Talk:Majority criterion

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[edit] What is the opposite?

I can imagine an opposite criterion, that if a majority of voters prefer all other candidates to a given candidate, then the given candidate should not win. Which criterion is this (I'm sure it's in here somewhere!) ? This article should perhaps have a link to it?


[edit] "This criterion is not accepted by all voting theorists"

This is not a useful statement, as it applies to any criterion. If it were useful to be in an article, it should go on every criterion page, not just the criterion that is failed by User:Fahrenheit451's favorite voting method. RSpeer 14:59, Apr 25, 2005 (UTC)

User:Rspeer|RSpeer is back to false accusations and POV editing. It is a useful statement because it is true and I would agree that such statements should qualify voting method criteria. So we are not disagreeing on the truth of the statement, but rather if it is "useful" or not. --Fahrenheit451 15:04, 25 Apr 2005 (UTC)

You made such arguments on the Borda count page also. I respond that it is essential for information in Wikipedia to be useful, neutral, and true, and that truth is not a justification for including uninformative and misleading information.

From your point of view. I consider Not putting such a disclaimer in the definition to be uninformative and potentially misleading. --Fahrenheit451 21:44, 25 Apr 2005 (UTC)

It is highly suspect that the one criterion page you happened to include this statement on is the one failed by your favorite method, the Borda count.(Removed personal attack), while I am trying to put all well-known methods and criteria on equal footing. Can you guess what my favorite voting method is from my edits? RSpeer 18:58, Apr 25, 2005 (UTC)

I am begining to wonder if you are a suspicious person. I have been working to make all method articles accurate, relevant, and neutral. I don't know what "equal footing" means to you, but it is not Wikipedia criteria. From your antagonistic remarks, you favorite method is clearly not Borda count, plurality voting, or IRV. I would say the Schulze method is a, but not necessarily the, favorite of yours. Incidentally, Borda count is not my only favorite. --Fahrenheit451 21:44, 25 Apr 2005 (UTC)

The statement that you removed as a personal attack was not an attack on you, but on your contributions. For the same reason, I have not removed your allegation that my edits are POV.

Not bad on your guesses. Overall, I'd say my current favorite voting method is Approval, but I generally advocate using the right method for the right purpose. Schwartz Sequential Dropping (is that what you mean by Schulze?) is good for a crowd of geeks, like the Debian project, but too complicated in its statement for nearly any other purpose. And I think that Borda is pretty bad for elections, true, but actually pretty good for contests.

My other favorites are the Approval voting methods. These are easier for most folks to understand and deal with. e.i. There are some who are revolted at the thought of having to score all candidates on a ballot, even though they were nominated by their parties and should be given their due. CSSD is the same as the Schulze method. I think Borda works very well for elections with pre-screened candidates and honest voters. There aren't many political scenarios where those conditions are extant, so some variety of AV is the way to go. We certainly agree on the worst ones. --Fahrenheit451 22:25, 25 Apr 2005 (UTC)

I'm still not convinced that a statement that "This criterion is not accepted by all voting theorists" needs to go on every criterion page. What would it mean if a criterion were accepted by all voting theorists? That all voting theorists agreed that methods that failed that criterion were unworthy of being considered? I don't think a reader would be expecting there to be any such criterion.

I never was interested in going to war over that point.--Fahrenheit451 22:25, 25 Apr 2005 (UTC)

The Voting method page already states that no method can meet all the criteria. This statement should possibly be expanded, to explain that you (the implementor of a voting system) need to look at the criteria and decide which ones are important to the situation, when evaluating voting systems. But I am still against redundant text being placed on every criterion page, and especially against it only being placed on this page.

RSpeer 22:01, Apr 25, 2005 (UTC)

[edit] Bad English

" The criterion states that if a majority of voters strictly prefers a given candidate to every other candidate and votes sincerely, then that candidate should win."

This sentence, taken from the article, is nonsense: (i) it is not the strictness of voters that is relevant, but the strictness of the majority; and (ii) how is the sincerity of voters intentions to be measured ?

A better sentence would be:

"The criterion states that if a strict majority of voters prefers a given candidate to every other candidate, then that candidate should win."

Thoughts ?--jrleighton 04:09, 6 January 2006 (UTC)

Once again, this wording comes from the electionmethods.org wording, where most criteria are defined in terms of sincere preferences.
(i) The term "strictly prefer" is used in case that "prefer" could be taken to mean "likes no less than."
(ii) Sincerity doesn't have to be measured. You set up a scenario and declare, "this faction is voting sincerely." Criteria aren't passed or failed based on actual elections.
KVenzke 00:04, 8 January 2006 (UTC)

[edit] Redundancy?

