[EM] Arrow's Theorem

[fsimmons at pcc.edu]

It depends on how you interpret the IIAC.

The IIAC says (in essence) that if one of the losers is disqualified, there is
no need to hold the election over again, because the winner wouldn't change.

If you just strike the disqualified candidate off of the ballot, and recount,
then FPTP and Range (including Approval) keep the original winner intact. So
these methods satisfy "ballot IIAC, " which is more than any (neutral) method
based on ranked ballots can say.

But if an actual new election is held, even though the voters don't change any
of their opinions about any of the remaining candidates, there will sometimes be
a new winner. 

In the case of Range this would come about by renormalization.  In the case of
FPTP this would come about by the supporters of the disqualified candidate
voting for one of the remaining candidates instead.  In the case of Approval,
the voters who originally voted ballots on which the disqualified candidate was
the only candidate not approved (or else the only candidate approved) would
naturally make a minimal change to reflect that fact.

This is related to the fact that these three methods satisfy "the ballot
Condorcet Criterion" but not the usual understanding of the Condorcet Criterion.
 For example, we can say that the FPTP winner P is the ballot Condorcet Winner,
because compared head to head with another candidate X, candidate P had more
votes (according to the original ballots) than candidate X.  The same goes for
the Range winner R in a Range election.



> From: Warren Smith
> To: election-methods
> Subject: [EM] Arrow's theorem
>
> >No election system in which voters rank candidates can have all
> properties that seem >democratic or appropriate.
> >--Stephen H. Sosnick (5/03/11)
>
> --and the obvious lesson to now draw from that conclusion is:
> you want voting
> systems in which the voters do NOT "rank candidates" -- such as
> approval voting and range voting. Arrow's "impossible" feat is
> actually possible using range voting
> (according to some authors' verbatim statements of the Arrovian
> 'impossibility'):
> http://rangevoting.org/ArrowThm.html