CR & Arrow

Alex Small asmall at
Sun Oct 20 07:48:11 PDT 2002

> 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.

I ran across a paper (can't remember the journal, but it was recent) by
a mathematician at Northwestern.  He defined IIAC to account for
strategy changes:  If a candidate is deleted, and voters change their
strategies to account for that, the outcome should be unchanged unless
the deleted candidate was the original winner.

Using the maximum-utility strategy causes Approval to flunk this
criterion.  If you vote for all candidates whom you find superior to an
expected utility, deleting a candidate changes the expected utility of
the race, which causes you to change strategies, which can change the

I wasn't terribly impressed.  First, this definition of IIAC isn't all
that useful (any election method flunks it, as far as I can tell).
Second, the failure can be proven by a single example, hence the more
elaborate aspects of the paper were unnecessary.

I know that Donald Saari strongly dislikes Approval Voting.  He used to
be at Northwestern.  My bet is that this guy is from the Saari school of
voting theory.  Nothing wrong with that (Saari has some fascinating
insights) but when a feeble work comes from a group with a known bias,
well, it isn't terribly impressive.

Incidentally, Saari's problem with Approval seems to be that you can't
predict the outcome from knowing the voters' preference orders.  This is
like saying that you can't predict the outcome of an experiment in one
field of physics based on information of an entirely different sort
(e.g. magnetic data, fluid dynamics experiment).


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