On Sun, Nov 17, 2002 at 09:47:27AM -0500, Raul Miller wrote: > > Alternatively, and IMO, simpler:
] Definition: A proposition is a pair of options, J and K, from ] the Schwartz set, such that J defeats K. ] ] Definition: V(X,Y) is the number of voters who prefer option X to ] option Y. ] ] Definition: A proposition J,K is weaker than a proposition L,M ] if V(J,K) is less than V(L,M); or V(J,K) and V(L,M) are equal ] and V(K,J) is greater than V(M,L). > Simpler doesn't count here, because you fail to handle pairwise ties. Sure I do: they're not propositions (since in a pairwise tie between X and Y, X doesnt defeat Y and Y doesn't defeat X). There's no point worrying about pairwise ties at all, afaics. Possibly worth thinking about: ] Definition: An uneliminated proposition is a proposition that has not ] already been eliminated. ] ] Definition: A weakest uneliminated proposition is an uneliminated ] proposition that has no other uneliminated proposition weaker than it. ] (There may be more than one. If there are any uneliminated propositions, ] there is at least one.) ] ] Step "x": the weakest uneliminated proposition (or all such propositions if ] there are more than one) is (are) eliminated. Give me tautological definitions any day. > I am tempted to use your definition of V(X,Y), but I'd prefer the thing > being defined be something more intrinsically meaningful than "V". "NV" for number of votes/voters? Cheers, aj -- Anthony Towns <[EMAIL PROTECTED]> <http://azure.humbug.org.au/~aj/> I don't speak for anyone save myself. GPG signed mail preferred. ``If you don't do it now, you'll be one year older when you do.''
