[EM] Arrow's axioms

[Ken Johnson]

>Date: Tue, 9 Mar 2004 00:41:56 +0100 (CET)
>From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
>
>Ken,
>
> --- Ken Johnson <kjinnovation at earthlink.net> a écrit : > 
>  
>
>>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.
>>    
>>
>
>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.  
>
But this is the precise sense of Arrow's Theorem. Following is a 
definition of IIA, as paraphrased by Rosengren:
"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 without 
changing the relative rank of X and Y, then the method should still rank 
X above Y."
http://www.d.kth.se/~d98-anr/Rapporter/Arrow's%20theorem.pdf

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".)

>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."
>  
>
Arrow's IIA criterion may not be realistic or meaningful, but I believe 
CR does satisfy the criterion.

Ken Johnson

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