Forest: In message # 10970, why did you say "wisely," as follows?:
> Kemeny (wisely) doesn't believe in cyclic symmetry removal [...] Do you mean to imply that the KR tie between A>C>B and B>A>C is more reasonable than the A>B>C outcome yielded by both Saari's and your decomposition of 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 SB --- In [EMAIL PROTECTED], Forest Simmons <[EMAIL PROTECTED]> wrote: > To focus on the order is to miss the boat. Sometimes one order is most > efficient and sometimes another. > > In the example you gave me the most efficient order is removal of five > copies of the cycle. > > The other order that you suggested did not reduce the ballot set to the > minimum of three ballots. > > Forest > > On Sat, 1 Mar 2003, Steve Barney wrote: > > > 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 = ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
