>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. ---- election-methods mailing list - see http://electorama.com/em for list info
