Re: Nov 16 draft of voting mechanics
On Sun, Nov 17, 2002 at 09:47:27AM -0500, Raul Miller wrote:
> > Alternatively, and IMO, simpler:
] Definition: A proposition is a pair of options, J and K, from
] the Schwartz set, such that J defeats K.
] Definition: V(X,Y) is the number of voters who prefer option X to
] option Y.
] Definition: A proposition J,K is weaker than a proposition L,M
] if V(J,K) is less than V(L,M); or V(J,K) and V(L,M) are equal
] and V(K,J) is greater than V(M,L).
> Simpler doesn't count here, because you fail to handle pairwise ties.
Sure I do: they're not propositions (since in a pairwise tie between
X and Y, X doesnt defeat Y and Y doesn't defeat X). There's no point
worrying about pairwise ties at all, afaics.
Possibly worth thinking about:
] Definition: An uneliminated proposition is a proposition that has not
] already been eliminated.
] Definition: A weakest uneliminated proposition is an uneliminated
] proposition that has no other uneliminated proposition weaker than it.
] (There may be more than one. If there are any uneliminated propositions,
] there is at least one.)
] Step "x": the weakest uneliminated proposition (or all such propositions if
] there are more than one) is (are) eliminated.
Give me tautological definitions any day.
> I am tempted to use your definition of V(X,Y), but I'd prefer the thing
> being defined be something more intrinsically meaningful than "V".
"NV" for number of votes/voters?
Anthony Towns <email@example.com> <http://azure.humbug.org.au/~aj/>
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