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

Richard Moore 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 
about "democracy".

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.

  -- Richard

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