[EM] Arrow's Theorem.
Eric Gorr
eric at ericgorr.net
Tue Jul 15 09:10:14 PDT 2003
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.
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