[EM] Fermat-Weber point

[Warren Smith]

>Rob LeGrand:
Perhaps a better generalization of median to higher dimensions is the
Fermat-Weber point, the point that minimizes the sum of the L2 distances
from it to each point.  (Average can be similarly generalized, minimizing
the sum of squared L2 distances.)  It always exists (of course) and is
unique unless you have an even number of collinear points and the middle
two are different.  It is also rotationally invariant.

--WDS:
my "nastier counterexample" has O = Fermat-Weber point, in 
addition to all its other nasty properties.  In the version
with a 9th voter exactly at O.