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Re: Borda count
Posted:
Nov 17, 2000 1:40 AM
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Guy Brandenburg wrote:
> Well, read it yourself. Here is the citation:
>
> http://www.colorado.edu/education/DMP/voting_b.html
I've given it a (very) quick scan, and I think that Saari doesn't claim
to contradict Arrow. Instead, he has exploited the observation I made
(that Arrow's result depends upon restrictive definitions, and, in
consequence, reaches a restricted conclusion) to find ways around
Arrow's Paradox. The real issue here is the common misstatement of
Arrow's Paradox as "They ain't no fair way to make societal decisions".
While I haven't gone deeply enough into the argument that Saari gives,
I think that has picked up on a facet of Arrow's work that means that
weighted voting can be fair--or at least doesn't lead to the same
paradox that other schemes do. I am not sure that Saari put his finger
on the same thing that I did, but from my limited reading of Saari, he
and Arrow both appear to be correct.
I presented my findings to members of my department about a year ago
in a departmental colloquium talk entitled "The Slings and Misfortunes
of Outrageous Arrow", in which I pointed out at the beginning of the
talk that Arrow's Theorem seems at first blush to imply that there is
no fair way to assign grades to students in a class, because, after all,
the homework assignments, quizzes, exams, etc., can be viewed as "voting"
on the relative rank of the students in the class. By the end of the
talk, we had concluded that Arrow's Theorem does not apply because it
requires a simple ranking--that is, function whose domain is the set
of natural numbers {1, ..., n} (where n is the number of people in
the class) and the members of the class. Most assessment instruments
are much more than simple ranking tools.
--Lou Talman
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