On Tue, Dec 05, 2000 at 03:24:34PM -0500, Raul Miller wrote: > An individual ballot prefers option A to option B, if: > (*) Option A is mentioned at some preference, and option B is not > mentioned at all, or > (*) Option A is mentioned at a lower cannonical preference number than > option B. (This also allows votes like: [1] First preference [2] Reasonable alternative 1 [2] Reasonable alternative 2 [3] Further disucssion say) But yes, that's how I understand it. > A set of ballots cumulatively prefers option A to option B if: > * more individual ballots individually prefer option A to option B than > prefer option B to option A, or > * There is an option C, where A is cumulatively preferred to option C, > and option C is cumulatively preferred to option B. This is combining two definitions needlessly. Better to use a term like `dominates' and just declare it to be: `An option (A) dominates another (B) if more individual ballots individually prefer option A top option B than prefer option B to option A.' What you've defined above is called a beatpath, and in circular ties there'll be beatpaths from A to B (directly say) and from B to A (via C, say). Some Condorcet methods go on to define the "strength" of a beatpath, and chooses a winner based on the strength of the various beatpaths. Cheers, aj -- Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/> I don't speak for anyone save myself. GPG signed mail preferred. ``Thanks to all avid pokers out there'' -- linux.conf.au, 17-20 January 2001
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