User talk:KelvinVoskuijl/Coombs with Bottom Two Runoff

Would this be a condorcet method? KelvinVoskuijl (talk) 21:40, 10 April 2024 (UTC)

Every bottom-two runoff method is Condorcet as long as it continues until some candidate has a majority or every candidate but one is eliminated, and only compares two candidates at a time (per round). That is, if three candidates tie for bottom in a particular round, only two of them are checked at a time, although such checks may happen multiple times in a single round.

General proof: suppose A and B are the losers currently being compared. Suppose A is the Condorcet winner. Then by the bottom-two rules, if A beats B pairwise, then A must not be eliminated. And since A is the Condorcet winner, A beats B pairwise no matter who B is. Hence A is never eliminated, and must win. So the method passes Condorcet. Kristomun (talk) 20:06, 11 April 2024 (UTC)