[EM] Meaning of preference

[Ken Johnson]

election-methods-electorama.com-request at electorama.com wrote:

>Message: 1
>From: "MIKE OSSIPOFF" <nkklrp at hotmail.com>
>To: election-methods-electorama.com at electorama.com
>Date: Mon, 16 Feb 2004 06:59:26 +0000
>Subject: [EM] Meaning of preference
>
>...
>
>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.
>
>...
>
>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