[EM] Re: Utilities?

[Jobst Heitzig]

James,

> 	I think that this is silly, 

Don't expect me to appreciate that... If I would think something someone
says on this list is silly (for example making unneccessary assumptions
about preferences) I would certainly not post such a comment.

> and that there are far more important voting
> methods problems to worry about than this. 

EXACTLY! Don't worry about cyclic preferences! I certaintly don't since
I know they are no problem at all for most serios methods we discuss
here! That's exactly my point! Don't worry what properties the
individual preferences might have that you might dislike or consider
silly, since those properties just don't matter at all! Exactly what I'm
saying all the time :-)

> I believe that I am getting
> towards the point where I have said all I can think to say about cyclic
> preferences per se, at least for the time being. 

Wonderful! Nobody asked you to evaluate them or to guess whether someone
has them. Just accept that they might occurr and go on with the
important things. Again, that's just my point...

> 	No ballot can perfectly express how voters feel about the different
> candidates. The purpose of the exercise is to get something that is a
> decent approximation, while being manageable and effectively functional.

How unanimous we are suddenly! We both know that all binary preference
relations are perfectly manageable!

> 	Again, it's an approximation. Most voters understand the concept of
> rating stuff on a scale from 0 to 100, and pretty much an rough indication
> of their relative preference strength (a gut reaction) will serve our
> purposes quite well. Over a large group of voters, these individual
> roughnesses will even out into a meaningful statistical pattern.

Sorry, but this is not about most but all voters.

> 	If you must have a more strict definition, though, I suppose you can
> continue my definition above via a thought experiment. Basically, you can
> define any rating in the scale through the use of halfway points.
> Candidate A at 100 is my favorite candidate. Candidate B at 0 is my least
> favorite. I can define 50 by making up an imaginary candidate C such that
> my preference strength of A>C is equal to my preference strength of C>B. I
> can define 75 by making an imaginary candidate D such that A>D is roughly
> equal in strength to D>C. And so on, with 62.5, 68.75, 84.375, and so on.

I am curious how voters will react to the suggestion of making up
imaginary candidates...

> 	By the way, if you like to make an issue of liberty in voter expression,
> I tend to think of cardinal methods as being more liberally expressive
> than ordinal, second-order ordinal, or explicit pairwise methods. Surely,
> there is a much wider range of possible expressions with a cardinal ballot
> than there would be with any of the above alone.

Ah, finally you get to the key point! Now we can go on without
misunderstanding, I think: I don't argue against giving voters the
*possibility* to express ratings. Nope. I argue against *requiring* them
to do so (and don't tell me that they can abstain from that since you
suggested to use some default rating in that case anyway!).

By the way, what do you think of my compromise suggestion?

Jobst