BPR-L Intransitives of Determination of Priorities

From: John Conover <john@email.johncon.com>
Subject: BPR-L Intransitives of Determination of Priorities
Date: Wed, 17 Aug 1994 20:31:52 -0700 (PDT)

John Conover wrote:

>> If all would be so kind, I would like to start a discussion on the
>> determination of priorities in the business environment. Specifically,
>> I would like to address the work done by the economist Kenneth
>> Arrow[1][2][3] in 1952 (using game theoretic methodologies) on the
>> intransitive nature of the determination of priorities in
>> groups. Although his original work was focused on the determination of
>> national economic priorities, the formalities are extensible into the
>> corporate environment. I would like to discuss the relationship
>> between the determination of corporate priorities, and BPR, in view of
>> the implications of Arrow's work.


> I'm not familiar with Arrow's work, but my gut reaction is to disagree that
> there are "no logical process that can be used for determination of
> priorities in groups."  There are logical processes; John named several.
> However, just because they may seem logical doesn't mean they are
> effective.


If you would be so kind, I would like to discuss this with you "off line"
from the BPR-L digests.

Quoting from, "Archimedes' Revenge," by Paul Hoffman, Fawcett Crest,
New York, New York, 1993, ISBN 0-449-21750-7, 213-262, Section IV,
entitled "One Man, One Vote," Chapter 12, entitled "Is Democracy
Mathematically Unsound?, pp 292"

        Arrow's demonstration, called the impossibility theorem (since
        it showed, in effect, that perfect democracy is impossible),
        helped earn him the Nobel Prize in economics in 1972. Today,
        the fallout from Arrow's "devastating discovery," one of the
        earliest and most astonishing results in game theory, is still
        being felt.

The reason that a "perfect democracy" is impossible is that there is
no way to place determination of priorities on a logically consistent
foundation. "Games and Decisions," by R. Duncan Luce and Howard
Raiffa, John Wiley & Sons, New York, New York, 1957, 327-370, Chapter
14, entitled "Group Decision Making," goes on for 43 pages to
formalize this (in case you have insomnia.)

Note that these do NOT state that democracy won't work, and they do
NOT state that groups can not arrive at strategies and tactics and do
decision making. What they do state is that there exists no logical
process by which groups do such things. (Hoffman goes through a
simple, illustrative, 3 person scenario that must decide on which fast
food restaurant that the group will eat lunch at-complete with formal
decision trees.)

According to Kenneth Arrow, in "History of Mathematical Programming,"
edited by J.K. Lenstra and A. H. G. Rinnooy Kan and A. Schrijver, CWI,
Amsterdam, Holland, 1991, ISBN 0-444-888187, 1-4, entitled "The
Origins of the Impossibility Theorem," by Kenneth J. Arrow, he was not
the first to prove this (although his proof is nice, compact, and
general.) It was first proven by the political philosopher and
probability theorist, Condorcet, in 1785, and was promptly
forgotten. (Although, there is some speculation that those attending
the Constitutional Convention were aware of the issues, since some of
the axiomatic methodology used in the U.S. Constitution addressed the
issues of determination of priorities, eg., balance of power, etc.,
which were new for the time, and, obviously clearly understood by the
authors of the Constitution.)  It was rediscovered again by Duncan
Black in the Journal of Political Economy, and promptly forgotten. It
was then, again, rediscovered by Abram Bergson in a 1938 paper, where
he described the "social welfare function," and forgotten, until the
works by Arrow.



John Conover, john@email.johncon.com, http://www.johncon.com/

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