[EM] Social utility is more important than median utility

[Bart Ingles]

MIKE OSSIPOFF wrote:
> 
> But we maximize our utility expectation, or that of our descendants or 
> relatives, in that future election if we advocate a voting system that 
> does very well by social utility, the sum of the voters' utilities.
> 
> That's a good reason to judge methods by SU, and I claim that it's 
> completely compellling.

I think there is a need for SU as a standard, but wish I could find a 
rock-solid justification for translating unbounded individual utilities 
to a common scale before summing them, as is commonly done.  It seems 
useful to do so, since it's close to what an election method does 
anyway, but technically your future expectation should be maximized by 
summing the *unbounded* utilities (at least if all voters are equally 
likely to have extreme utilities some time in the future).


> If distances in issue-space are measured by city-block distance, then 
> the CW always maximizes SU in spatial models.
> 
> If distance in issue-space is measured by Euclidean distance, then the 
> CW maximizes SU under the conditions assumed in all spatial simulations.
> 
> If, for any line through come central point in issue space, the voter 
> population density distribution is the same in both directions along 
> that line from the central point, then, even with Euclidean distance, 
> the CW maximizes SU.
> 
> The condition in the above paragraph is met, for instance, if the voters 
> are normally distributed about a central point in each issue dimension, 
> as is routinely assumed in spatial model simulations.

This doesn't seem possible for more than one dimension-- don't Merrill's 
models show sincere Borda yeilding slightly higher SU than the CW in two 
dimensions, and Approval higher than both when there are only three 
candidates?

Bart