[EM] Re: Utilities? / terminology

[Jobst Heitzig]

Dear James!

James Green-Armytage wrote:
> Jobst Heitzig <heitzig-j at web.de> writes:
> 
>>And we *must* *not* assume that
>>preferences are *acyclic* as long as there is evidence that people can
>>have cyclic preferences. 
> 
> 
> 	Why are you so adamant about this point? In what situation do you think
> cyclic individual preferences would be important and meaningful enough to
> be worth paying attention to? You make it sound like a matter of life and
> death or something, for a voter to be able to express preferences such as
> (A>B, B>C, C>A). In what situation would this have any major practical
> benefit?

That's simply not the question! Why the hell should we *assume* some
strange property whithout any need whatsoever? Can you tell me why it is
so damn important to force people to distort their true preferences so
that they can fit a ballot someone ignorantly designed? I just can't
understand the whole attidute. I always try to be as liberal as possible
with voters opinions...

> 	By the way, if you don't want to look seriously at weighted pairwise
> because ratings are incompatible with cyclic preferences, I might as well
> point out that you can put a few candidates in a cycle with each other as
> long as you give all of them the same rating, and it wouldn't be a total
> contradiction with the WP method. I personally don't see it as a good
> idea, but it is a possible variation.

My orininal criticism of ratings had nothing to do with cyclicity. It
was about completeness, and I think you should at least admit that
people sometimes want to (and should be able to) abstain from some
decisions.

And it was about the non-existence of utility or, more practically,
about the non-definability of "rating". I mean, when we search for a
method which helps avoiding strategic voting then how can we require
voters to give some information they simply cannot determine in a
sincere way? What would you tell a voter a sincere rating is? When s/he
cannot determine the rating sincerey from his/her preferences, then how
do you think they will make up their ratings? Well, you gave the answer
yourself implicitly: they will use the possibility to express ratings in
a strategical way, which is exactly what we want to avoid, isn't it?

My best,
Jobst


PS:

1. Clarification of terminology:

Transitivity: A>=B & B>=C ==> A>=C
Quasi-transitivity: A>B & B>C ==> A>C
Acyclicity: never A>B>C>...>Z>A

Uncomparedness (i.e., "abstention"): A?B :<==> neither A>=B nor B>=A
Completeness (mathematically: totalness):
	no uncompared pairs, i.e. A>=B or B>=A for all A,B

Equivalence (i.e., a "tie"): A=B :<==> A>=B and B>=A
Antisymmetry: no equivalent pairs, i.e. never A>=B and B>=A


2. Some variant of a statement of yours:

In what situation do you think our unfounded assumptions about
properties of individual preferences would be important and meaningful
enough to be worth paying attention to?