Utilities? (was Re: [EM] Re: river, ROACC)

[Steve Eppley]

Hi,

Jobst & James have been discussing whether it's reasonable 
to model voters' preferences as if voters have utility 
functions.  Jobst wrote:

> You would be right if I was to admit that there is 
> anything like a "utility function" -- which I do not: 
> I believe that it is absolutely misleading to think 
> the utility of an option could be measured in any way. 

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.

In another class, Dick McKelvey covered Groves' mechanisms, 
in which it's a Nash equilibrium (not a group strategy 
equilibrium, unfortunately) for each voter to reveal her 
sincere utilities.  The winning alternative is the one 
for which the sum of voter utilities is highest--the
conventional utilitarian notion.  A tax is imposed 
on each voter whose vote is pivotal, if any; just 
the right amount of tax that no voter would have an 
incentive to misrepresent utilities if all others 
vote sincerely. (I don't recall the simple formula 
for the amount of tax.)  Then the collected tax, 
if any, is destroyed.

> 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?

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