[EM] Re: Utilities?

[Steve Eppley]

Hi,

I haven't had time to read all the messages on the topic
of utilities and cyclic preferences, so I apologize if
anything I write here is redundant.  But I think it's
important to clarify the misimpression I may have left
regarding Rod Kiwiet's poll that *may* have revealed 
some voters had cyclic preferences.  And while at it,
I may as well post what I wrote in response to the
other portion of Jobst's reply...

Jobst wrote:
> Steve 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.

Does Jobst mean a common price everyone must pay, 
as in competitive markets?  I assume he doesn't.

How will a voter behave if he places no price on some 
alternatives yet is only allowed to vote as if he does
place a price on each alternative?

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

Here's a bit more detail.  Suppose a voter not only has
the preference order A > B > C, she also is indifferent
between the following two lotteries:

1. A has a 1/3 chance of being elected, and C a 2/3 chance.

2. B is elected with certainty. (A "degenerate" lottery.)

How should that be interpreted?  It's not what I would 
call a utility since it's not something that can be 
compared between voters, which is needed to identify 
the classical utilitarian social choice.  It does give
an idea of the voter's relative preference intensities--
her utility difference between A and B is apparently 
twice her utility difference between B and C--but I don't 
know that this information, even if sincere, has as much 
value for making social choices as some people believe 
it does.  For one voter, the difference between A and C 
could mean life or death.  For another voter, it might 
merely mean a tax refund of $400 or not.

By the way, I think it might be fairer to measure 
the prices in Duggan's bundles in terms of hours 
of community service the voter would be willing 
to perform, rather than in dollars he'd pay,
since our lifespans tend to be more similar than 
our financial assets are.  But even that would 
give an unfair advantage to the leisure class 
and retirees by penalizing people who are busy.

-snip-
>> 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.
> 
> 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?

I don't recall whether Rod mentioned those particular 
details, but he's a very thorough guy, so I doubt 
he would have neglected to allow the respondents to 
express equivalence or undecidedness. (It's possible
he lumped equivalence and undecidedness together.)

He did point out that the number of voters whose
preferences appeared intransitive was small enough
it could have been due to recording errors made by 
the polling staff.  I think it could also have been 
attributed to glitches by the respondents answering
too hastily, so I suggested to Rod that if he someday 
conducts a similar poll, he should consider providing 
technology to the polling staff to alert them immediately 
when a respondent expresses intransitive preferences, 
so they can ask the respondents to explain or amend 
their intransitivities.  That would also provide 
a check against some possible recording errors.

Jobst, does a person behave differently when forced
to choose between two alternatives about which he is 
undecided than when forced to choose between two he 
believes are equivalent?  Why should the distinction 
affect the design of the voting method?

I don't see anything clearly wrong with allowing
the voter to express intransitive and/or incomplete 
preferences, as long as the default ballot interface 
makes it as easy as possible for voters to express 
orderings.  For the few "irrational" voters who want 
to express intransitive or incomplete preferences, 
let them select an alternate interface that'll accept 
whatever they need to express.

--Steve