What is the difference between Majority criterion and Condorcet criterion? Why are there separate articles for them?

The majority criterion only applies to first preferences: it says that an option should win if a majority has that option as their first choice. It is implied by Condorcet, because anyone who is the first choice of a majority necessarily beats every other candidate pairwise. rspeer / ɹəədsɹ 15:17, 21 April 2006 (UTC)
Thank you for clarification. I think that the wording of the article could be improved to emphasize the difference, but I feel I do not know the subject well enough to make the correction. When I read the article I thought that it meant pairwise comparisons.

[edit] Range Voting

I notice that the change 02:01, December 23, 2006 by 71.252.99.34 added that range voting does not satisfy Majority criterion. There is a current issue as to the factuality of this on the range voting page. Does anyone have a citation to back up this claim? Thanks. WilliamKF 23:48, 12 March 2007 (UTC)

There are alternate wordings and interpretations of the Criterion. It's actually a mess. Depending on the exact wording, Range might or might not satisfy the Criterion. We might ask, what is the *intention* of this criterion? It is often conflated with "majority rule," but that's an error. Election methods in general produce conflicts with "majority rule," if by the latter, we mean how the majority would decide given full deliberative process. For starters, the latter is *at least* Condorcet compliant. But because it also incorporates the collection of preference strength information, it can consider far more than any ballot could indicate. Range probably comes closest to collecting the necessary information, but "majority rule" would require that the result not only be indicated by the method, but explicitly ratified by the majority. Election methods, in general, attempt to short-circuit the process in the name of efficiency.

Under the simplest interpretation of the Majority Criterion, which is reflected in the current definition as I write this, Approval satisfies the Criterion and Range does not. This is because Range allows the expression of preference strength, whereas the Criterion only looks at raw preference, a tiny preference is considered the same as a gotta-get-it-or-die preference. If you consider preference strength, you *must* violate the Majority Criterion, unless you use a trick like adding a ratification vote, in which case the criterion is satisfied by the overall process. In the end, the majority decides, perhaps, that it actually prefers a different candidate, one more widely acceptable. Abd 19:17, 16 May 2007 (UTC)

[edit] Non-rank ballots

The previous wording of the criterion makes reference to "preferences" and "sincere voting" that are not valid elements of a voting criterion. Voting criterion should only refer to ballots and results. I added an alternate wording of the criterion (taken from one of the previously included external links, and referenced accordingly) that allows it to apply to non-rank methods. I also removed the example of Approval voting because it does not serve as a valid counter-example, given the corrected wording. I am reasonably sure that my changes are all factually correct, but am certainly open to being proven wrong here on the talk page. --Sapphic 19:47, 2 April 2007 (UTC)

[edit] Weaker than the Condorcet critereon?

Um, majority is STRONGER than Condercet, not weaker. If a majority of all voters prefer A to *each* of the other candidates, then in a one on one with any candidate, he will be preferred, and win in FPTP.

This page is backwards.

--Michael —The preceding unsigned comment was added by 161.253.23.172 (talk) 01:42, 3 May 2007 (UTC).

I don't understand what you're saying. Majority is weaker than Condorcet. The way these criteria are usually understood, every method that satisfies Condorcet also satisfies Majority. KVenzke 23:22, 20 May 2007 (UTC)

[edit] Standard Definition of Majority Criterion

Wikipedia should reflect the near universal consensus for the definition, as it would appear in a text book, and not be distorted with a special exemption for Approval/Range, which was probably inserted to fulfill the POV of its advocates. The old existing citation (to Antioch) is to THIS corrected definition (my edit today) without the addition. The citation left the false impression that the source accepted the Approval-exempting re-definition. It does not. The citation lists Approval as NOT complying. It does have a footnote that offers some variants of how the Majority Criterion MIGHT be applied to non-ranked methods, but does NOT include the addition that I removed today.

The old link leads to this definition

"Majority criterion (MC): If more than half of the voters rank candidate X over every other candidate, then the winner should be candidate X.


