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Re: Constitutional voting, definition of cummulative prefererence



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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