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

[James Green-Armytage]

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

	Okay, let me clarify my position. I'm not trying to make an ontological
statement about individual utility functions. I just want a method which
allows voters to give a rough measure of the relative strength of their
various preferences. There are well-defined reasons why I think that this
is useful and important. I decided that the simplest, most intuitive, and
best way to do this is with a cardinal ratings ballot. 
	So my method (weighted pairwise) uses ratings. I probably made a mistake
by using the word "utilities" in my paper, because of course there is a
logical gap between expressed cardinal ratings and real utilities. So,
I'll go back and correct that when I get a chance.

>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.

	There is one method called the "demand-revealing process", aka the
"pivotal mechanism" proposed by Edward Clarke... I don't know if this is
what you're describing, but it is interesting anyway.
	Let's say that there are two mutually exclusive options A and B, which we
want to decide between. Voters come forward and say how much they are
willing to pay to get A, or how much they're willing to pay to get B. Then
you sum up the pledged amounts for both A and B, and select the one with
the higher total.
	Now we determine how much tax people will pay, if any. Let's say A beats
B, and the margin of victory is M. Any voter who pledged more than M for
option A is considered to be pivotal. For any voter who pledged an amount
N for option A, where N>M, that voter will have to pay a tax of N-M. This
was later named the "Clarke tax".
	This is an elegant idea which is rather perfect in theory, although I'm
not convinced that it would work in practice. 
	I believe that if you look at it logically, there is no individual
incentive for a person to either overstate or understate their valuation
of a particular option. In this sense, it is perfect. 
	However, if people are able to form collectives, then a distorting
incentive can appear rather easily, I think. Also, I think that it is
problematic to define utility in terms of dollars (not an uncommon
assumption in economics). There is a proposal to weight a person's pledge
in inverse proportion to their income, but I think that this is an
incomplete solution.

references:
1. Edward H. Clarke, "Multipart Pricing Of Public Goods: An Example," in
Selma Mushkin (ed.), Public Prices for Public Products, Washington: The
Urban Institute, 1972, 125-30.  
2. T. Nicolaus Tideman and Gordon Tullock. "A New And Superior Process For
Making Social Choices," Journal of Political Economy 84 (1976), pp.
1145-60.
>
>> If it could, people would always have complete 
>> preference orders, which they don't. 
>
>Why "always?"  Can't some or most voters have nice 
>preference utilities, making it a useful concept?

	I agree with this sentiment as it applies to cyclic individual
preferences. I'm not interested in methods that allow for cyclic
preference orderings. First of all, I don't think that they make sense,
but even if they did, I think that they would be sufficiently rare and
inconsequential as to be insignificant. I think that reporting preferences
along a one-dimentional spectrum helps voters to organize their
preferences between particular pairs. Tied rankings should be essentially
adequate for the expression of ambiguous preferences between a set of
candidates.
>
James