CR & Arrow

Sat Oct 19 23:43:39 PDT 2002

Yes, when the IRV promoters use Arrow to claim that we should give
up on finding anything better than IRV, I point out that Approval
meets Arrow's criteria (if we don't count rank-input as a criterion)
and IRV doesn't. That Approval meets all of Arrow's _behavior_ criteria,
as opposed to rules criteria.

Of course that depends on how one defines IIAC. By the simple way
that I define it, Approval & CR comply.  But people have told me that
they believe that IIAC means something other than what I say it
means. But no one who has told me that has supplied a complete &
precise definition of what he thinks IIAC means.

As I interpret it, IIAC says that deleting a nonwinning candidate
from the ballots, and then recounting those ballots, should never
change who wins.

A rewording that might sound more compelling would be:

No candidate should be caused to lose by the deletion of someone
else from the ballots, and the recounting of those ballots.

That's like my interpretation of the probabilistic Regularity Criterion
that Markus mentioned here some time ago, except of course that it
refers to reduction in a candidates probability of winning. Probabilistic 
criteria are for the purpose of extending criteria's
applicability to probabilistic methods. Not really of practical
importance, since probabilistic methods are unlikely to be adopted
for public political elections.

It also probably means the same as my interpretation of Heritage,
mentioned in a book by Nurmi, whose title refers to voting paradoxes
and how to avoid them. A candidate who wins should also win among
any subset of the candidates to which he belongs. I interpret that to
mean: If, by a certain set of ballots, a certain candidate wins, then
he should still win among any subset of the candidates to which he
belongs, if we delete from those ballots everyone how is outside that
subset, and then recount those ballots.

Mike Ossipoff

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