# [EM] Meaning of preference

Sat Feb 21 20:07:02 PST 2004

```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

```