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

Rob Speer rspeer at MIT.EDU
Thu Apr 1 09:28:06 PST 2004

```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."

> -> If the Arrow's theorem depends on the IAA criterion, it is a false "theorem", no matter how famous it is. (To go ahead, I think we must ignore authority arguments and to have a discussion between equals.)

Arrow's theorem proves, mathematically, that no voting method can
satisfy non-dictatorship, Pareto-optimality, and IIA. This much is true,
regardless of whether you think IIA is a reasonable criterion.

What you may be calling "false" is the popular paraphrasing of the
theorem as "No voting method is fair". Arrow didn't say that -
pop-science magazines reporting on his theorem did. Specifically, you
can disagree with this paraphrasing because you can disagree that IIA is
necessary for a voting method to be "fair".

The reason that Arrow's theorem is famous is that IIA sounds like a
perfectly reasonable criterion, and it is surprising to find out that
hardly any methods satisfy it. Arrow's theorem explains _why_ hardly any
methods satisfy it (they would either have to be dictatorial or
non-Pareto-optimal).
--
Rob Speer

```