I erroneously stated (following Ossipoff, who had also claimed this) that a "trivial proof" would show that the location of the median voter (median in all dimensions simultaneously) would automatically be (if a candidate happened to be there) a Condorcet winner.
That's false. Here is a counterexample: o\xBxx|xxxxxxxxxxxxxxxx oo\xxx|xxxxxxxxxxxxxxxx ooo\xx|xxxxxxxxxxxxxxxx oooo\x|xxxxxxxxAxxxxxxx ooooo\|xxxxxxxxxxxxxxxx oooooo|xxXxxxxxxxxxxxxx oooooo|\xxxxxxxxxxxxxxx oooooo|o\xxxxxxxxxxxxxx ------O---------------- oooooo|ooo\xxxxxxxxxxxx oooooo|oooo\xxxxxxxxxxx oooooo|ooooo\xxxxxxxxxx ooCooo|oooooo\xxxDxxxxx oooooo|ooooooo\xxxxxxxx oooooo|oooooooo\xxxxxxx oooooo|ooooooooo\xxxxxx oooooo|oooooooooo\xxxxx In this picture, there are two candidates "O" and "X." O is located at the origin which is the median x-coordinate and median Y-coordinate of all voters. There are 10 voters in the quadrant labeled "A", all in the "x" region. There is 1 voter located at B, and one located at D. Finally, there are 10 voters in the quadrant labeled "C". The voters support X over O by 12 to 10. --- It is true, however, that IF a candidate is located at the all-way-median, and IF utilities are decreasing functions of L1 distance, THEN that candidate is the utility maximizer (albeit not necessarily the Condorcet winner). In conclusion, essentially everything Ossipoff has ever said about Condorcet winner vis-a-vis city block distance, has now been shown to be false and does not constitute any reason to prefer Condorcet methods. Warren D Smith http://rangevoting.org ---- election-methods mailing list - see http://electorama.com/em for list info
