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Talk:Favorite betrayal criterion: Difference between revisions
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== Condorcet and FBC ==
12.73.128.232 changed the article from saying that most or all Condorcet methods fail FBC to claiming that all Condorcet methods fail.
Is it proven that all Condorcet methods fail FBC?
:That was me (12.73.128.232). On the EM list I recently was able to show that a method that satisfies Condorcet necessarily has situations in which changing an equal ranking A=B to a strict ranking A>B on some ballots increases the probability that the winner is either A or B. This incentive isn't compatible with FBC. [[User:KVenzke|Kevin Venzke]] 07:02, 7 Jul 2005 (PDT)
Why is that necessarily incompatible with FBC? Obviously, if A>B gives a probability that the winner is either A or B that is not only greater that what A=B gives but also greater than what B>A gives, that is a FBC failure. However, if both A>B and B>A give a greater probability that the winner is either A or B than what A=B gives, and A>B and B>A give the same probability as each other, then that is not necessarily a FBC failure. (As the criterion is currently stated, ranking one sincere co-favorite over another does not qualify as a favorite betrayal.) - DPJ, 2006-07-24 07:18 UTC▼
▲::Why is that necessarily incompatible with FBC? Obviously, if A>B gives a probability that the winner is either A or B that is not only greater that what A=B gives but also greater than what B>A gives, that is a FBC failure. However, if both A>B and B>A give a greater probability that the winner is either A or B than what A=B gives, and A>B and B>A give the same probability as each other, then that is not necessarily a FBC failure. (As the criterion is currently stated, ranking one sincere co-favorite over another does not qualify as a favorite betrayal.) - DPJ, 2006-07-24 07:18 UTC
== Criterion for lowest support ==
Is there a corresponding criterion for making it safe to give lowest support to your least-favorite candidate? — [[User:Psephomancy|Psephomancy]] ([[User talk:Psephomancy|talk]]) 15:55, 8 December 2019 (UTC)
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