[EMAIL PROTECTED] wrote:
Message: 1 From: "MIKE OSSIPOFF" <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] Date: Mon, 16 Feb 2004 06:59:26 +0000 Subject: [EM] Meaning of preference
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A statement that some particular voter prefers X to Y is a statement of an order relation between X & Y, for that voter. For the purposes of my criteria, "prefer" needn't mean more than that.
Preferences needn't be transitive. The only requirement is that a particular voter can't prefer X to Y and Y to X.
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Mike Ossipoff
The theoriticians use the notation ">" for "prefers". In my view, this is not just an analogy - preference is, in fact, a quantitative relationship. A voter "prefers" X to Y if, based on the voter's personal value judgements, X is more acceptable than Y. To the extent that "acceptability" is quantifiable, preference is a quantitative relationship and is hence transitive. There is no need to introduce transitivity axiomatically.
From the above perspective, group preference can be defined by putting all the individual preferences on a common scale (e.g. ask the voters to rate each candidate's acceptability on a scale of 1 to 5), and define the group acceptability rating as the average of the individual ratings. It seems to me that the average rating satisfies all of the supposedly-inconsistent properties of Arrow's Theorem (someone tell me if I'm wrong) and is, in fact, the intuitive basis of these properties. For example, the group preference inferred from the group acceptability rating is automatically transitive, and it satisfies IIA in the sense that the group preference relationship between two particular candidates has no dependence on voters' ratings of other candidates.
One thing I've never quite understood - maybe someone could enlighten me - is what's wrong with Average Rating as an election method? Are there specific theoretical results or illustrative scenarios that demonstrate its inferiority to other methods?
Ken Johnson
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