[EM] Arrow's Theorem.

Forest Simmons fsimmons at pcc.edu
Tue Jul 15 17:29:10 PDT 2003

On Tue, 15 Jul 2003, Markus Schulze wrote:

> Dear Eric,
> FPP is a preferential method according to the definition
> of preferential methods. First: FPP can be applied to
> every possible set of orders of merit; the FPP winner is
> the candidate with the largest number of first preferences.
> Second: 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.

So whether or not plurality satisfies the IIAC depends on the
interpretation, the same ambiguity that I recently remarked on with
regards to Approval.

In the case of Approval, if the original Approval ballots are the sole
source of information, the ballots with a name deleted may well approve
all the remaining candidates (or approve none) which would give these
ballots zero influence on the outcome, an unlikely choice if the voters
themselves could revise the ballots.

So Approval may formally pass the IIAC, but only at the expense of some
voters' ballots turning out to be dummy ballots.

The same goes for plurality.


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