Some methods that pass MC: Smith/minimax, sequential dropping, ranked pairs, beatpath, river, cardinal pairwise, minimax, plurality [*], IRV, two round runoff

Some methods that fail MC: approval [*], ratings summation, Borda"

Tbouricius 15:28, 9 October 2007 (UTC)

Tbouricius did not read the complete reference. I'll give him some time to do so before I respond in detail. In summary, Mr. Green-Armytage, the author of the reference, expresses his awareness that the definition of Majority Criterion, designed for ranked methods, is of problematic application to Approval Voting, so he attempts to come up with a definition designed for Approval and Range. Of course, this is altering the criterion to fit the method, and a strong suspicion must arise that the Criterion is being designed to fit some conception of pass or fail. I've seen numerous attempts to reword the Criterion to address the problem I have raised. And I specifically discussed this with Mr. Green-Armytage.
Tbouricius did not understand, apparently, the new definition. It was not designed to make Approval and Range *pass*, it was designed to make them *fail*. This shows that he is seeing all this through his political advocacy eyes. Approval satisfies the Criterion as written, the simple one. And, if not, then I suggest that how it fails be made explicit. Warning: there is a trick in the explanations I have seen, a sleight-of-hand over the meanings of "rank." It must have one very specific meaning if it is to make any sense. What does it mean to "rank" a candidate "over all others." Can you do this on an Approval Ballot? Can you do it on a Plurality Ballot? Can you do this on an IRV ballot? The answer is yes in all cases, I'll affirm. And in all cases, such a candidate must win the election. What in the world is the "consensus of the experts" talking about? I say that if we want to know expert opinion on this, we need to ask the experts. So I will. The mechanisms are in place, now, to do this fairly easily. It may take some time, though. Abd 06:25, 10 October 2007 (UTC)
But Abd, the REASON I was suspicious of this non-standard addition to the ususal definition is that YOU referenced it as evidence that Approval Voting PASSED this criterion when you reversed my edit correcting this fact on the Approval article. Perhaps it was an accident, but when you undid my edit you not only restored the special case diefinition for cardinal systems, but also removed Approval Voting from the list of systems that fail it (although in this discussion you admit that it does. I will fix that, and let the non-standard definition stand with a caveat.
Tbouricius 14:55, 10 October 2007 (UTC)
I didn't want to quibble, but the non-standard definition addition only applies to Range, not to Approval, as Approval doesn't use ratings. The cited source offers a different variant as a possible definition for approval and range...""If more than half of the voters prefer candidate X over every other candidate, and votes are sincere, then the winner should be candidate X." I would not object to someone replacing the text in the article with this, but I basically think the whole add-on should be removed as a non-standard definition.
Tbouricius 15:07, 10 October 2007 (UTC)

(unindent)Well, if you want to quibble, you would be a *little* wrong.... Approval is a Range method with only two ratings, 0 and 1. However, I have taken out the suggested definition, because the Majority Criterion is broadly accepted and stated. Now, please take the trouble to describe how it is determined that Plurality satifies the criterion and Approval does not, not leaving out any steps. For example, saying that a voter "prefers" one candidate over another is useless if the voter does not actually mark a ballot accordingly. If you look at the Talk page above, you will see that the user who inserted the extended definition, User:Sapphos is not identifiable as a Range or Approval supporter... she was simply trying to be accurate, and she mentions specifically the problem that a voting method cannot mind-read the voter. So what does "rank" mean?

Is it a mental state or is it an action? Same with "prefer," as was used in some versions of the Majority Criterion, including one that was here earlier this year. To "prefer" can mean a mental condition or it can mean an action that selects. When applied to ranked methods, it clearly meant to mark the ballot to indicate preferences. Can the voter in Approval mark the ballot to indicate the preference involved in the Majority Criterion? There is one and only one way, which is to vote exclusively for that candidate. Otherwise the voter is not indicating an exclusive preference, rather the voter is indicating a *group preference*. So I have argued elsewhere, with some support and some opposition from election methods experts, that Approval (but not Range) satisfies the Majority Criterion. The "failure" of Range -- loaded language, that -- takes place because the voter, with Range, (i.e., add an extra rating or more to Approval) can express preference in a finer way, and this allows a minority candidate to win under certain circumstances -- which happen to be circumstances where it is arguable that the Majority Criterion is better being not satisfied.

What I've seen in arguments over this is that, in order to make Approval fail the Criterion, experts make the Criterion more and more complicated, tacking on clauses like, "Without impairing their ability to vote sincerely," and then when it is pointed out that there is no standard for "sincere voting" in Approval, i.e., all votes are sincere, practically by definition, if seen as indicating an approval cutoff, which can be set anywhere, they then must define "sincere vote" in a way which makes sense in Approval, and, in the end, it can all be seen as an attempt to avoid the basic problem: there is a subjective aspect to this criterion, *as conceived*. If we make it objective, taking it as stated, and interpreting "ranked" to mean something observable from the ballot, Approval passes, and a great deal of effort is wasted trying to make it otherwise.

