Arrow's Social Choice Theorem

From: Robin Hanson (
Date: Wed Apr 12 2000 - 09:13:59 MDT

T.0. Morrow wrote:
>"Arrow's Impossiblity Theorem," named after its author,
>Kenneth Arrow and proven in his book, Social Choice and Individual Values
>(2nd ed., New Haven, CT: Yale Univ. Press, 1970). ... Arrow ...
>made a few plausible assumptions about the form of
>social welfare functions and then proved that no possible means of moving
>from individual to "social preferences" could satisfy all of the assumptions.
> It would be going a bit overboard to claim that Arrow's Impossibility
>Theorem proves that a social welfare function is *logically* impossible. One
>might assert, for instance, that "The Revolutionary Vanguard alone knows the
>social welfare function." But Arrow did make it pretty hard for reasonable
>folks to claim that they can generate group preferences out of individual
>preferences. Collectivists note: You cannot get there from here.

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.

Hal Finney wrote:
>The more general lesson is that it is impossible to create a fair and
>reasonable society. Even an omniscient, omnipotent being cannot create
>a world which satisfies the most basic postulates of fairness, ...

That may be true, but it doesn't follow from Arrow's work.

I don't actually think it is very hard to define plausible "group" preferences
out of individual ones. In fact you could say it is too easy; there are lots
of such plausible choices. The hard thing is the fact that most individuals
are going to disagree with whatever specific "group" preferences you define,
and will act on their individual preferences when possible.

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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