Talk:Mutual majority criterion

This article was nominated for deletion. Please review the prior discussions if you are considering re-nomination:

Speedy keep, 19 October 2024, see discussion.
Procedural close, 19 October 2024, see discussion.

2005 Comment

I replaced MCA with Bucklin for two reasons. 1. MCA is a type of Bucklin. 2. Three-slot methods can't satisfy MMC as worded here. KVenzke 15:05, Jun 19, 2005 (UTC)

References?

Has this criterion been used "in the literature", and if so where? Who first used the term? CRGreathouse (talk | contribs) 06:37, 22 August 2006 (UTC)[reply]

I would guess Mike Ossipoff or someone he was in contact with coined the term. It was referenced by James Green-Armytage in an article in Voting Matters. Douglas Woodall uses "Majority" to refer to this criterion. I'm certain he used it (the criterion, not this name) in "Monotonicity of single-seat preferential election rules", Discrete Applied Mathematics 77 (1997), pp. 81–98. KVenzke 15:12, 10 May 2007 (UTC)[reply]

Am I right in thinking that this, like the majority criterion and the Condorcet criterion, is one of those criteria that can be worded in several ways (all of them equivalent for rank-order ballots), and whether Approval passes it depends on which wording you take?Jack Rudd (talk) 22:08, 23 May 2008 (UTC)[reply]

Proportionality for Solid Coalitions redirect

There was a single line that essentially mentioned that these two were mathematically the same in the single-winner case, but that does not justify deleting the entire article and redirecting to the Proportionality for Solid Coalitions article. The two criteria were developed independently for different purposes. The mutual majority criteria is for single-winner elections and the Proportionality for Solid Coalitions is for proportional representation. There are already quite a few articles on various single winner methods and their comparisons that rely on this mutual majority article, such as here for example https://en.wikipedia.org/wiki/Comparison_of_voting_rules#Comparison_of_single-winner_voting_methods, where mutual majority is one of the more prominent criteria listed for comparison. If this article is deleted and replaced with a redirect again, then any person coming to one of those articles on single-winner methods looking for more detail on what the mutual majority criteria is referring to would be sent to a page that talks entirely about proportional representation and be misled to believe that those single-winner systems are actually proportional, which is incorrect. 180 Degree Open Angedre (talk) 11:51, 19 October 2024 (UTC)[reply]

That's a fair point, thanks. What about merging into the page on solid coalitions? – Closed Limelike Curves (talk) 18:19, 19 October 2024 (UTC)[reply]

They're not quite the same thing, though? Perhaps a mutual majority could be considered a subtype of a solid coalition where the coalition encompasses a majority of the electorate, but there are other solid coalitions where that is not the case. Solid coalitions are also not really a type of criteria, a method does not really "pass" or "fail" solid coalitions in the same way that they would either mutual majority or proportionality of solid coalitions. 180 Degree Open Angedre (talk) 18:35, 19 October 2024 (UTC)[reply]

Right, so in this case, we would make it its own subsection on the solid coalitions page, and discuss it as "Majority for solid coalitions". – Closed Limelike Curves (talk) 19:34, 19 October 2024 (UTC)[reply]

Is it referred to as "majority for solid coalitions" in any academic publication, or is that just a term that you made up? 180 Degree Open Angedre (talk) 19:35, 19 October 2024 (UTC)[reply]

The term has been on this page for about 20 years at this point, so if it's not an acceptable term that's news to me. – Closed Limelike Curves (talk) 02:58, 20 October 2024 (UTC)[reply]

Just try to see if you can find a reliable source that uses the term. I'm not necessarily opposed to it being renamed to that, I just don't want it to lead to another situation where someone is unable to find the name being used anywhere and decides to delete the whole article as a result. 180 Degree Open Angedre (talk) 11:32, 20 October 2024 (UTC)[reply]

Oh, I'm not proposing a rename—I think the current name is fine. When I suggested "Majority for solid coalitions", this was under the assumption that this page would be merged into the page solid coalition, in which case I think MSC is a clearer name, since it makes the connection to solid coalitions more explicit. (Though, maybe it's still be a good idea, because MSC is quite short at the moment?) – Closed Limelike Curves (talk) 19:09, 20 October 2024 (UTC)[reply]

Misunderstanding about clone independence at Wikipedia:Articles for deletion/Mutual majority criterion

Mutual majority doesn't imply Clone independence and majority: Bucklin voting passes mutual majority but fails clone independence.

The other direction is closer to being true, but it isn't true either: we can't say that a mutual majority set is a clone set, as the minority may rank them in any order. The members of a clone set need to be ranked consecutively by every voter, not just a majority. Wotwotwoot (talk) 13:25, 19 October 2024 (UTC)[reply]

Clone-independence page doesn't seem to say anything about this. I was thinking of the other implication, i.e. clone independence + MFC ⇒ MSC, but looks like I was wrong. Maybe we can merge it with the page on solid coalitions, keeping most of the material on this page?

OTOH, is there any way we could consolidate some of this information? My thoughts were something like "MSC/clone independence are both axioms ruling out the traditional vote-splitting effect in FPP, so we can just combine them into one article". It feels like we have some "duplicate" information between the two criteria, since a solid coalition is a set of voters treating a group of candidates like clones. – Closed Limelike Curves (talk) 18:16, 19 October 2024 (UTC)[reply]

Let's say you create a "clone-independent Plurality" by attaching a stage that looks for clone sets and then replaces them with a single candidate. This method fails mutual majority because, if the minority ranks the candidates in some arbitrary order, the mutual majority set is no longer a clone set. The concepts are related since the mutual majority set looks like a clone set within the solid coalition. But from another perspective it's tautological because that's how solid coalitions are defined: you'll always have some solid coalitions whose voters treat some candidates like clones.

So the relationship is more complex than it appears. If we have any sources that deal with the connection between the two, then we could refer to them and explain what they're saying. But trying to synthesize something this complex risks WP:OR, IMHO. Wotwotwoot (talk) 20:11, 19 October 2024 (UTC)[reply]