[EM] Arrow's Theorem.
Eric Gorr
eric at ericgorr.net
Tue Jul 15 08:39:01 PDT 2003
At 8:18 AM -0700 7/15/03, Alex Small wrote:
>Eric Gorr said:
>> At 9:51 AM +0200 7/15/03, Markus Schulze wrote:
>>>To be a preferential method, the method must be defined
>>>on every possible set of orders of merit and must not
>>>take more into consideration than just the orders of
>>>merit.
>>
>> Would you agree that Plurality is covered by Arrow's Theorem?
>
>Plurality does not _need_ preferential ballots, but the results of a
>plurality election could be inferred from preferential ballots: Count the
>number of voters who ranked each candidate first. If the results of an
>election method can always be uniquely determined from preferential
>ballots, then the method is equivalent to a preferential method, even if
>some clever implementation avoids using preferential ballots.
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.
So, the question becomes, does Plurality fail Arrow's Theorem?
I believe the answer to this question is 'Yes'.
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