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From: buzzard@world.std.com (Sean T Barrett)
Subject: Re: Of IF Comp, IMDB, and Bayesian Averages
Message-ID: <GL4FF9.9vB@world.std.com>
Date: Sat, 13 Oct 2001 01:42:44 GMT
References: <20011009040806.07073.00001120@mb-co.aol.com> <MPG.162d01d656598dfa9896da@News.CIS.DFN.DE> <GKyKIG.6Az@world.std.com> <slrn9sf0h4.i4.tilford@ralph.caltech.edu>
Organization: The World Public Access UNIX, Brookline, MA
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Mark J. Tilford <tilford@ugcs.caltech.edu> wrote:
>On Tue, 9 Oct 2001 21:47:03 GMT, Sean T Barrett <buzzard@world.std.com> wrote:
>>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
>>
>>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.
>
>In this case, IIR would be violated if changing the rank of a third game Z
>would change whether X or Y wins.

Umm, that's not what that web page says--there's no mention of
a third game Z, and it's rather explicit about changing the
ballot without changing the *relative* ranking of X and Y--no
mention of not changing the *absolute* ranking of X and Y.

So, based on that web page, you're wrong. You didn't offer
an alternative web page; you didn't offer any credentials for
why you claim to know this; and you didn't trim the post you
replied to at all; so I don't believe you.

Or rather, you're no doubt right that in the condition that
you're describing, IIR would be violated; but I don't see
any evidence that the simpler scenario I described--which does
apply to our voting system, unlike yours--isn't a violation
of IIR, which you certainly seem to be implying.

SeanB
