Talk:Condorcet ranking

If there are pairwise ties or cycles, do Condorcet rankings reflect this? For example, if there is a 3-candidate Smith Set and a 4th candidate, are the Smith candidates considered to be in a tie for 1st, with the 4th candidate in 2nd place? BetterVotingAdvocacy (talk) 22:35, 20 February 2020 (UTC)

I don't think it reflects cycles, though it could reflect ties. Reflecting cycles would be a "Smith ranking", not a Condorcet ranking. So a Condorcet ranking is only defined when there's a sequence of candidates so that A beats everybody, B beats everybody but A, C beats everybody but A and B and so on. A bit like criteria, that a method that always returns a Condorcet ranking doesn't say anything about what happens when there isn't one. Kristomun (talk) 00:25, 21 February 2020 (UTC)

I'd like to build a consensus for a "generalized Condorcet ranking criterion"; a voting method complies with this criterion if it ~~(Edit: here's a more succinct way to put it: if we take any two groups of candidates, with the two groups not necessarily amounting to all candidates together, and any candidate in the first group can pairwise beat any candidate in the second group, then all candidates in the first group must be ranked higher than all candidates in the second group.)~~ (Edit 2: This is actually wrong, since it implies that in a 3-way Condorcet cycle, one candidate must be ranked above another above another above the first, which is impossible.) always says that A is at least as good as B when A pairwise beats or ties B. In essence, if a group of candidates pairwise beat all others, they must be ranked higher than all of them, but if within the group there is a cycle or pairwise ties, then the voting method can either rank some candidates in the group above others or show ties between some of them. From there, we can consider a "generalized Condorcet ranking" one where candidates in a cycle or pairwise ties are considered to be tied in the generalized ranking. The reason I'm proposing this is that it will help us pick out the "good" Smith-efficient methods (since I'd say this is at least one pretty decent standard of deciding what a good order of finish looks like), and further, helps us explain to the public how it is that Smith-efficient Condorcet methods in general go about deciding which candidates are better than others in the order of finish. In general, I just like the idea of clearly showing to people which groups of candidates are better than others based on pairwise preference, rather than solely pairwise preferences between two individual candidates. What do you think? BetterVotingAdvocacy (talk) 00:55, 21 February 2020 (UTC)