[EM] CW & SU

[Michael Ossipoff]

Ok, sure, it’s obvious (when my claim is challenged)  that, though a 
candidate at the voter median is the CW, it’s plausible that the CW needn’t 
be at the voter median: Suppose no candidate is at the voter median. Might 
not a candidate who is much closer (in some sense) to the voter median than 
any other candidate is be the CW?

And if the CW isn’t at the voter median point, it’s possible to suggest a 
scenario in which s/he doesn’t maximize SU: Maybe, though most voters are 
closer to X than to Y, those who are closer to X are far away, but those who 
are closer to Y precisely share Y’s position in issue-space. So, though X is 
preferred to Y by a majority, Y has more SU than X does.

But, with just one issue-dimension, when X is preferred to Y by more voters 
than prefer Y to X, I couldn’t make Y have more SU than X. Even if all those 
preferring Y to X share Y’s position, while those preferring X to Y are far 
away.

I could be worthwhile to find out if the CW can fail to maximize SU when 
there are more dimensions and candidates, and what that would take--what 
kind of voter-distribution it would take. Could it happen if the voters are 
normally distributed in each dimension, for instance?

Maybe Warren’s authors (you know, the ones he says have their heads up their 
ass) have answered that question. If Warren has their books or papers, and 
if they answer that question, and if their answer isn’t unfavorable to 
Warren’s position, maybe he’ll tell us their h.u.t.a. answer. <smiley>

In any case, though, if the a candidate at the voter median point is CW, and 
if, with city block distance, a candidate at the voter median point 
maximizes SU (as I’ve demonstrated here a few days ago), then at least that 
means that there’s some connection between CW and SU maximization. And  if 
the candidates tend to thickly populate the region of the voter median, as 
will probably be the case, that could make it more difficult for a candidate 
away from the voter median point to be CW.

The fact that the CW might not be at the voter median isn’t quite so bad 
when you consider that there might not even be a CW. At least one can say 
that, in spatial voting, the wv Condorcet methods will tend to do well by 
SU, even if one can’t make the stronger guarantee that I wanted to make.

Mike Ossipoff