Abd 04:50, 11 October 2007 (UTC)

It is very simple and standard to apply the majority criterion to a variety of voting methods regardless of whether they use ranked ballots.
There is a claim made by Approval (and Range voting) advocates that the system is exempt from Arrow's Impossibility Theorem, and manages to side-step such tests as the Majority Criterion, because it is not a ranked voting method. I do not believe this assertion is supportable. For now let me limit my point to the Majority Criterion under discussion.
The majority criterion sets out a hypothetical scenario of voter preferences and then tests different voting methods in that unique scenario. The scenario imagined is one in which voters DO have clear preferences, and in this particular election a majority of voters consider one particular candidate to be the absolute best choice. This scenario exists PRIOR to deciding which voting method is to be used. The Majority Criterion test is simply; Is a given voting method certain to elect this candidate? If these voters in this scenario vote using certain methods (FPTP plurality, Condorcet, IRV, etc.) that particular candidate is certain to win, and thus they meet the majority criterion. If these voters vote using Approval (or Range, or Borda, etc.), that candidate may or may not win. Thus by definition, Approval fails the majority criterion.
One can argue whether the majority criterion is a good or useful criterion, but there really is no debate among political scientists about whether Approval fails this particular test. The fact that a particular voting method does not allow voters to express details about their full set of preferences, does not mean that voting system cannot be tested for a specific scenario, and cannot exempt it from the criterion.
I am restoring the definition of majority criterion to its more standard form, without the carve-out exemption of voting systems using unranked ballots.
Tbouricius 14:16, 18 October 2007 (UTC)
You are absolutely correct that neither Approval or Range voting is exempt from Arrow's theorem. Approval is interesting in that it fails different parts of Arrow's criterion than Condorcet methods do, but that's another issue entirely.
As far as the 'ranked ballots' issue goes, that confusion is my fault- certainly something like Plurality voting passes the Majority criterion, even though it doesn't express complete preferences. Range Voting, on the other hand, can still fail the Majority Criterion even if no one expresses complete preferences on their ballot.
There are variations of approval voting that (clearly) pass the majority criterion, and my suspicion is that basic Approval Voting should not pass the criterion- After all, Approval voting is about voting in the most accepted candidate, not the most favored one. However, as several long debates on this page in others have demonstrated, whether Approval voting passes or fails depends heavily on the wording with which the majority criterion is defined. Even if approval voting is based on unexpressed preferences, and all voters vote sincerely, voters must also have incomplete information about each other's preferences in order for Approval voting to fail the Majority criterion. (If the majority favor a candidate and know it, they will always win in Approval voting). Paladinwannabe2 19:21, 22 October 2007 (UTC)

[edit] Discussion of Majority Criterion opening on EMIG-Wikipedia

Quite recently, the Election Methods Interest Group was organized, and it has so far attracted as members a few prominent election methods experts and at least one political scientist, and, knowing this community, I expect that we will see membership from many of the published writers and theorists in this field.

Membership in EMIG is open to all persons interested in the topic; however EMIG is developing a structure to address the noise problem in large-scale discussions. Cutting to the chase, EMIG can be thought of as a voluntary association of a series of individual "meetings." Each meeting is autonomous and self-defined. The goal is for all interested persons to register as members of EMIG at the top level (right now, that means subscribing to the EMIG mailing list), but that specific discussions are channeled to independent lists, virtual committees they might be called. EMIG has a delegable proxy mechanism in place, which allows, if used, all members to be represented in every discussion (ideally), without requiring personal and continual attention. So it is not time-expensive to belong to EMIG, you could join, look around, name a proxy you consider reasonably trustworthy, and then set your list membership to Special Notices. You would get hardly any traffic. Your proxy would let you know if something needs your personal attention.

So, if you are interested in editing articles on Election Methods, here on Wikipedia, other than simple grammatical and cleanup work, you may be interested in joining EMIG. There is a Wikipedia committee that has been formed, EMIG-Wikipedia, and a topic was opened there on the Majority Criterion, to attempt to settle, or at least explore in depth, differences of opinion that have appeared here. All are welcome to participate.

EMIG is not going to issue any controlling opinion, but if a Report is issued from the discussions of any EMIG committee, and if that report is accepted with the general agreement of a large body of election methods experts, reporting that consensus can be done by anyone, with clear implied authority, similar to a publication in a peer-reviewed journal.

Instead of having mere assertions about what "election experts believe," we can actually find out. Here are the links:

http://groups.yahoo.com/group/electionmethods/ is the top-level EMIG list and is where the proxy table is currently kept as well.

http://groups.yahoo.com/group/EMIG-Wikipedia is the Wikipedia committee.

Before posting to EMIG itself or a committee list, please consider reading the history of posts for EMIG as a whole and for the committee in question. —Preceding unsigned comment added by Abd (talk • contribs) 01:52, 13 October 2007 (UTC)

[edit] How does the majority criterion apply to non-ranked methods?

