[EM] L1 distance, Condorcet, etc [Ossipoff]

[Warren Smith]

>Ossipoff:
Say there’s a candidate at the multidimensional median point. As Warren 
said, s/he is the CW.

--WDS: false.  Ossipoff was wrong. I, in agreeing with him, was also wrong.

>Ossipoff:
Starting from the CW, say we move some distance from the CW, in a direction 
parallel to one of the axes by which we measure city-block distance. By 
moving in that direction from the median candidate, we’re moving away, by 
city-block distance, from the CW, and from everyone on the other side of the 
CW--that entire half of the candidates who are on the other side of the CW, 
in the dimension in which we’re moving. Of course we’re also moving away 
from everyone whom we’ve passed while moving. Now, say, from there, we move 
in direction perpendicular to the one in which we initially moved. Again, by 
city-block distance, we’re moving away from the CW, and from the half of the 
candidates who are on the other side of the CW, and from everyone whom we’ve 
passed, in the dimension that we’re now moving. In both of those moves, 
we’re moving away from more voters than we’re moving toward, by the same 
distance.

Maybe that isn’t rigorously-stated, and maybe, taking more time, I could 
word it better. But it seems convincing

-WDS:
your "proof" is wrong.

A counterexample to both the claim and the proof, is collected (with other coutnerexamples)
here
   http://rangevoting.org/BlackSingle.html#condmyth

Also, Ossipoff in his original post did not have the assumption
"say there's a candidate at the multidimensional median point".
He had claimed it was simply true without that asumption.  But either way, he was wrong.

Bottom line:
L1 distance has nothing good to do with Condorcet winners.
L2 distance is in fact more related than L1 distance, far as I can see.
I agree with Ossipoff L1 distance is better, and therefore I conclude that Condorcet 
methods are worse than they had appeared based on L2 distance.  IEVS will implment L1
distance soon and so we'll see.  Ossipoff in trying to make an argment
for COndorcet methods exactly failed.

Warren D Smith
http://rangevoting.org