[EM] [OT] Kenneth Arrow theory... anyone?
moore3t1 at cox.net
Fri Nov 21 18:38:02 PST 2003
--- In election-methods-list at yahoogroups.com, David GLAUDE
<dglaude at g...> wrote:
> [[Do you know that a multi-cultural society cannot be democratic?
> The Nobel Prize Kenneth Arrow mathematically showed, in 1952, that
> 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)]]
In the words of Wolfgang Pauli, "This is not right. It's not even wrong."
First, Arrow's theorem has nothing to do with "culture". Imagine a
county whose residents are all of the same culture. Now make them vote
to choose one of three sites for a toxic waste dump. How does their
monocultural society make this election immune from Arrow's theorem?
Second, "democracy" cannot be defined simply in terms of voting
systems. It is about consent of the governed, and giving the people a
voice in their government (which goes beyond merely having elections,
including the rights to speak, to assemble, and to petition the
government). Arrow's theorem is about social choice functions, not
Third, the theorem only gives a list of criteria and proves the
impossibility of meeting all those criteria. Whether those criteria
are necessary for a method to be acceptable to a democracy is outside
the scope of the theorem (and is in fact a philosophical question
rather than a mathematical one). For example, I think IIA (one of
Arrow's criteria) is not useful in determining the merits of a method.
Arrow also disallows an entire class of methods: those that do not
allow full ranking by individuals.
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