Re: April 23rd Draft
On Wed, 23 Apr 2003 16:36:00 +1000, Anthony Towns
<aj@azure.humbug.org.au> said:
> 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.
> 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:
>> 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).
> 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).
Umm. Now you lost poor simple folks like me. The first wording
tells me about defeats -- a term I can understand. The second set, by
itself, is somewhat more complex.
Secondly, you imply that a pair of options is in the list of
defeats -- which is even more confusing. Is it a list of defeats,
or a list of options? I think you mean that (A,B) represents a
defeat -- perhaps:
4. From the list of undropped options, we generate a list of
pairwise defeats.
a) For a pair of undropped options A nd B, a defeat D(A,B) is in
this list of defeats 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.
> 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.
Hmm. I guess I agree with qualifying the options as
_undropped_ options here. Again, adding the nomenclature for a defeat:
a. An option A transitively defeats an option C if D(A,C) is in the
list of defeats, or if there is some option B, such that
D(A,B) is in the list of defeats and B transitively defeats
C.
>> 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.
> 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.
D(A,B) D(B,A)
> b. A defeat (A,X) is weaker than a defeat (B,Y) if V(A,X) is
D(A,X) D(B,Y)
> less than V(B,Y). Also, (A,X) is weaker than (B,Y) if
D(A,X) D(B,Y)
> 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.
I do like the second version better.
manoj
--
So so is good, very good, very excellent good: and yet it is not; it
is but so so. William Shakespeare, "As You Like It"
Manoj Srivastava <srivasta@debian.org> <http://www.debian.org/%7Esrivasta/>
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