[EM] More on city block distance, Condorcet winners, and social-utility maximizers

[Warren Smith]

Also, if you have voters distributed normally in multidimensions, then the candidate
closest to the center of the normal distribution in L2 distance
is both the utility-maximizer and Condorcet winner if utilities are decreasing functions of
L2 candidte-voter distance.

BUT that doesn't work in L1 distance.  (In fact that theroem is all about L2 distance and
not Lp distance for any other p.)   In this example,
the voter-gaussian has center at * which would be
L1-equidistant from A,B,C,D,E except B is moved very slightly closer to *
and D very slightly further.  Then E is Condorcet winner.
I think B is actually the Condorcet loser, but is the SU maximizer.

......................
.............C........
......................
...............E......
......................
.............*...B...
......................
...............D......
......................
.............A........


Warren D. Smith
http://rangevoting.org