Talk:IRV Prime: Difference between revisions
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:: (emphasis mine.) The crossed properties are participation, four different monotonicity properties, later-no-help, and later-no-harm. Woodall then proceeds to prove this impossibility; if it were indeed only true some of the time, then one would imagine these proofs would contain the necessary qualifications, but they do not claim any such qualification beyond that the method must pass Condorcet. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 09:17, 4 August 2021 (UTC)
There is a problem with the proof, though; it starts with:
Without loss of generality, suppose a is elected in P. But c becomes the Condorcet winner, and so must be elected by CONDORCET
The theorem begins with the premise that both of those are possible, i.e. that a wins & c can become the Condorcet winner simply by modifying later preferences. But I believe those premise may be unsatisfiable.
The question is: how does a win? And if a wins, is it possible to make c the condorcet winner without putting c above a? (in IRV-prime, it's impossible to fulfill both premises; either a doesn't win, or c cannot be made a condorcet winner)
It's like starting with "suppose the tree exists and the tree doesn't exist" - you can make a lot of faulty theorems by starting with premises that cannot all be satisfied.
--[[User:Marcosb|Marcosb]] ([[User talk:Marcosb|talk]]) 16:41, 4 August 2021 (UTC)
== Arrow/IIA ==
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