On Fri, 5 Nov 2004 13:33:03 +0000, Paul Crowley <[EMAIL PROTECTED]> wrote: > > On Thu, 04 Nov 2004 21:33:19 +0100, Markus Schulze > > <[EMAIL PROTECTED]> wrote: > > > your Condorcet/RP variant sounds like Steve Eppley's > > > "minimize thwarted majorities" (MTM) method.
> MTM is exactly equivalent to my method. Found the definition of MTM: http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-February/003600.html Minimize Thwarted Majorities (MTM) ---------------------------------- If Vij > Vji and the social ordering ranks j ahead of i, then the social ordering "thwarts" the Vij majority who ranked i ahead of j. Select as the social ordering the ordering which minimizes thwarted majorities. It turns out not to be exactly equivalent. Using Eppley's notation, if #R(a, b) > #R(b,a), then #R(b,a) plays no role in MTM as far as I can tell. My method (call it SortAffirmed) treats #R(a, b) the same way no matter what its relation to #R(b, a) and so is somewhat simpler and cleaner. Proven weak Pareto. Also proven a sort of "spirit of Pareto" property which says that if a particular ordering wins, then there is no ordering that makes no-one any less happy and at least one person strictly happier. Still working on strong Pareto - I suspect that spirit of Pareto implies strong Pareto where voters have no "don't care" option but I can't see how to prove it. -- __ \/ o\ Paul Crowley /\__/ www.ciphergoth.org ---- Election-methods mailing list - see http://electorama.com/em for list info