[EM] What is the ideal election method for sincere voters?
scott at open-vote.org
Sun Mar 4 23:04:29 PST 2007
On Sun, 2007-03-04 at 23:41 -0500, Abd ul-Rahman Lomax wrote:
> Let's consider the method of deriving social utility from individual
> utilities to be a detail. There seems to be some general agreement
> that simple summing is not without value, but it is also clear that
> summation is a simplification and that some other function may be
> more ideal. However, political reality may intrude. Summation has a
> history, more complex functions don't, as far as I know.
This isn't quite true. There's a whole field of study in welfare
economics about different social welfare functions. "Indifference
Curves" are defined as the curves where the social utility function is
held at some constant - moving towards a higher indifference curve,
then, is a social improvement.
There are MANY possible indifference curves, however they all have a few
things in common. Imagine that we set my utility and your utility as
x-y axes, and then start plotting the social utility indifference curves
for some given social welfare function. By definition, these
indifference curves can't intersect (since that would mean some utility
combination of me and you has two different social utilities)
Anyway, for any reasonable social utility function:
*Moving away from the origin should put us on a higher indifference
curve (or at least keep us on the same one) - this is a pareto
*Indifference curves should be convex - ie, taking both our utilities
and averaging them should land us on a higher (or the same) curve.
There are likely a few others that I'm forgetting.
Anyway, there are two extremal indifference curves that meet these
criterion. The first one is simple summation, as you noted. Another is
taking the minimum of our two utilities - a so-called "Rawlsian"
indifference curve (Since Rawls was a philosopher who insisted that the
only way to judge societies was by their worst off.)
These two extremes serve as bounds for reasonable indifference curves
passing through a given point. There are an unlimited number of curves
between them, and some are even named by welfare economists. A good
example would be a hyperbola passing through the point we've selected.
> I don't think that Condorcet methods were developed to maximize
> utility; rather I think that the idea of the pairwise winner was seen
> as intuitively correct. In fact, if all voters are fully informed and
> aware of the general status, that is, the opinions and strengths of
> preference of others, Condorcet methods should actually be ideal.
> Range, however, is what collects this information more directly, a
> ranked poll only, sometimes, approximates it.
It's quite possible that Condorcet methods maximize a reasonable social
utility function, or that they at least do so "on average".
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