouldn't expect the sentence "A drawback of this car is that runs on gas and pollutes the air" under Ford Focus. KVenzke 15:39, May 23, 2005 (UTC)

[edit] Patriot Party

Can you provide a link showing that MCA is one of the voting methods used and advocated by the Florida affiliate of the American Patriot Party? That is interesting information. KVenzke 23:45, May 23, 2005 (UTC)

Markus Schulze provided one link, but there is another for the by-laws: http://www.patriotparty.us/state/fl/bylaws.htm Look under article vii meetings.--Fahrenheit451 16:04, 24 May 2005 (UTC)

[edit] MMC

Note that MCA doesn't satisfy MMC. Imagine that there are 10 candidates, for instance. KVenzke 22:33, Jun 19, 2005 (UTC)

Acccording to the MMC article, Bucklin methods do satisfy MMC and MCA is a Bucklin method. Can you prove that it does not satisfy MMC? If not, I am reverting your change in 24 hours. --Fahrenheit451 29 June 2005 01:07 (UTC)

MCA doesn't allow strict ranking, so even when votes are sincere, the wrong candidate can be elected. Suppose the majority are solidly committed to the set {a,b,c} in some order, using the top two slots to vote for them, and suppose the following choice of everyone in this majority is candidate D, whom they also place in the second slot. Suppose all of the other votes place D in the top position and vote for no one else. Then although the majority has voted sincerely, the winner is D, and not one of {a,b,c}. KVenzke June 29, 2005 15:29 (UTC)

O.K. then Bucklin does not satisfy MMC. That information should be corrected wherever extant.--Fahrenheit451 1 July 2005 00:29 (UTC)

Bucklin satisfies MMC when strict ranking of all candidates is permitted. I don't think Wikipedia says anywhere that "MCA is Bucklin." For one thing, Bucklin doesn't allow equal-ranking. KVenzke July 1, 2005 14:14 (UTC)

[edit] Reversal symmetry

How about adding this to the article:

MCA also fails reversal symmetry, a criterion that states a candidate shouldn't win in both the result of an election and the result of a virtual election with inversed voting patterns. While this failure is pretty unintuitve, proponents of MCA argue that people with opposite preferences are unlikely to actually vote in reversely symmetric ways.

Proof of reversal symmetry failure by Markus Schulze

I guess I might prefer a different Median Rating method. --R.H. 06:27, 14 August 2005 (UTC)

Well, how important is reversal symmetry? Perhaps Woodall's QLTD method satisfies it. KVenzke 15:10, August 14, 2005 (UTC)

[edit] Majority criterion

If voters are free to mark multiple candidates as favored, then the majority criterion is not satisfied. Example:

• 2:A>B>C>D (Favored={AB},Accepted={C},Disapproved={D})
• 1:B>C>D>A (Favored={B},Accepted={C},Disapproved={DA})

Notice that voters are voting sincerely. -- Dissident (Talk) 20:16, 26 December 2005 (UTC)

That's just for the hidden-preferences version of the majority criterion. In the votes-only version, no candidate is the sole first choice of a majority, so nothing is required by the majority criterion.

But then, I guess the same reasoning applies to Approval, and we've declared Approval to fail Majority based on hidden preferences...

rspeer / ɹəədsɹ 21:50, 26 December 2005 (UTC)

Using that argument one could also claim that plurality voting satisfies the Condorcet criterion (unless voters are to submit a preference ranking). Anyway, the majority criterion speaks about sincere preferences before they are expressed, so I think that settles it. -- Dissident (Talk) 22:18, 26 December 2005 (UTC)