[EM] Re: Utilities?

[Jobst Heitzig]

Dear Steve!

you wrote:
> When I audited a social choice theory class taught by John Duggan two
> years ago, he made no mention of utilities, only preference orders,
> until I asked about it.  He replied that he prefers to think of 
> utilities as preference orders on a "wider" set of options.  For
> instance: 1. A preference order regarding bundles, where each bundle
> combines an alternative with a price each voter would have to pay if
> that alternative is the one elected. 2. A preference order regarding
> lotteries, where each lottery gives each alternative a probability in
> the range [0,1] of being the one elected.

The first example sounds familiar to me, and this kind of arguing is
exactly what I'm criticizing: There is not always a measurable
real-valued "price" of each option or candidate.

However, the second example sounds very interesting since it makes no
reference to prices. Could you explain that in more detail?

Commenting a statement of mine, you continued:
>>> If it could, people would always have complete preference orders,
>>> which they don't.
> 
> -snip-
> 
> Why "always?"  Can't some or most voters have nice preference
> utilities, making it a useful concept?

I'm sorry here for not having made my point more clear. I'm not someone
who neglects that *some* voters might have preferences with whatever
mathematically desirable properties you like (like completeness,
antisymmetry, acyclicity, transitivity, cardinal utilities or whatever).
 Quite contrary, one of my most serious points is that we must not
assume that *all* voters' preferences have any of these properties! Most
people on the list seem to agree that we must not assume that
preferences are antisymmetric since there are voters who consider two
candidates equivalent. But also we *must* *not* assume that preferences
are *complete* as long as there are voters who cannot decide upon every
pair or want to abstain for some pairs. And we *must* *not* assume that
preferences are *acyclic* as long as there is evidence that people can
have cyclic preferences. Also, we *must* *not*  require all voters to
express a utility function when only some of them have one! (James
proposes "default" ratings for voters who don't express ratings. To me
this is almost as ridiculous as if one would suggest to order the
unranked voters of a truncated ballot in some default way... When I
don't express ratings then I don't want someone to "guess" them.)

So, my point is simply to allow each voter to express each binary
preference s/he has without forcing her/him to express any preference or
utility or approval or whatever thing s/he does *not* have! Almost all
of the methods discussed on this list can easily cope with this
information...

> Last year, Rod Kiwiet polled likely voters in California on their
> preferences regarding pairs of the 4 candidates most likely to win
> the Gray Davis recall election.  That is, each voter was asked for
> his preference in 6 pairings.  Most voters (about 90%? I don't recall
> the figure) responded with transitive preferences.  According to Rod,
>  no one had ever previously bothered to test the assumption that
> voters' preferences are consistent with orderings.
> 
> --Steve

That is interesting too since it shows that 10% don't have even
*transitive* preferences, which is a far more intuitive property than
completeness! I guess that his respondents had only the choice to select
A>B or B>A for each pair, but did not have the choice to express A=B
(equivalence) or "A?B" (undecidedness), am I right? So he did not test
antisymmetry or completeness, but only transitivity? Could you give more
details here, too?

My best, Jobst