[EM] Arrow's Theorem.

Adam Tarr atarr at purdue.edu
Tue Jul 15 09:12:04 PDT 2003

Eric Gorr 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.

It does not necessarily follow.  The point is, the results of a plurality 
election can be _uniquely determined_ from a set of preference ballots.  In 
contrast, a common criticism of approval is that the results cannot be 
derived from voters' preference orders.

>Therefore, if Plurality fails Arrow's Theorem, so would Approval.

Perhaps this follows only if you can show a case where some set of 
preference order ballots MUST cause approval to fail IIA, regardless of the 
choice of approval cutoff.  The difference between approval and plurality 
is that approval ballots cannot be uniquely derived from preference orders 
beyond the two-candidate case.

I guess you could argue that since you can derive some reasonable approval 
ballot from a preference order, and make that fail IIA, that this implies 
approval fails IIA.  One could counter, however, that it is impossible to 
say whether this derivation of the approval ballot is at all accurate or 
would ever happen.

>So, the question becomes, does Plurality fail Arrow's Theorem?
>I believe the answer to this question is 'Yes'.

I agree with this.


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