Forest: Isn't that just another way of saying Kemeny's Rule does not respect cyclic symmetry?
SB >From: Forest Simmons <[EMAIL PROTECTED]> >To: <[EMAIL PROTECTED]> >Subject: RE: [EM] Saari's Basic Argument > >On Wed, 15 Jan 2003, Alex Small wrote: > >... > >> I'm not convinced >> that symmetry is a particularly compelling reason to pick an election >> method, > >... > >especially not the symmetry of {ABC,BCA,CAB}, which has a rotational bias. > >True, it favors no candidate, but it does favor its three orders over the >other three orders. > >One way to see this is that the average Kemeny distance from any order of >the cycle to the three orders in the cycle is (0+2+2)/3, while the average >Kemeny distance from a fully ranked order outside the cycle to orders of >the cycle is (1+1+3)/3. > >On the other hand reverse symmetry has no effect on the Kemeny distance: > >If xyz is any order of the three candidates, and {rst, tsr} is any >opposite pair, then the average Kemeny distance (d(xyz,rst)+d(xyz,tsr))/2 >is 3/2. > >So removal of a reverse pair cannot affect the Kemeny order. > >In the fully ranked three candidate case the Kemeny order is the same as >the Ranked Pairs order, etc. > >Forest Steve Barney Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/hare.htm>. Did you know there is an 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