From: T0Morrow@aol.com
Date: Tue Apr 11 2000 - 23:55:06 MDT
I wrote:
>> Set aside Joy's disappointingly juvenile views on political economy
(lifted
>> straight out of Dickinson) and his muddled thinking about how some
collective
>> "we" chooses the shape of the world (ignoring Arrow's Theorem).
Robert asked:
>"Arrow's Theorem"? Ref by any chance?
The fuller title is "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). You might think of the
theorem as a similar but more general version of Condorcet's famous voting
paradox: Given individuals 1, 2, and 3 voting on outcomes A, B, and C and a
preference ranking as illustrated below, a majority vote cannot generate a
"socially preferred" outcome.
Ranking 1 2 3
1st A B C
2nd B C A
3rd C A B
It's an intransitive ordering, natch. Condorcet eliminated majority rule as
a possible definition of social welfare; Arrow eliminated practically
everything else. He 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.
("Dickinson" is no obscure lefty economist, by the way; I meant to say
"Dickens.")
T.0. Morrow
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