[EM] Andrew: Sincere methodsd

[Jobst Heitzig]

Dear Mike!

Although I don't believe in measurable individual utilities in the first
place, here's some thoughts on the even more questionable notion of
"social utility":

In replying to Andrew, you stated a seemingly trivial truth:

> That's CR. If voters have no wish to maximize their own utility expectation, 
> and only want to rate truly in order to maximize social utility, then CR is 
> what maximizes social utility.

But that depends heavily on how you choose to define "social utility".
You seem to take for granted that social utility should be measured by
the sum, or equivalently by the arithmetic mean, of the individual
utilities. But there is absolutely no reason to believe that this is a
good measure of social utility!

I suggest to see this as a problem of descriptive statistics: You want
to summarize an unknown distribution (that of the true individual
utilities) by using some statistics of the empirical distribution (that
of the expressed individual utilities), and this statistics you call
"social utility" then.

Welfare statistics, for example, usually measures the "mean" income not
by the arithmetic mean but by the median or some other quantile of the
income distribution, in order to avoid giving the high incomes to much
weight.

The median is a simpler, more accurate, and more robust measure of
social utility than the sum! It has the additional advantage that we
need not assume that utilities possess an additive scale. (Perhaps it
corresponds to the "median voter theorem" for single-peaked
one-dimensional preferences in some way?)

I would even go so far and suggest to use an even lower quantile to
measure social utility, since the goal to get "the most utility for the
most people" implies that it is more important to give some additional
utility to the many who possess few instead of giving much additional
utility to the few who possess much already.

So I suggest to measure social utility by the LOWER QUARTILE of the
individual utilities (= that utility value where one quarter of the
voters is below and three quarters of the voters are above).

Perhaps this will even make CR a somewhat more strategy-resistant method
since we use a much more robust measure of social utility.

Yours, Jobst