Tbouricius has edited the article back to use "prefer" instead of "rank," following arguments that discriminate between "prefer" and "rank." This is continuing a confusion of language that appears to go back to the original use of "majority criterion." It appears that the context was that of an expressed preference order allowed on the ballot, and it was assumed that the voter simply transferred an internal set of preferences to the ballot, "sincerely." There seems to be little difficulty defining "sincere" in this context, and any difficulties that remain seem, at least to me, to be irrelevant with respect to this criterion. It is enough, for this criterion, that if the voter has a preference for a single candidate over all others, that this candidate be ranked above all others, and on a complete preferential ballot, there is no difficulty doing this and the voting of the voter is not restricted.

The problem arises when a method does not allow complete ranking, and two examples of this would be Plurality and Approval. If we interpret the verbs "prefer" or "rank" to be literal actions, represented by marking a ballot, then Approval, we can readily see, passes the Majority Criterion.

If, however, we interpret those terms to refer to mental states devoid of action, but then translated into actual votes by some process called "sincere" in expanded definitions of the Criterion, it is arguable that Approval does not satisfy the Majority Criterion.

Bouricius maintained the citation in this article to the writing of James Armytage-Green, who clearly was, on the referenced page, struggling with the problem of defining "sincere voting," when it comes to Approval. He proposed a definition of "sincere" that, for him, resolved the question in favor of Approval failing. However, this was his own original research, as far as I can tell, (but it may be echoed elsewhere, or he may have gotten it elsewhere).

The question of how the Majority Criterion is defined is currently under discussion in the Election Methods Interest Group, but numerous questions remaining there have not been answered. No citations, for example, have yet been provided to primary sources for the exact wording of the Criterion. The question of how "sincere voting" is defined has not been addressed except by me.

These exact questions have previously been raised here, and the article came to be in a state where the interpretation that "prefer" refers to marks on the ballot was clearly the most accepted. Mr. Bouricius is a political scientist, we understand, and he often refers to an alleged consensus of "political scientists," but political scientists are not the only people who study and become expert regarding election methods. Further, the claim regarding a consensus of such has not been sourced. Is there any kind of review of the literature on this question, itself peer-reviewed, that addresses the problem? If there is, I'd love to see it!

I intend to add a section on the controversy over the Majority Criterion and its application to non-preferential methods. Otherwise this article is likely to oscillate, as new editors discover that the emperor has no clothes and act to fix the problem they perceive.

If the Majority Criterion is proposed as an objective method of comparing election methods, then it is crucial that every aspect of the Criterion be susceptible to objective application, or else we will have a subjective judgement being presented as if it were objective. Mr. James Armytage-Green, for example, does conclude that Approval Voting does fail the Criterion, but he has also acknowledged -- and it is plain from his cited page -- that he was looking for a way to define the Criterion so that Approval would fail, that being his intuition.

What he ended up with was pretty complex, and, in my opinion, failed to resolve the issue. His discussion is at the bottom of the cited page, [[1]] under the header: Note on criteria definitions for non-ranked methods. My comments are as follows:

I apply ranked ballot criteria to non-ranked methods as follows. 1. Change ranking-based wording to preference-based wording. For example, a criterion with the wording "a voter ranks A over B" is changed to "a voter prefers A to B". The wording "a voter ranks A equal to B" is changed to "a voter is indifferent between A and B".

Note that he clearly considers "rank" as different from "prefer." Both words, however, can refer to mental preferences or to actions, so simply changing the words is not enough. It must be explained.

2. Assume that votes are cast sincerely. In order to do this, I provide an operational definition of sincerity for plurality ballots and for approval ballots. 2a. Assume that a sincere vote on a plurality ballot entails voting for one's favorite candidate.

While that is reasonable, why is not the same assumption applied to all methods which allow that kind of expression? If we create separate versions of the Majority Criterion for each method we consider, we aren't applying an objective standard, for we can pick and choose between versions of the Criterion. My own opinion is that to resolve this issue, we are going to have to go back to roots. What is the most *useful* definition of the Majority Criterion? And it is not going to be easy to answer that question, I suspect. On the other hand, there *is* an approach which might succeed.

2b. Assume that an insincere vote on an approval ballot entails approving B but not approving A, if the voter prefers A to B, or is indifferent between A and B.

This is not a definition of "sincere," it is a definition of "insincere." Not all actions that are not insincere are therefore sincere. There is another definition of sincere vote: a vote that does not conceal a material preference. If the preference between A and B is "important," then, it could be argued, it is insincere to conceal it, and not concealing it, but revealing it, is sincere. A sincere vote must reveal what is material about the voter's preferences. I don't know how James came to think he had solved the problem with this assumption regarding an insincere vote.

