Forest: What do you mean by "the order of removal isn't important as along as you recognize that whenever you have two non-adjacent factions left, more symmetry reduction is possible."
I showed you with my example: 3:A>B>C 5:A>C>B 0:C>A>B 5:C>B>A 0:B>C>A 5:B>A>C that the order of those operations matters in some cases. Please show me what you mean. SB --- In [EMAIL PROTECTED], Forest Simmons <[EMAIL PROTECTED]> wrote: > On Thu, 27 Feb 2003, Steve Barney wrote: > > > Forest: > > > > Apparently, as I thought, your method of decomposition is to simply to remove > > cycles first, and then reversals. My point remains, then, that your > > decomposition method does NOT NECESSARILY yield the same outcome as Saari's > > matrix decomposition method. > > Actually, the order of removal isn't important as along as you recognize > that whenever you have two non-adjacent factions left, more symmetry > reduction is possible. In other words, you can reduce the total number of > ballots in the set by addition and subtraction of cycles and reverse > pairs. > > I don't know if Saari is aware of this or not. [...] Steve Barney Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/Hare/>. Did you know there is a web site where, if you click on a button, the advertisers there will donate 2 1/2 cups of food to feed hungry people in places where there is a lot of starvation? See: <http://www.thehungersite.com>. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
