[EM] Arrow's axioms

[Kevin Venzke]

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 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."

> The theorem's conclusion is basically that ranked methods 
> cannot satisfy all the remaining criteria, but my impression was that it 
> does not address the question of whether cardinal methods could satisfy 
> those criteria. (Although the formal statement of the criteria such as 
> IIA may technically only apply to rank methods, they could be easily 
> generalized to be meaningful in the context of cardinal methods.)

CR looks better if we don't try to generalize IIA to apply to it.  It could
only make CR look worse.

> The main objection I have to the theorem is the way it is popularly 
> portrayed as proving the fundamental inadequacy of ALL voting systems, 
> whereas in fact it doesn't (I don't think) say anything about cardinal 
> methods.

I think the other theorem is more interesting when it comes to "the fundamental 
inadequacy of all voting systems."

Markus wrote:
>You wrote (29 Feb 2004):
>> So is it correct to say that Arrow did not prove that "there
>> is no perfect voting system"; he only proved that the methods
>> he deems to be acceptable are imperfect?
>
>Even though the presumption that the used single-winner
>election method is a rank method is necessary to prove
>Arrow's Theorem, this presumption is not necessary to prove
>the Gibbard-Satterthwaite Theorem. The Gibbard-Satterthwaite
>Theorem says that there is no paretian non-dictatorial
>method that isn't vulnerable to strategical voting.

Kevin Venzke
stepjak at yahoo.fr



	

	
		
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