[EM] [OT] Kenneth Arrow theory... anyone?

[Paul Kislanko]

This is a terrible example of taking something out of a valid context and
mis-applying it in a different context. It is in the same category as the
arguments that Heisenberg's Uncertainty Principle says there can be
communication with the dead (it doesn't). What Kenneth Arrow proved in his
doctoral dissertation was that when there are more than two choices and more
than one voter it is impossible to devise a method that unambiguously
determines the group prefence from individual preferences in a manner that
satisfies certain specific criteria.

The leap from that to "there can't be a democracy in a pluralistic society"
is groundless. For one thing, any time it happens there are only two
choices, there IS an unambiguous method that satisfies all of the criteria.
Also, every practical method used or proposed to promote democratic
elections involves replacing one or more of Arrow's very general criteria
with different, more specific criteria that many would agree result in a
"democratic" election. Many of those involve mechanisms for reducing the
number of candidates to two, in which case there can be no paradox.

As to your specific questions:
* - I haven't heard of an extremist party using this argument, but the only
"extremist" views I'm usually exposed to are the Approval/anti-approval
folks (grin) --- I'm tempted to mention the US Republican Party, who haven't
stated this view but sometimes act like they believe it....
* - Yes, part and parcel of Arrow's proof is that if you define "perfect" a
certain way, there can't be one. Others have gone farther and shown how to
develop such examples for any given criterion.
* - I don't have a "title", but anyone who knows basic logic can see that
there's no correlation between a theorem about "more than two choices" and
whether there can be a democracy, since a trivial counterexample (for these
two choices can a pluralistic society choose one democratically? = yes)
shows the conclusion to be false.
* - Dr. Arrow was in the Stanford online directory last year, and was kind
enough to answer questions.
* - There is no question as to whether the proof is valid - they don't give
Nobel prizes for conjectures, and the prize was awarded over 20 years after
publication (as is somewhat usual). See
http://almaz.com/nobel/economics/1972b.html


-----Original Message-----
From: David GLAUDE <dglaude at gmx.net>
To: Election-methods at electorama.com <Election-methods at electorama.com>
Date: Thursday, November 20, 2003 6:54 PM
Subject: [EM] [OT] Kenneth Arrow theory... anyone?


Hello,

I am back to you with something that could be out of topic...

A extreme right wing party (more likely racist) did produce a small text
reproduced below: (original in french first... then approximated
translation).

<<Savez-vous qu'une société multiculturelle ne peut être démocratique?
Le prix nobel Kenneth Arrow a démontré mathématiquement, en 1952, qu'il
n'y avait pas de démocratie possible via un système de vote (théorème de
l'impossibilité), sauf si les électeurs partagent une même culture et
des valeurs proches (prix nobel Amartya Sen)>>

[[Do you know that a multi-cultural society cannot be democratic?
The Nobel Prize Kenneth Arrow mathematically showed, in 1952, that there
was no possible democracy via a voting system (theorem of
impossibility), except if the voters share the same culture and close
values (Nobel Prize Amartya SEN)]]

A friend of mine is trying to rebute that statement and gather as much
information as possible on this topic.

He did try to explain to me what he found.
Assuming there are 3 topics on wich to spend the budget: A, B, C.
And when citizen get ask (> = is more important)
33% find A > B > C
33% find B > C > A
33% find C > A > B
Then we have a (basic) problem.
The theorem would be related to that???

So I have a few questions:
* Do you know of any other extremist party using that argument and
making reference to Kenneth Arrow?
* I remember reading that there are no perfect voting system and that
given some realistic assumption on the goal and choosing a voting method
it is possible to create a set of ballot that will give "unexpected" or
"unsatisfying" result... is it true and related to the statement above?
* Would anybody (with some scientific title or experence to backup what
he say) willing to speak out and say... "This is a misunderstanding of
the theorem." with some explanation. (to be reproduced and publish on
the internet).
* Would that Nobel Prize be alive and ready to speak out and say that
his view on the topic.
* If that "mathematical proof" turn valid, would there be some
assumption that can be proven wrong or discuss enough to say that it
does not apply to the real world.

Thanks for your help anyway.

David GLAUDE




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