[EM] Re: Utilities?

[James Green-Armytage]

>
>>>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! 

	I insist that it is, or at least, it is the question when one is talking
about serious public proposals. 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 your proposal has drawbacks relative to
other proposals, then you have to argue that the practical benefits
outweigh the practical drawbacks. If you cannot, then the other proposal
should be chosen instead.

>Why the hell should we *assume* some
>strange property whithout any need whatsoever? 

	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. 
	Again, if you are interested in the theory of acyclic ballots, I welcome
your efforts. But I don't think that you should use it as a criticism of
other methods as serious public proposals, that they don't allow for
acyclic preferences... I just don't think that there's too much to be
gained from that, and you haven't convinced me otherwise. 
	Simply arguing from the standpoint of free-form voter expression is not
sufficient for me. Ranked and rated ballots seem eminently useful to me,
and I don't think that we will be committing a grave voting rights
violation by limiting voters to such formats. I think that they surely
beat the heck out of plurality ballots when it comes to fullness of voter
expression.

>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? 

	Do you mean a ranked ballot? A ratings ballot? I think that it's a pretty
big overstatement to described either ranked or rated ballots as ignorant
in design.
	Why is it important to use ranked ballots rather than individual
preference pairs? Well, on the one hand, it's vastly easier when the
number of candidates is large. The formula for the number of pairwise
comparisons is (n(n-1))/2. So, with 10 candidates, it's 45 pairs. With 20
candidates, it's 190 pairs.
	Also, I don't know that single transferable vote proportional
representation methods can cope with cyclic ballots, so that may limit the
application to single winner voting.
	Also, I have to imagine that allowing such disjointed preference
relationships would allow some even more unwieldy strategic possibilities.
If my sincere ordering is A>B>C>D, what might it mean that I have the
ability to vote A>B, A>C, A>D, B>C, C>D, and yet D>B? Might this make it
easier for me to use burying strategies against candidate B? Since you're
the advocate of cyclic preference ballots, I'd rather leave the burden of
proof on you, to demonstrate that there are no extra strategic
possibilities with cyclic ballots. Maybe you don't accept that burden
though...
	Anyway, it's not like I passionately hate the idea of cyclic ballots. I
mostly just think that it's an unnecessary hassle, and may present more
strategic possibilities than we will want to deal with. 
>
>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.

	Nobody has to vote in the first place; they can abstain from the whole
thing if they want. Other than that, they can leave candidates tied, which
saves them from having to make a decision as to which one is better. I do
think that it is important to allow ties. If you don't rank someone, the
convention is that they're tied for last place. You could also do a
variation of this where you can quickly throw candidates you really hate
(like Bush) behind the mass of candidates whom you have left unranked. A
lot of voters might find this helpful.
	There's also the no opinion option, which allows you to leave a candidate
out of your rankings altogether, such that your ballot doesn't count for
or against that candidate in any pairwise comparison. I don't like this
for public elections, because I want candidates whom many voters have no
opinion about to be at a distinct disadvantage, but for other purposes it
can be useful.
	So, I don't see a problem here.
>
>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? 

	"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.

>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?
>
	No, not exactly. The point isn't necessarily to avoid strategy
altogether. The point is for strategy to tend towards equilibrium rather
than disequilibrium. Defining equilibrium is another question. Equilibrium
could be a sincere CW, or perhaps a candidate with very high utility
(read: very well-liked) across the board... Perhaps I would also like to
think of equilibriums where no candidate is sincerely unbeaten, but one
candidate's beat consists mostly of people who are relatively sympathetic
to that candidate anyway... which is the idea of weighted pairwise under
sincere voting. Disequilibrium could be when somebody other than a sincere
CW wins, or someone who is very widely disliked. Perhaps it happens as a
result of a strategic action, a state of confusion, or a misguided tally
mechanism.
	Anyway, the plan is to set a definition of equilibrium, and then to
design a method which generally tends toward that equilibrium given most
(hopefully almost all) sets of sincere preferences (including strengths of
preferences).

my best,
James