[EM] Does the 'Independence of Irrelevant Alternatives Criterion' Imply a Condorcet Winner ?

[Forest Simmons]

On Thu, 1 Apr 2004, Rob Speer wrote:

> On Tue, Mar 30, 2004 at 05:26:02PM -0300, Marcos C. Ribeiro wrote:
> > THE CONCLUSIONS ARE:
> > -> If IAA is a false criterion, it doesn't make sense to verify if any method fulfils it. We must be very secure with the principles from which we start. To verify false criterions is to go in a wrong line of thought. Simple so.
>
> What do you mean by "false"? You can say that IIA is a condition that is
> _unreasonable_ to satisfy, but there's nothing that can be false about
> it. It's just a definition: "If a method has these properties, it is
> defined to satisfy IIA."

I think he just means that no reasonable method can satisfy the criterion
at the level of actual voter preferences.

To make this really simple, suppose that there is only one chooser, and
that there are three choices, and that the chooser prefers A to B to C to
A, with varying levels of intensity.  Suppose that the chooser finally
decides to choose A.  But before announcing her decision she finds out
that option B has been withdrawn.  Is she going to stick with A?

In other words, not even a dictator method can satisfy the IIAC at the
fundamental level of actual preferences.

Of course, the IIAC can be satisfied at the ballot level, as it is by
random ballot, for example.

Forest