Note: I am not entirely convinced by either of these definitions (in 2a or 2b), but they seem to serve our current purpose as well as anything else. Other applications are possible, and strictly speaking it's hard to argue that any single application is definitively correct. One approach is to ignore the possibility of unexpressed preferences and evaluate plurality and approval only with respect to expressed preferences. In that case, they pass just about anything you can think of, but this doesn't tell us very much, or capture the intent of the criteria themselves. Hence, I use the methods above for my tables.

Yet he never explicitly defined "sincere" vote! We know what is "insincere," and, indeed, there is no controversy over this. Would Armytage-Green want to put "not-insincere" in the definition? What if we do and we expand it?

If more than half of the voters prefer candidate X over every other candidate, and vote not insincerely, then the winner should be candidate X. "Not insincerely" means "not (reversing preference)".

It works for his intended effect, because a vote equating two candidates in the presence of some preference (even an infinitesimal one) is not a preference reversal and is therefore not insincere as he has defined it.

But is it "sincere?" Suppose there are only two candidates, and a voter has a preference between them, and votes to equate them (i.e., votes for both of them or votes against both of them). Is this a "sincere vote"?

Frankly, I don't think so. But why not? It is "not insincere," by the definition given by Armytage-Green. And not only does Approval fail by this "not-insincere" definition, so does Plurality.

To apply the majority criterion to non-ranked methods, it can be re-worded as follows: "If more than half of the voters prefer candidate X over every other candidate, and votes are sincere, then the winner should be candidate X."

Notice the sleight-of-hand. I know Mr. Armytage-Green, and I have utterly no suspicion of any dishonesty on his part (if he were dishonest, he would not have written so openly about his doubts), but somehow a definition of "insincere" was taken as adequate as a definition of "sincere."

The Majority Criterion is considered important because it seems intutitively related to the principle of majority rule. When Approval allegedly fails MC, it is because a majority has essentially voted Yes for two incompatible outcomes. There are two ways to resolve this, in democratic process, the presumption method and the deliberative method. The presumptive method assumes that, if more voters voted Yes for one option than the other, it is likely that a pairoff between the two would result in the election of the first option. It is an assumption which would usually be correct, and the presumptive option is law in several states that have referenda for multiple conflicting questions getting a majority. It saves a runoff. And the other option is to confirm the winner with further process, such as a runoff or even runoffs, as needed to gain a simple majority for one candidate over all remaining candidates. (There could be three candidates with a majority!). This would be what Robert's Rules prefers.

What seems clear to me is that Approval satisfies the *intention* of the Majority Criterion, even if it does not *technically* satisfy it under this difficult mental-preferences interpretation, so I'm not offended by the result of using only expressed preferences to analyze Criterion compliance. Yes, most actually-proposed election methods do satisfy the Majority Criterion, but not all, so it remains useful, within limits. For example, Range does not satisfy it, because Range allows expression of the necessary preferences, and it takes a more difficult definition of the Criterion to allow Range to pass. With Approval, it's the *simplest* interpretation.

Indeed, because raw Range Voting does not satisfy the Criterion, I would want to see a runoff triggered whenever ballot analysis in a Range election shows, as it would, that a winner was *not* the first preference of a majority, and, indeed, I'd make it stronger than that, I'd trigger it if there was any pairwise winner over the Range winner, making Range not only MC-compliant, but also Condorcet-compliant.

Basic question: what if many "political scientists" have written that Approval voting fails the criterion? Does this mean that we can ignore the Criterion itself and how it is applied, and simply rely upon, say, majority opinion among political scientists? If so, would we not need some measure or source for this? Is the statement of one political scientist, here, sufficient? Abd 18:15, 18 October 2007 (UTC)

