[EM] The issue of comments about Arrow's theorem

MIKE OSSIPOFF nkklrp at hotmail.com
Sat May 14 20:39:59 PDT 2005

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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