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Re: Request for comments [voting amendment]



On Wed, Nov 13, 2002 at 06:13:14PM -0500, Buddha Buck wrote:
> The Schultz Set = { A | A>>>A }
> Note:  Because A==A, it isn't the case that A>>A,

This is clever, but wrong. Consider an election with people voting:

	30 x ABCD
	40 x ACDB
	50 x ADBC

A wins unanimously and is the only member of the *Schwartz* set. However,
B beats C beats D beats B, so { x | x >>> x } = {B, C, D}.

Alternately, consider something like:

	40 x AB CDE
	30 x AB DEC
	20 x BA DEC
	50 x BA ECD

A and B are equal (70 votes each), and C > D > E > C, but A,B both beat
each of C,D,E, but { x | x >>> x } = {A,B,C,D,E}.

The correct restatement is something more like:

	{ x | forall y: y >> x --> x >>> y }

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.

 ``If you don't do it now, you'll be one year older when you do.''

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