Category talk:Condorcet-reducible PR methods

I don't agree with this move, and I'd like to discuss it. I think it's fairly obvious any "____ PR" method must reduce to "___" method in the single-winner case. On top of that, I think Schulze's Condorcet criterion for the multiwinner case shouldn't have that name, since technically in the single-winner case Score passes it (the Score winner has more points than any other candidate in pairwise matchups) yet is not a Condorcet method. And I'm sure Schulze wouldn't consider cardinal PR methods to be Condorcet PR methods, despite many of them likely passing his criterion. It seems for the sake of avoiding confusion it's actually Schulze's criterion that ought to be renamed. Edit: My idea for resolving this is to make "Condorcet-reducible PR methods" a subcategory of the larger "Condorcet PR methods" category. We can use the "Condorcet PR methods" category to hold all the different subcategories ie. methods which pass Schulze's M+1 criterion, etc. Edit 2: Here is something that ought to totally disqualify Schulze's criterion from being considered a serious "Condorcet PR" criterion: Bloc Score voting passes it. If I take the top M scoring candidates and eliminate everyone else except them and any one other candidate, the top M scoring candidates are guaranteed to win. BetterVotingAdvocacy (talk) 20:04, 19 February 2020 (UTC)

I have no issue with that every "X PR method" must reduce to X in the single-winner case". I was rather trying to avoid two types of confusion: first, that there's some kind of "multi-winner Condorcet property" that all of the categorized methods pass, and second, that this multi-winner property is the Schulze one. Since there is no general agreement about what a multi-winner Condorcet property is, I thought it best to not give the impression that there is and that Condorcet PR methods satisfy it.

Regarding Schulze M+1 not implying Condorcet, it's funny you should say that, because it closely parallels an ambiguity in the single-winner criterion. Schulze gave his generalization in the context of preferential methods (the paper starts off by defining preference orders and methods taking these as inputs). Every preferential method I can think of (except pathological ones) reduce to majority when there are only two candidates, so you get the (ordinary) Condorcet criterion in the single-winner case. Schulze simply does not mention rated balloting as an alternative, like Condorcet didn't for the single-winner criterion.

Because Condorcet was ambiguous that way, Warren Smith argues that the Condorcet criterion should also apply to Range. Quoting from http://9mail-de.spdns.de/m-schulze/votedesc.pdf p.27: Condorcet himself may have had a slightly different definition in mind, which I shall call CW′: replace the words “plurality election compatible with the original votes” with “election of the original type, with the same votes with all candidates but these two omitted.” The two definitions are equivalent when applied to virtually every rank-order-ballot based method, but differ for, e.g,range voting. Range voting disobeys CW but obeys CW′.

Now clearly that's not what we think of as the Condorcet criterion, so CW' hasn't been used much elsewhere. I think we can take that precedent for the Schulze M+1 criterion as well, even though you're right that the criterion, strictly speaking, leaves other options open. Kristomun (talk) 00:20, 20 February 2020 (UTC)

As for the second edit, that's correct. Even if you go with the implication of the single-winner Condorcet criterion, Schulze's multi-winner criterion may fail to imply PR. Bloc Ranked Pairs can be shown to pass it using similar logic as you gave, since Ranked Pairs satisfies LIIA. I was reading "Condorcet PR methods" as "PR methods that are also Condorcet", not "methods that are also Condorcet PR". (E.g. by analogy, if we had a category for "Candidate-monotone PR methods", those would be methods that are both PR and satisfy the candidate monotonicity criterion given in the Expanding Approvals paper.) Kristomun (talk) 00:35, 20 February 2020 (UTC)

I have made the "Condorcet PR" category more prominent than this one. I think the current situation is a good compromise between our views: Condorcet PR gets to be the main thing people click on, but the only real content in it will be "Condorcet-reducible PR methods", so people can click on that for further information. To be honest, I'd prefer to erase the Condorcet-reducible category and write its description in the Condorcet PR category description, because I don't think anyone will get confused so long as that clear distinction is made on the page itself. BetterVotingAdvocacy (talk) 08:13, 23 April 2020 (UTC)