[EM] Arrow's axioms

[Ken Johnson]

>Date: Fri, 5 Mar 2004 21:38:59 +0100 (CET)
>From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
>
>I should have been clearer.  You said that "if the theorem were generalized 
>to encompass cardinal methods, its conclusion would be that rank methods cannot 
>satisfy the axioms whereas CR can."  This is strange because Arrow's conclusion
>*already* includes that non-rank methods could meet all of *the other three*
>axioms.
>
Kevin,

Maybe I don't understand the theorem. (Most of what I know about it 
comes from the popular media, like Scientific American, which tends to 
oversimplify things.) 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. 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.)

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.

Ken Johnson