On 11 Jan 2005 at 14:40 PST, Jobst Heitzig wrote: >> >> But ... your argument that, if W differs from A, this implies "that W >> beat every candidate that A beats head to head" does not follow. It >> only implies that W has highest approval in U(A). > > No, Forest is right, he defined: >>> Let U(A) be the set of uncovered candidates that cover the approval >>> winner A. > > Hence every member of U(A) not only defeats A but covers A (or is equal > to A), so it defeats all candidates A defeats, by definition!
Unless I'm confusing something, "cover" doesn't mean direct defeat. It means there is a beatpath of length 1 or 2. Maybe I'm arguing myself in circles. U(A) is the set of candidates that cover A. If this set is of size > 1 and includes at least one candidate besides A, they don't cover each other. If W has highest approval in that set, there might be another candidate that defeats W. I guess I wanted to say that W doesn't have a particularly strong property other than the highest approval one. BTW, how does one choose the Dutta minimal covering set from the set of uncovered candidates? Ted -- Ted Stern tedstern at u dot washington dot edu http://www.drizzle.com/~goldstar home: 206-783-2725 home address: http://tinyurl.com/2pexz work: 206-701-2182 work address: http://tinyurl.com/35srs cell: 206-383-1049 FAX: 206-701-2500 Frango ut patefaciam -- I break that I may reveal ---- Election-methods mailing list - see http://electorama.com/em for list info
