Talk:Condorcet ranking: Difference between revisions

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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)

Revision as of 22:36, 20 February 2020 (view source) BetterVotingAdvocacy (talk \| contribs) (Created page with "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 consid...")		Revision as of 00:25, 21 February 2020 (view source) Kristomun (talk \| contribs) No edit summary Newer edit →
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	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? [[User:BetterVotingAdvocacy\|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy\|talk]]) 22:35, 20 February 2020 (UTC)		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? [[User:BetterVotingAdvocacy\|BetterVotingAdvocacy]] ([[User talk: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. [[User:Kristomun\|Kristomun]] ([[User talk:Kristomun\|talk]]) 00:25, 21 February 2020 (UTC)