On Wed, Apr 23, 2003 at 12:45:46AM -0500, Manoj Srivastava wrote:
> I have incorporated Rauls latest efforts on A.6. Jochen, do
> you still think we need to edit A.6.8 for clarity?
I don't think this is any better than the previous drafts.
> A.6 Vote Counting
> 4. From the list of undropped options, we generate a list of
> pairwise defeats.
> a. An option A defeats an option B, if V(A,B) is strictly greater
> than V(B,A).
> 5. From the list of [undropped] pairwise defeats, we generate a
> set of transitive defeats.
> a. 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.
> 6. We construct the Schwartz set from the set of transitive defeats.
> a. 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.
> 7. If there are defeats between options in the Schwartz set,
> we drop the weakest such defeats from the list of pairwise
> defeats, and return to step 5.
> 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 defeat is a defeat that has no other defeat weaker
> than it. There may be more than one such defeat.
> 8. If there are no defeats within the Schwartz set, then the winner
> is chosen from the options in the Schwartz set. If there is
> only one such option, it is the winner. If there are multiple
> options, the elector with the casting vote chooses which of those
> options wins.
Since we're saying "undropped defeats" (5, eg) explicitly in some cases,
it'd seem logical to assume that when we don't say it, we're talking
about all the defeats, which is wrong and stupid, but won't stop people
from assuming it anyway.
If you want to make it obvious and programmatic, how about:
4. From the list of undropped options, we generate a list of
defeats.
a. A pair of undropped options (A,B) is in the list of defeats
if V(A,B) is strictly greater than V(B,A).
5. We construct the Schwartz set from the set of transitive defeats.
a. An option A transitively defeats an option C if (A,C) is in
the list of defeats, or if there is some option B, such that
(A,B) is in the list of defeats and B transitively defeats C.
b. An undropped option S is in the Schwartz set if for all
options X, either S transitively defeats X, or X does not
transitively defeat S.
6. If there are defeats between any options in the Schwartz set,
we remove all the weakest such defeats from the list of defeats,
defeats, and return to step 5.
a. There is a defeat between options A and B, both in the
Schwartz set, if either (A,B) or (B,A) is in the list
of defeats.
b. 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).
c. A weakest defeat is a defeat that has no other defeat weaker
than it. There may be more than one such defeat.
7. If there are no defeats between any options in the Schwartz set,
then the winner is chosen from the options in the Schwartz set.
If there is only one such option, it is the winner. If there
are multiple options, the elector with the casting vote chooses
which of those options wins.
?
Cheers,
aj
--
Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
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