[EM] Arrow's Theorem.

[Eric Gorr]

At 9:02 AM -0700 7/15/03, Alex Small wrote:
>  > The point is that if Plurality is covered by Arrow's Theorem, then so
>>  is Approval since if in an Approval election the voters only vote for  a
>>  single option, that election would be equivalent to a Plurality
>>  election.
>  > Therefore, if Plurality fails Arrow's Theorem, so would Approval.
>
>For Approval to be equivalent to plurality, we'd have to know that voters
>would ALWAYS vote for just one.  But since voters are free to pick their
>strategy, Approval is not equivalent to plurality, nor is it equivalent to
>any other ranked method.

If Approval fails Arrow's Theorem in any example of an Approval 
election, it simply fails Arrow's Theorem. Nothing more needs to be 
said.

I did not state that in all cases Approval is equivalent to Plurality.

My only point is that I can state a case where it is and, in that 
case, it fails Arrow's Theorem.

Not that this is necessarily a bad thing nor would it remove Approval 
from all due consideration.