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From: buzzard@world.std.com (Sean T Barrett)
Subject: Re: Of IF Comp, IMDB, and Bayesian Averages
Message-ID: <GKyKIG.6Az@world.std.com>
Date: Tue, 9 Oct 2001 21:47:03 GMT
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Carl Muckenhoupt  <carl@wurb.com> wrote:
>For those interested, the theorem in question is 'Arrow's Theorem'.
>http://www.csc.vill.edu/faculty/bartlow/html/mat1220/arrowthm.html

Neat!

>If I understand Arrow's criteria correctly, the current Comp rules
>violate the criterion of Universality.  Universality states that any
>(non-empty) set of votes must produce a "complete ranking".  For the
>purposes of the Comp, this seems like the most innocuous of Arrow's
>criteria to violate.

I doubt that universality means "no ties", since I don't think
anything else is reasonable for an exactly 50-50-split vote, and
I take it that's what you mean?

If I understand it correctly (solely from reading that web page),
the comp violates "the Criterion of independence of irrelevant
alternatives"; we can take a single ballot and change the votes
for X & Y--without changing that ballot's relative rank of X & Y--
and cause a change in whether X or Y wins in the total score.

I'm not sure what "without changing the relative rank of X and Y"
means in the context of assigning them scores; if it simply means
"not changing which one is above the other", it's possible for
somebody to change their votes from X=10, Y=1 to X=10, Y=9, and
for that to move Y into the lead over X.  If "relative rank"
means their position on the list, then of course if I assign
all games a 1, X=10, and Y=2, I can still raise Y to 9 and have
the same effect.

With more stringent rules (say the numeric difference between
X and Y, or their proportion) I can still have a similar effect
because the final scores for X and Y are computed by dividing
by the number of votes for each, so my vote for Y might have
more weight than my vote for X (if more people voted for X);
so raising them the "same amount" could still cause Y to move
into the lead over X.

Of course, if one is familiar with how the voting system works,
one might thing it perfectly intuitive that changing my vote
from "X=10,Y=1" to "X=10,Y=9" might cause X to lose to Y; but
I can certainly see why it's less than ideal.

SeanB
