On 20 Jan 2005 at 14:54 PST, Ted Stern wrote: > So your defeat rankings should actually be > Bi>Ai , strength 11 (the 3 "straight upward" beats) > A1>A2>A3>A1 , strength 10 (the "upper clockwise" 3-cycle) > B1<B2<B3<B1 , strength 10 (the "lower counter-clockwise" 3-cycle) > Ai>Bj (i!=j), strength 8 (the 6 "diagonal downward" beats)
Hi Jobst, One other comment about the twisted prism example: If defeats are sorted using approval-weighted pairwise, you get an approval weighted defeat matrix like this: - 4 0 0 4 8 0 - 4 8 0 4 4 0 - 4 8 0 3 0 0 - 0 4 0 3 0 4 - 0 0 0 3 0 4 - Ai>Bj (i!=j), strength 8 A1>A2>A3>A1 , strength 4 B1<B2<B3<B1 , strength 4 Bi>Ai , strength 3 With this ranking, immune methods will drop the Bi>Ai defeats, and you won't get the paradox you found originally. In my opinion this is a(nother) strong argument in favor of combining RP/Beatpath/River with approval weighting. Ted -- Send real replies to ted stern at u dot washington dot edu Frango ut patefaciam -- I break that I may reveal ---- Election-methods mailing list - see http://electorama.com/em for list info