[EM] With standard assumptions, CW is always SU, even with Euclidean distance.

[MIKE OSSIPOFF]

I defined two kinds of radial symmetry, and said that even with the weaker 
radial symmetry, the CW is always SU, even when Euclidean distance is used.

The weaker radial symmetry requires only that, for each ray from the center, 
there's a ray in the opposite direction from the center, along which the 
population density distribution is the same as on the original ray.

The usual, standard voter distribution in simulations has that weak radial 
symmetry. The standard assumption is that the voters are normally 
distributed with respect to each issue-dimension. That distribution has the 
weak radial symmetry.

So, with that standard assumption, the CW always maximizes SU, even with 
Euclidean distance.

And, if city-block distance is used, the CW maximizes SU. Period. No 
requirements.

Though SFC is the only one of the majority defensive strategy that mentions 
the CW, it's still true that all the defensive strategy criteria are about 
properties that make it easier to elect a CW.

Why is SU important? Say there's going to be an election at some time in the 
future. We don't know what the candidate lineup willl be, or what kind of an 
example it will be.  All we know is what method will be used.

The better the SU promise of that method is, the better your expectation for 
that future election is.

Mike Ossipoff

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