# [EM] More CWs who maximize SU with more than 1 issue-dimension

MIKE OSSIPOFF nkklrp at hotmail.com
Tue Jan 27 00:07:01 PST 2004

```Yesterday I defined a kind of radial symmetry, in which the voters'
population density distribution is the same along every ray leading from the
center of the distribution.

But it seems to me that I've heard a weaker definition of radial symmetry:
It requires only that for every ray leading from the center, there's another
ray leading from the center in the opposite direction, along which the
population density distribution is the same as on the original ray.

It seems to me that if voters have even that weaker radial symmetry, the CW
is always the SU maximizer.

I'd said that maybe, if there's a point that's median with respect to all
the space's dimensions, the CW is SU maximizer.

What I meant by "median" there is: Say the issue space has N dimensions. An
(N-1)-dimensional section through the issue-space--I'll just call that a
section. If a section divides the voters into 2 equal parts, I'll call that
an equal section. If an equal section is made perpendicular to each of the
rectangular co-ordinate axes, and if they all intersect at a point, I call
that point the "median point".

So I'd said that maybe if there's a median point, then the CW will be SU
maximizer. I don't think that there's a CW at all if there isn't a median
point, when we're looking at it in terms of rectangjular co-ordinates, so
I'll drop the wording "If there's a median point".

I found an example in which, when Euclidian distance is used, the CW seems
to not be SU maximizer.

But if city-block distance is used, then the CW is SU maximizer.

You may prefer city block distance, or you may prefer Euclidian distance.
But there's no compelling case for one over the other as the only meaningful
distance measure.

What that means is that there's a meaningful sense in which the CW will
always be the spatial SU maximizer, even with issue-space with more than 1
dimension.

And I claim that it's unfair to invoke non-spatial disutility, because, as I
was saying, there's no reason to believe that, in a wv election, an
unpopular, unknown, or non-committal candidate would have the voter-median
position all to himself.

The claims in this posting are from a brief glance at the subject.
Conclusions from a brief glance are sometimes incorrect, but these seem
right. If you look it up, you'll probably find that these statements are
correct. Maybe some here can comment on the accuracy of these statements. If
one or more of them isn't correct, then I'd be glad for someone to mention
that.

Mike Ossipoff

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