Jonathan Lundell wrote:
I don't have his proof in front of me (I'm on the road), but I'm pretty sure
that it assumes ordinal ranking.
It seems fairly obvious that the theorem also holds for ratings, because
ratings can be projected onto rankings without affecting any of Arrow's
criteria. To put it another way, the proofs I have seen all apply to
range-based methods in a straightforward way--there needs to be some
fiddling with the proof to deal with ties, but that issue is not essential.
Letting voters give ratings doesn't mean you escape Arrow's Theorem.
-- Andrew
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