I'm trying to research the issue, and my best answer so far seems to be that the Majority Criterion does not apply to Approval voting (That is, it does not pass or fail the method). My second best answer is that it fails the Majority Criterion. Any reasonable wording of the Majority Criterion that causes Approval voting to pass also causes Plurality voting to pass as well. Keep in mind that if Approval voting does not pass the Majority Criterion, that's not necessarily a bad thing- it just means that someone acceptable to everyone is better than a candidate favored by 51% of the population. Paladinwannabe2 21:35, 18 October 2007 (UTC)
The purpose of a Wikipedia article is to present scholarly consensus when it exists. When a small group of advocates dispute a schoplarly consensus, that MIGHT be worthy of mention, but the scholarly consensus should receive top billing and prominence. There is scholarly consensus about this issue. If someone can find a text book (not a Blog by an advocate) on election theory that says Approval is either not measurable against the Majority Criterion, or passes it, please let us know. I have NEVER found a legitimate source that disagrees with the statement that Approval fails the Majority Criterion. The only sourced link in the article on this states this as well.
Abd agrees that Range Voting fails the criterion. He also often states that Approval is merely a version of Range Voting (with limited scoring). This is further support for the general consensus among scholars that Approval (which Abd agrees is a subset of Range) does not pass.
Perhaps the problem is simply the name ... whcih implies majority rule. Maybe we just need to put that disclaimer in the introduction..."This criterion is one of many and does not mean a system assures or does not assure majority rule."
Plurality, which clearly can have non-majority winners and defeat majority rule, DOES pass the criterion, because the scenario presented in the test is so extreme. IF candidate A is preferred by an absolute majority of voters, and the voters express this preference to their best ability using the rules of the voting method in question (plurality), then A is certain to win. That makes it pass the Majority Criterion, as universally understood by election systems scholars. In the identical scenario (A preferred by a majority), but using Approval Voting, candidate A may win, or may not depending on how voters set their approval cutoffs for other possibly acceptable candidates. Since A is not CERTAIN to win, by definition Approval fails the criterion.
Tbouricius 20:33, 19 October 2007 (UTC)
The problem I've been running into that the majority of sources I can find don't list Approval at all under the majority criterion, either as passing or failing (though they mention it elsewhere). You've given us 1 source to support Approval voting failing MC, and while I can find none that say it succeeds, that's still not enough evidence. Range voting obviously fails the majority criterion. This does not imply that Approval fails. Paladinwannabe2 20:50, 19 October 2007 (UTC)
Voting criterion are useful only if we can apply them to ALL voting methods as a means of comparing. There is a simple, and rather standard definition for Majority Criterion that makes it meaningful and useful. "IF one candidate is preferred over all others by a majority of voters, does election method X assure the election of that candidate?" This definition obviously assumes voters express their sincere preference as best they can using the means available by method X. We don't need to debate what is a "sincere" vote with a situation of equal preference, because the test scenario sets out a situation where that is not the case. Unless one believes that the ONLY sincere vote under Approval voting was to vote exclusively for one's most preferred choice (and that is nonsense), then it fails the majority criterion, because the test situation is one in which voters have a range of preferences (and a nearly infinite number of possible cut-off points), but a majority distinctly prefer one particular candidate, and that candidate is not assured election.
It is obviously nonsense to debate whether the majority criterion should apply only to the marks on the ballot, rather than to the actual preferences of the voters. Imagine this hypothetical voting method...All ballots have one big box to mark that is so big that all candidate names fit against it. When the ballots are counted, any marks in the single box count towards the candidate who filed petitions for inclusion on the ballot first. So the marks become essentially meaningless. If we only consider the marks on the ballots, this candidate will win because he/she has a majority of non-blank ballots, without regard to the actual preferences of the voters. Arguing that this method passes the majority criterion (because we only look at the marks and the rules for counting them), or that the majority criterion does not "apply" to this method, defeats the entire purpose of having invented the criterion in the first place --- to compare voting methods. The criterion CAN be applied to this method. This foolish method would fail the criterion because the candidate ACTUALLY preferred by a majority of voters is not assured election.
Note that the "majority criterion" is not the only criterion dealing with majority issues (there is the mutual majority criterion, condorcet winner criterion and condorcet loser criterion, etc.)
As for additional references, they are uncommon because Approval Voting is a relatively recent name (recent re-invention in 1970s) while many others are centuries old. I know that The Mathematics of Voting and Elections: A Hands-On Approach by Jonathan Hodge and Richard Kilma deals with Approval Voting on pages 91-96. Rather than saying criterion do not apply (such as Arrow's five fairness criterion) they point out that Approval voting fails at least one of the five criterion (the universality criterion), and conclude that "Arrow's Theorem tells us that certain fairness criteria are incompatible with each other no matter what voting systems we consider." Unfortunately they do not discuss Approval specifically in terms of the majority criterion.
Tbouricius 19:05, 20 October 2007 (UTC)
One more point...If we all agree Range Voting fails the Majority Criterion, and that Approval is merely one specific subset of Range (with a score limited to 0 or 1), then why would we say the Criterion magically stops applying to this favored subset of a method that fails? The only reason is because someone wants Approval protected from getting a "bad rep." Approval advocates have pushed the myth that Arrow's Theorem does not apply to Approval for the same reason...miss-representing arrow's theorem as being limited to voting methods using ranked ballots (rather than to human communities with individuals with rankable preferences seeking to make a collective decision.)
Tbouricius 19:17, 20 October 2007 (UTC)

