[EM] [OT] Kenneth Arrow theory... anyone?
phil.errembault at skynet.be
Sat Nov 22 04:39:01 PST 2003
I do not completely agree with Paul Kislanko analysis.
1/ The fact that there is 2 or more candidate has no importance, because at no time you are asked to sort them to more than two classes. So there are the candidates you like and the candidates you dislike, but at no time you have candidates you like more and others you like even more. In fact, you can see the problem as multiple question with yes/no answers. so there is no possibility of transitivity
2/ Nevertheless, The Arrow Impossibility theorem does NOT necessarily restrain to the way people vote, but can aslo be applied to the relation between collective decisions and what people THINK instead of what they VOTE. In this case, there is an implicit priority graph between people preferences, so the theorem IS applicable.
... BUT ...
As the collective choices of the group are proven not transitive by the theorem, the human preference graphs themselves are not transitive and can contain contradictions (cycles), and even will vary in time and according to the weather or other non-pertinent data; and this, mostly because human decisions themselves are resulting from contradictory pulsions, feelings and thoughts. SO you cannot ask a human democracy to respect constraints that human beings themselves will not respect.
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