[EM] Arrow's Theorem.

[Forest Simmons]

Dear Markus, Alex, et.al.

I understand what you are saying, and have acknowledged that your points
of view are perfectly logical and valid interpretations of the IIAC.

I'm not sure if there is a universally accepted version of the IIAC, but I
prefer the version that doesn't require the voters to go back to the polls
if a losing candidate withdraws between the time the ballots are collected
and the time they are counted.

This scenario seems much more likely to happen than getting the voters to
return to the polls or adding a candidate after the ballots have already
been collected.

Forest

On Wed, 16 Jul 2003, Markus Schulze wrote:

> Dear Forest,
>
> it is true that FPP isn't a preferential method according to
> the everyday use of the term "preferential." However, FPP is a
> preferential method (even when lone mark ballots are being used)
> according to Arrow's use of the term "preferential" since FPP
> can be used to every possible set of orders of merit and since
> the FPP winner doesn't depend on information that is not included
> in the set of orders of merit.
>
> > It is interesting that FPP plurality fails the IIAC when the method
> > makes use of ranked preference ballots, but passes the IIAC when
> > lone mark ballots are used, since second place preferences cannot be
> > inferred from the lone mark ballots ... those voters who voted for
> > the candidate that drops out just end up without a vote in this
> > latter case, and the original plurality winner still has the greatest
> > number of votes.
>
> To be a "preferential" method it is necessary that the winner doesn't
> depend on more than the set of orders of merit. It is not necessary
> that the winner doesn't depend on less than the set of orders of merit.
> The fact that every election method collects only that information that
> it needs to calculate its winner is obvious but irrelevant.
>
> Markus Schulze
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