Kevin,Date: Fri, 5 Mar 2004 21:38:59 +0100 (CET) From: =?iso-8859-1?q?Kevin=20Venzke?= <[EMAIL PROTECTED]>
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.
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
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