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steven0461 comments on Arrow's Theorem is a Lie - Less Wrong
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Even if you can only state a preference ordering and nothing else, there's no reason to keep IIA, as the ranking of irrelevant alternatives is evidence of preference strength.
Apparently Arrow's theorem and the Gibbard-Satterthwaite theorem are the same thing, so there's a real impossibility theorem in there, with the real lesson being that you can't avoid tactical voting.
The Gibbard-Satterthwaite theorem is like Arrow's theorem, in that it only applies to voting systems which work solely based on preference ordering. Under my system, there's no incentive for "tactical voting", in the sense of giving a higher score to a candidate who you think is worse; a candidate can only do better if they're ranked more highly.
But there's lots of incentive to misstate preference strengths. (I think you can prove this always has to be true by applying G-S to preferences over gambles. Rejecting determinism here means saying the winner can depend on something else than anyone's preference strengths, which is bad.)