On Fri, Apr 18, 2003 at 04:05:06PM -0500, Manoj Srivastava wrote: We're not going to ever get anywhere here, are we?
> >> Raul Miller <[EMAIL PROTECTED]> said:
> > I've also made explicit that only undropped defeats are used in
> > determining the schwartz set.
> Whoa there. I think A transitively defeats option C if a
> defeats B and B defeats C, whether or not the defeat is dropped.
It doesn't. Once defeats are dropped, they are *entirely* irrelevant to
the vote, and it's utterly useless to have terms that refer to them.
A minimalist change is just to add the qualifier "undropped" to lots of
places:
4. We construct the Schwartz set based on undropped options and
undropped defeats:
a. An option A defeats an option B, if V(A,B) is strictly
greater than V(B,A). If A defeats B, then (A,B) is called
a defeat.
b. An option A transitively defeats an option C if A
defeats C or if there is some other option B where A
defeats B AND B transitively defeats C.
c. An option A is in the Schwartz set if for all options B,
either A transitively defeats B, or B does not transitively
defeat A, considering only undropped defeats.
5. If there are undropped defeats between options in the Schwartz set,
we drop the weakest such defeats, and return to step 4.
a. A defeat (A,X) is weaker than a defeat (B,Y) if V(A,X)
is less than V(B,Y). Also, (A,X) is weaker than (B,Y)
if V(A,X) is equal to V(B,Y) and V(X,A) is greater than
V(Y,B).
b. A weakest undropped defeat is an undropped defeat that
has no other undropped defeat weaker than it. There may
be more than one such defeat.
6. If there are no undropped defeats within the Schwartz set,
then the winner is chosen from the options in the Schwartz
set. [...]
Cheers,
aj
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