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# 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,
>>      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/>
1024R/C7261095 print CB D9 F4 12 68 07 E4 05  CC 2D 27 12 1D F5 E8 6E
1024D/BF24424C print 4966 F272 D093 B493 410B  924B 21BA DABB BF24 424C

```