[EM] Absolute Utilities

Forest Simmons fsimmons at pcc.edu
Mon Apr 30 15:52:56 PDT 2001

(See my comment below Craig's message.)

On Mon, 23 Apr 2001, LAYTON Craig wrote:

> Martin wrote:
> >Other people might suggest electric shocks, or amounts 
> >of cash.
> I like the sound of electric shocks.
> >I'm not advocating this - but that's how I'd measure Absolute (though 
> >not all sincere) utilities for non-factual issues. Myself, I'm sticking 
> >to the concept of normalised utilities, and I'll rashly claim that, in 
> >the absence of any other information we might be able to obtain, that 
> >normalised sincere utilities are the best estimate of absolute sincere 
> >utilities.
> >
> >In other words, the aim for me is to maximise ASU, but this isn't 
> >remotely possible, because you can't collect the info. Maximising 
> >normalised SUs is possible, and it's as close to ASU-maximisation as we 
> >can get.
> I agree.  My question was, if we could measure absolute utilities
> accurately, should that measure be used as an indicator for how good
> election methods are?  If you think that election methods should be measured
> by normalised SUs, then you should have to answer yes to that question.
> My other point was that the acknowledgement of the existence of absolute SUs
> leads to an understanding that the "worst case" scenario is equally as bad
> in all election methods, in the real sense of how happy people are with the
> outcome.

Suppose that we could measure absolute utilities, and that statistical
analysis showed that absolute utilities had a Cauchy distribution with
probability density function

f(x)=1/Pi/(1+x^2) .

Then average utility as a measure of best candidate would be nonsensical
(if not intellectually dishonest) since random variables with a Cauchy
distribution have no well defined expectation (i.e. mean or average)
because the defining integrals do not converge. At a practical level this
means that the outliers would dominate the averages. 

By way of contrast, every random variable has a median value, and the
sample median is an estimate of that value which is not sensitive to

Perhaps we should start investigating the use of utility medians as
standards of comparison. 

In CR every candidate has a median score. Suppose that candidates A and B
have median scores of x and y, respectively, with x > y.  In high
resolution CR this means that among ratings of A, more were above x than
below y. By way of comparison, among ratings for B, more were below x than
above y. This is pretty strong evidence to me that the group preference is
A to B, especially if both A and B were rated on all of the ballots.

When we use maximum expected utility as a measure of social utility, the
utilities of the upper end outliers (those with most to gain) receive
undue weight.

That's why the the median income of the country can go down while the
administration continues to pronounce the economy a success.  The mean
(average)  income rises because of the increase in number of
multi-millionaires, while the median income drops because of the general
degradation of the economy for the great majority of the people (the so
called "lower 80 percent").

Medians are more democratic measures of general utility than are means.

Economists like to use expected utility (means) because the theory is
cleaner mathematically that way, not to mention that results that serve
monied interests are more likely to get corporate funding. 


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