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<blockquote type="cite"
cite="mid20040309173309.4406.12806.Mailman@geronimo.dreamhost.com">
<pre wrap="">Date: Tue, 9 Mar 2004 00:41:56 +0100 (CET)
From: =?iso-8859-1?q?Kevin=20Venzke?= <a class="moz-txt-link-rfc2396E" href="mailto:stepjak@yahoo.fr"><stepjak@yahoo.fr></a>
Ken,
--- Ken Johnson <a class="moz-txt-link-rfc2396E" href="mailto:kjinnovation@earthlink.net"><kjinnovation@earthlink.net></a> a écrit : >
</pre>
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<pre wrap="">My impression was that Arrow stipulated several
basic criteria that any "reasonable" social choice system should
satisfy, with one criterion being that it be based on ranked preferences
and the other criteria being stated in terms that only apply to rank
methods.
</pre>
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<pre wrap=""><!---->
I don't think this last part is so. It's clear that CR meets Pareto,
non-dictatorship, and in a sense IIA. I say "in a sense" because we would
have to assume that no one changes their rating of any candidate when a new
candidate is introduced. </pre>
</blockquote>
But this is the precise sense of Arrow's Theorem. Following is a
definition of IIA, as paraphrased by Rosengren:<br>
"Independence of irrelevant alternatives - If one set of preference
ballots would lead to an overall ranking of alternative X above
alternative Y and if some preference ballots are changed <i>without
changing the relative rank of X and Y</i>, then the method should still
rank X above Y."<br>
<a class="moz-txt-link-freetext" href="http://www.d.kth.se/~d98-anr/Rapporter/Arrow">http://www.d.kth.se/~d98-anr/Rapporter/Arrow</a>'s%20theorem.pdf<br>
<br>
A simpler statement of IIA would be that the group preference
relationship between any two candidates does not depend on how voters'
rank other candidates. (In the context of cardinal methods, change
"rank" to "rate".)<br>
<blockquote type="cite"
cite="mid20040309173309.4406.12806.Mailman@geronimo.dreamhost.com">
<pre wrap="">But this doesn't seem at all realistic. I would
say that CR doesn't meet IIA in a meaningful way.
Actually, I don't know of any deterministic method that meets IIA in a "meaningful
way."
</pre>
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Arrow's IIA criterion may not be realistic or meaningful, but I believe
CR does satisfy the criterion.<br>
<br>
Ken Johnson<br>
<br>
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