Re: Arrow's Social Choice Theorem

Date: Wed Apr 12 2000 - 22:36:41 MDT

Robin Hason wrote of my description of Arrow's Impossibility Theorem

>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.

At any rate, I think that the more tangible problems with social choice
arise, as Robin's reference to people pursuing individual preferences
notwithstanding collective ones indicates, from *public* choice problems.
Arrow's theorem is fun for showing the limits of social choice theory, but
I'd wager that no institution ever gets close enough to perfection to give it
much traction. Problems with vote-buying, rent-seeking, diffuse costs, and
so forth, kick in long, long before.

T.0. Morrow

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