Talk:Condorcet winner criterion: Difference between revisions

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Smith set with two members

"If the pairwise champion exists, they will be the only candidate in the Smith set; otherwise, the Smith set will have three or more members."

If there are two weak Condorcet winners, wouldn't the Smith Set have exactly two members? BetterVotingAdvocacy (talk) 02:18, 4 January 2020 (UTC)

It's pretty much impossible to have a Smith set of two members, because it's impossible to have a pairwise cycle with only two members. The Smith set can have three members (A, B, and C) when A beats B, B beats C, and C beats A. But it's not possible to have a Smith set with only two members (A and B), because if A beats B, then B can't beat A. -- RobLa (talk) 04:32, 5 January 2020 (UTC)

Doesn't "weak" mean the two are tied? — Psephomancy (talk) 06:23, 5 January 2020 (UTC)

Revision as of 04:32, 5 January 2020 (view source) RobLa (talk \| contribs) (→‎Smith set with two members: can't have a Smith set of only two members) ← Older edit		Revision as of 06:23, 5 January 2020 (view source) Psephomancy (talk \| contribs) (respond to User:RobLa) Newer edit →
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	:It's pretty much impossible to have a Smith set of two members, because it's impossible to have a pairwise cycle with only two members. The Smith set can have three members (A, B, and C) when A beats B, B beats C, and C beats A. But it's not possible to have a Smith set with only two members (A and B), because if A beats B, then B can't beat A. -- [[User:RobLa\|RobLa]] ([[User talk:RobLa\|talk]]) 04:32, 5 January 2020 (UTC)		:It's pretty much impossible to have a Smith set of two members, because it's impossible to have a pairwise cycle with only two members. The Smith set can have three members (A, B, and C) when A beats B, B beats C, and C beats A. But it's not possible to have a Smith set with only two members (A and B), because if A beats B, then B can't beat A. -- [[User:RobLa\|RobLa]] ([[User talk:RobLa\|talk]]) 04:32, 5 January 2020 (UTC)

			:: Doesn't "weak" mean the two are tied? — [[User:Psephomancy\|Psephomancy]] ([[User talk:Psephomancy\|talk]]) 06:23, 5 January 2020 (UTC)