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 <[EMAIL PROTECTED]> <http://azure.humbug.org.au/~aj/>
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``Thanks to all avid pokers out there''
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