Re: Arrow's Social Choice Theorem

From: Robin Hanson (
Date: Thu Apr 13 2000 - 07:04:21 MDT

T.0. Morrow wrote:
> >>Arrow did make it pretty hard for reasonable folks to claim that they
> >>can generate group preferences out of individual preferences.
> >I think you overstate your case. For example, Arrow required that *all*
> >preference orderings over outcomes be allowed. If you restrict attention
> >to creatures who preferences can be described by expected utility, then
> >Arrow's Theorem no longer applies, and in fact the other axioms are
> >satisfied by any increasing function of each person's expected utility.
>I addressed that point in another post, where (to recap) I admitted that
>Arrow's Theorem does not hold if you assume you can make interpersonal
>utility comparisons. The problem lies with that assumption, though; one
>person's marginal dollar does not equal another's. One might, per Marshall,
>assume the contrary and get some pretty good approximations--and perhaps
>that's all we can ask of any science. But philosophers should, at least,
>note the oversimplification.

I agree that the point you make is reasonable, but disagree that it has
anything to do with Arrow's Theorem. Objecting to making comparisons
across people is essentially objecting to the very idea of *any* social
welfare ordering. In contrast, Arrow accepted the general concept as
valid, but then found a certain set of axioms he liked constraining such
orderings could not all be valid.

I consider one of Arrow's axioms to be far from reasonable, and so don't
think there is much to learn from Arrow's Theorem. I also don't object
to the basic idea of comparing preferences across people. But I
do agree that more essential issues are:

>... vote-buying, rent-seeking, diffuse costs, and so forth ...

Robin Hanson
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030
703-993-2326 FAX: 703-993-2323

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