(unindent) I see that I did not respond to the last comments of Tbouricius; I will ignore the implied assertion of bad faith beyond mentioning it. The application of Arrow's theorem to "all methods" is controversial, and certainly Arrow did not make that claim. Rather, Arrow's theorem implies that any election method which satisfies a series of conditions cannot satisfy all of a certain series of criteria. Arrow's theorem is about the translation of a set of individual preferences, in rank order, to a single social preference order that satisfies the stated conditions. It's actually not about election methods, except that we may think of an election method as taking individual preferences and translating them into a *partial* social preference order, where we are only concerned about, say, a single winner. Arrow's theorem is proven, it is not controversial. If there is to be debate over the application of Arrow's theorem on Wikipedia, it should be in Talk for that article. The claim that Arrow's theorem does not apply to Approval is not at issue here, however, and Arrow's theorem is not an element in the arguments over whether or not Approval satisfies the Majority criterion. What I've been seeking -- and have not found, so far -- is a definition of the Majority criterion, reliably sourced, which can be objectively applied to all methods without making unstated assumptions. Thus, for example, notice that the article currently preserves the ambiguous wording of the criterion. Does "prefer" or "rank" refer to voter mental states or to an actual expression of preference or rank? If to the action, Plurality and Approval pass the Majority criterion. If to mental preference, then we must assume a certain correspondence between voter mental state and expressed vote, or *no* method passes the Majority criterion. (In particular, consider Plurality. A majority prefer one candidate, but are unaware that they are in the majority, and thinking that two other candidates are the frontrunners, prefer one of them and so vote. The majority preference fails to win. So it must be specified that the vote is "sincere." With ranked methods, that's easy. We require, for a vote to be sincere, that every rank be expressed, but, most notably, that the majority favorite be ranked ahead of all others, clearly that is a sincere vote, and any other vote is insincere, because it necessarily reverses rank. However, when ranks are truncated, and if equal ranking is allowed, it gets tricky.

This was all discussed above. Armytage-Green, as cited above, clearly is attempting to create a special definition of sincere vote that will cause Approval to fail, for he is aware that the standard definition causes it to pass! What he ends up with is a definition of an insincere vote: preference reversal, same as with ranked methods, and then he *assumes* that a vote that is not insincere is "sincere," and thus he can claim that Approval fails the criterion. Approval, however, does not ask the voters to vote for candidates, per se, but for a candidate *class*. Most voters will probably place only one candidate in that class, but they have the option of putting more in it. It is this additional freedom, not required by the method, which allows them to *conceal* their first preferencer. That concealment is not a sincere expression of the preference involved. But neither is it an insincere vote. (Oddly, critics of Approval will claim a tactical voting "vulnerability" for Approval, which requires defining a vote for more than one candidate as "insincere," or, alternatively, bullet voting in the presence of an asserted "sincere" approval -- which makes no sense as tactical voting, since the vote is for the preferred candidate of the two, i.e., is clearly sincere -- so critics, in that argument, claim that multiple approvals are "insincere." Yet, when the same critics assert Majority criterion failure, they are effectively calling the multiple approvals "sincere." Approval can't win for losing.)

In the ordinary meaning, Approval *always* rewards sincere voting; that is, the voter strategically has an incentive to vote for a set of candidates, each of which is preferred to every candidate in the not-preferred set. The *set* is sincerely and individually preferred to every non-member. Thus Approval is not vulnerable to tactical voting, period. However, that does not mean that there is no strategy, for there is no automatic boundary between the approved and non-approved sets. Strategy enters into the setting of that boundary; voters are advised, generally, to include in the Approved set, at least one frontrunner, and likewise, at least one frontrunner in the not-Approved set.

My *personal* opinion, though, is quite in line with Armytage-Green: Approval fails the Majority Criterion. (And, by the way, should be proud of it. The criterion is defective due to its total neglect of preference strength. And the problem with democratic principles only arises in very limited situations, of vanishingly rare negative consequence, and is avoided completely if there is a runoff whenever no candidate gains a clear and exclusive majority, quite in line with existing practice in many places. And this method -- Approval plus runoff -- *does* satisfy the Majority criterion.)

However, that opinion does not automatically give me a definition of the criterion. I did come up with one, I've proposed it, and nobody has written accepting it, as far as I recall, though formal process for peer-review hasn't begun. Essentially, it is the "not insincere" approach which merely formalizes what Armytage-Green found, with "insincere" meaning expressed preference reversal. In order to put this in the article, properly, it should be subjected to peer review and, if found acceptable, "published." That publication would not establish exclusive authority, but, given that the known reliable sources don't really address the situation, it might be effectively conclusive. --Abd (talk) 18:34, 27 December 2007 (UTC)