Date: Mon, 01 Mar 2004 18:36:33 -0800
From: Richard Moore <[EMAIL PROTECTED]>
...
Theorems are facts, not judgements, so it is incorrect to state that Arrow proved anything about a value judgement.
However, the theorem is based on a set of (unproved) premises that supposedly (according to Arrow's value judgments) characterize any reasonable voting system.
From: "[EMAIL PROTECTED]" <[EMAIL PROTECTED]> ...
But why did Arrow stipulate #1? (rank method)
Because it was necessary for his method of proof. ...
From: Bart Ingles <[EMAIL PROTECTED]> ...
Because he was interested in ranked voting systems. ...
Based on the preceding discussions, I infer the following:
(1) Arrow's theorem is based on an unjustified and (according to the theorem's conclusion) indefensible bias in favor of ranked methods.
(2) If the rank-method stipulation is removed, then the theorem's conclusion no longer applies - the remaining premises defining Arrow's desired criteria are mutually consistent, with CR and Approval providing examples of methods satisfying the criteria.
(3) The popular characterization of Arrow's result as demonstrating the inadequacy of ANY voting system is patently false and either uninformed or intellectually dishonest. (The March Scientific American article, "The Fairest Vote of All" exemplifies such a characterization.)
Most people (but not those reading this post) have the intuitive notion that plurality voting is a perfectly reasonable method , even though the method is fundamentally flawed when more than two options are on the ballot. Perhaps Arrow's theorem is giving us a hint that our intuition about the superiority of rank-based majority rule could be similarly flawed.
From: Eric Gorr <[EMAIL PROTECTED]>
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As an almost off-topic side note, there was a story by Asimov, I believe, in which statistical analysis had become so advanced that a computer was able to select a single citizen who simply would, whether they lied or not (for such things were taken into account), select the winner who would have won had everyone been allowed to vote.
This is reminiscent of something I read once about the electoral college. Proponents of the electoral college have argued that it increases individuals' "voting power", but someone once pointed out that the best way to increase "voting power" would actually be to randomly select one voter and let them decide the election.
Ken Johnson
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