[EM] Re: Utilities?

[Jobst Heitzig]

Dear James!

Why do you try to give the impression that I want to introduce something
strange? It's all only about giving voters the freedom to answer the
question whether they like A better than B independently from their
answer on the question whether they like B better than C!

I did never suggest that voters should be *forced* to answer n(n-1)/2
questions. All my arguments are *against* forcing voters to do anything
they don't want. Of course they must also have the possibility to make
just one checkmark for their first choice when they have a first choice
and don't want to express more preferences! Or to make several
checkmarks when they have a preferred set and only want to express that
they prefer these to all others! Or to give a ranking when they have
one. Or to answer each pairwise comparison separately if they want to.
Just as they like!! But this is of course only a question of ballot
design (if interested, look at the ballots at www.groucho.info).

You wrote
> If you want to go ahead and
> experiment with cyclic ballots in the theoretical realm, I say sure,
> have fun. It's not a bad project or anything from the standpoint of
> general curiosity and mathematical interest. But if you want to make
> a serious public proposal, you have to argue that the differences
> between your proposal and other proposals has a substantial practical
> benefit. 

If you want to go ahead and experiment with *acyclic* ballots in the
theoretical realm, I say sure, have fun. It's not a bad project or
anything from the standpoint of general curiosity and mathematical
interest. But if you want to make a serious public proposal, you have to
argue that the assumptions you made theoretically are indeed fulfilled
by *all* of your voters (we still want to have equality of voters, right?)

> Why should we assume that voters have acyclic preferences? I don't
> know how hardcore my assumption of this is, but it does make sense to
> me, and I don't see a need to take its negation into account when
> doing election methods design for public use. It's not that I'm sure
> that acyclic preferences are impossible; I just don't think that
> they're especially important or worth worrying about. 

Sorry, but this is completely wrong. I don't assume anything. You do.
How can we assume that some voters' preferences are not important???

Concerning incomplete preferences, you wrote:
> Nobody has to vote in the first place; they can abstain from the
> whole thing if they want. 

So again you want to force them to abstain from the whole thing when
they have the preferences A>B and C>D but no preference between either
A,C or A,D or B,C or B,D? Well, that's not very liberal... :-)

As to how ratings could be defined, you wrote:
> "Rate the candidates on a scale from 0 to 100. 100 is a candidate you
>  like the most, 0 is a candidate you like the least. 50 is a
> candidate such that you prefer this candidate over a 0 candidate
> about as strongly as you prefer a 100 candidate over a 50 candidate."
> etc.

So, what would my ratings be when I prefer K to B much more than I
prefer D to K? Would they be D 100 > K 90 > B 0, or perhaps D 100 > K 95
 > B 0 or D 100 > K 80 > B 0? WHO CAN TELL?

Cordially,
Jobst