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

David GLAUDE dglaude at gmx.net
Thu Nov 20 16:55:02 PST 2003

```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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