When I read Curt's posting about Arrow, it was obvious to me that he was saying that Arrow's impossibility theorem is flawed by the unimportance of its criteria.
Sure, who appointed Arrow to decide what criteria are "reasonable" or necessary or important?
Arrow's result can best be reported as: Arrow proved that a few criteria that he likes are incompatible with eachother.
For some reason, many people have given those criteria undeserved status as the important criteria.
Curt mentioned IIAC. We'd all cheerfully do without IIAC, to have methods like wv. IIAC isn't important.
Anyway, when an invoker of the impossibility theorem is pressed to define its criteria, he never gives a usable definition of IIAC. To this day, I don't know what Arrow meant IIAC to be. I haven't seen his original paper, but most likely Arrow's own paper won't tell what Arrow means by IIAC.
I've posted here a simple votes-only IIAC. It's, so far, the only actual definition of IIAC that I've heard:
Deleting a loser from the ballots, and then recounting those ballots, should never change who wins.
[end of IIAC definition]
With that IIAC definition, Approval meets all of Arrow's results criteria.
I say "results criteria", because one of Arrow's criteria is a rules criterion rather than a results criterion. At least in the version of Arrow's theorem that I ran across, one of Arrow's incompatible criteria is one that says that a method must be a rank method.
As I've been saying, rules criteria are no good, and say nothing about methods that fail or pass them. That goes for criteria that don't apply to Pluralilty, or which Plurality fails by definition. And it goes for Arrow's rankings criterion.
Anyway, that's the other flaw of Arrow's impossibility theorem, the fact that it contains a rules criterion.
People could debate what Arrow, or some other voting system academic, is trying to say, but does it reallly matter? If he wanted his meaning to be known, it's for him to say it. We shouldn't have to try to decrypt it or guess it.
Mike Ossipoff
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