From: John Conover <john@email.johncon.com>
Subject: Re: Intransitives of Determination of Priorities
Date: Fri, 26 Aug 1994 21:07:05 -0700 (PDT)
David Rader writes:
>
> There is related work on a variety of voting schemes (I remember
> a Scientific American article from some number of years ago) and
> on the use of "markets" to auction (buy) the firm's resources to
> conduct a project (Return on investment, net cashflow, etc are
> one form of these auction models as is the widely practiced, but
> not acknowledged, "position power points" model -- "whatever the
> boss wants...").
>
Hi David. Yea, there was also some work done, also, by the fuzzy logic
theorists, but they openly admit that the paradigm is based on
transitive priorities.
>
> I think the way to interpret this Theorem is that there is no formal
> logic which is guaranteed to generate a provably "best" outcome.
> However, given that the group will indeed take some action, there
> are processes which will help the group function effectively (including
> selecting a course of action).
>
Yea, but many theorist assume a stronger position. Their
interpretation is that the concept of ordering priorities (which I
guess includes a "best" order) makes no sense.
>
> Again, I think this is an extreme interpretation of the Theorem. I see
> it as another form of Godel's Theorem, Heisenberg Uncertainty and work
> by Turing (I think) -- all related to the ultimate unpredictability of
> complex systems (and firms are certainly complex). "Logically", if I
> cannot predict the results of my choices, how do I make good choices?
>
Actually, it is more serious than that. Not only can priorities not be
ordered, but if you have a formal process that attempts to order them,
it can be abused since there is no way of proving what the best order
is. Specifically, the concept of "insincere voting" in the congress
was addressed by Arrow and found (empirically) to be so widespread
that it could almost be called a modus-operandi. This is where it is
assumed that everyone will vote according to the priorities as they
see them, but in reality, they vote so as to manipulate the outcome of
the process, (eg, I may want something I know is going to loose as 1st
priority, therefore I vote my second priority as my 1st priority
because I know that a lot of my contemporaries support that-ie., we
can actually make the second priority the 1st priority.)
Unfortunately, the outcome of such things is often that everyone can
get their least desirable priority, at least in principle. The 1956
House vote on a bill calling for federal aid for school construction
was a case in point.
An amendment was offered that would provide federal aid only to states
whose schools were integrated. The House was essentially divided into
three interest groups: Republicans, northern Democrats, and southern
Democrats. The Republicans, being against federal aid but in favor of
integration, favored no bill at all but preferred the amended bill to
the original. The northern Democrats favored the amended bill but
preferred the original to no bill. The southern Democrats, being from
states with segregated school, favored the original bill but preferred
no bill to the amended bill. On the ballot on the amendment, the
Republicans provided the winning votes, with the northern
Democrats. But on the second vote, between the amended bill an no
bill, the Republicans joined forces with the southern Democrats to
defeat the amended bill. The paradox here is that in the absence of
the amendment, in a straight vote between the original bill and no
bill, the original bill would undoubtedly have won! As William Riker
("Mathematical Applications of Politcal Science,") points out "As if
it were not enough that the choice may depend on the voting order,
this fact can be used to twist the outcome of the legislative
processes."
>
> The answer is that one should not "predict the future", one should
> "create the future" (this is a paraphrase of another famous and more
> capable thinker than myself).
>
The future was not only predicted by the Republicans in the above
vote, it WAS ordained by them-yet they were a minority!!!! Let me
state that I am not against Democracy, (the game-theoretic analysis of
the more structured social systems, like communism, socialism, etc.,)
is even more damning. The issue is that we assume that we can make it
work in a systematic fashion, which Arrow's work says we can't. Note
that Arrow does not say that Democracy won't work, simply that it
won't work in a systematic, logically consistent fashion.
>
> I see the central problem with groups as one of leadership. What is
> the role of the leader in the group. I have found groups very good
> at generating ideas so I use them for completeness in assessing problems
> and brainstorming options. However, I find groups very poor at doing
> analysis or breaking rules. I prefer to identify a leader who will
> paint a picture of the future and build "consensus" with the group
> members on the path to achieve it.
>
I tend to agree with you, but some of the military folks in BPR-L
would take issue. They are trying to get away from the leadership
issue because it leads to the "leader syndrome," which is roughly,
what they would call, "cowboy management." As far as consensus is
concerned, I personlly tend, again, to agree with you. However, as one
pundit stated "compromises between two alternatives are a prescription
for mediocrity-you will do neither alternative well."
Thanks for the comments,
John
--
John Conover, john@email.johncon.com, http://www.johncon.com/