From: John Conover <john@email.johncon.com>
Subject: Re: Economics is a science
Hi Robert. There is an excellent chapter for the lay on the
implication of Arrow's so-called Impossibility Theorem in "Archimedes'
Revenge", Paul Hoffman, Fawcett Crest, ISBN 0-449-21750-7, Part IV,
Chapter 12, pp. 213-248. It sites Paul Samuelson in 1952:
"The search of the great minds of recorded history for the perfect
democracy, it turns out, is the search for a chimera, for a
logical self-contradiction. Now scholars all over the world-in
mathematics, politics, philosophy, and economics-are trying to
salvage what can be salvaged from Arrow's devastating discovery
that is to mathematical politics what Kurt Godel's 1931
impossibility-of-proving-consistency theorem is to mathematical
logic."
At best, the undemocratic paradoxes inherent in democratic voting mean
that there can be never be a perfect social system-which is taken by
many as the reason the many gave power to the few during the invention
of civilization.
However, the intransitivity of priorities does make good fodder for
stump speeches in election years, though.
John
Robert Vienneau writes:
> Arrow's impossibility theorem is an apriori argument, that is, a
> matter of mathematics. I looked it up. One statement of the theorem
> is as follows.
>
> 1.0 THE THEOREM
>
> Let a set of individuals and alternatives be given. Each individual
> has a preference ordering for the set of alternatives. For any
> individual, his or her preference ordering is such that given
> any two alternatives x and y, the individual either prefers x
> to y, y to x, or is indifferent between them (completeness). For
> any individual, if that individual prefers x to y and y to z,
> then he or she prefers x to z (transivity).
>
> The profile is the set of preference orderings for all individuals.
> A constitution assigns to each profile a social ordering for
> alternatives in an opportunity set (e.g., a set of alternatives).
>
> Consider the following conditions:
>
> U. The constitution is defined for all logically possible
> profiles.
>
> I. (Independence of Irrelevant Alternatives) Let S be a
> set of alternatives. Two profiles which have the same
> ordering of the alternatives in S for every individual
> determine the same social ordering for alternatives
> in S.
>
> P. (Pareto principle) If every individual prefers x to y,
> then x is preferred to y in the social ordering.
>
> D. The constitution is not a dictatorship, where a dictatorship
> is DEFINED to be a constitution in which there is some
> individual whose strict preferences are the social preference
> according to that constitution.
>
> Theorem: There is no constitution satisfying conditions U, I, P,
> and D.
>
> 2.0 COMMENTS
>
> This use of the term dictatorship differs from common usage. If
> some individual always happened to vote for the winner, he might
> be a dictator in Arrow's sense. However, he would not be imposing
> his will on society with guns or whatever.
>
> I think utility theory and methodological individualism do not
> describe how people behave. Therefore, I don't hold out much hope
> for social choice theory, as little as I know about it, to describe
> or predict actual behavior. I think, though, that it might still
> be useful in exploring logical possibilities when comparing and
> contrasting voting systems such as proportional representation,
> winner-take-all, at large districts, regional districts, etc.
>
> I don't know that social choice theory addresses what to me is
> an important characteristic of democracy since the Greeks -
> discussion in the public square. Peope can debate, outline
> the consequences of decisions to one another, persuade, and
> then come more-or-less to a consensus. One can imagine such a
> process happening in democratically run firms. One can imagine
> such happening in some sort of federal assembilities consisting
> of representatives elected from each firm, industry, profession,
> region, or whatever.
>
> Capitalist corporations do not provide workers with any
> instutionalized mechanism of debating and voicing their
> opinion. They are dictatorships. This seems so self-evident
> to me that it does not need argument. If you want some
> discussion, I suppose you can read Hirschman on voice and
> exit.
>
> There have been lots of organizations operating in the kingdom
> of necessity that foreshadow what might be possible. Apparently,
>
> "a cluster of market co-ordinated, worker co-operatives has
> endured for decades in the Mondragon district in Spain."
> -- Geoffrey M. Hodgson, op. cite.
>
> --
> Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/Bukharin.html
> r c
> v s a Whether strength of body or of mind, or wisdom, or
> i m p virtue, are found in proportion to the power or wealth
> e a e of a man is a question fit perhaps to be discussed by
> n e . slaves in the hearing of their masters, but highly
> @ r c m unbecoming to reasonable and free men in search of
> d o the truth. -- Rousseau
--
John Conover, john@email.johncon.com, http://www.johncon.com/