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Re: April 17th Draft of the Voting GR

>> On Fri, 18 Apr 2003 14:40:03 -0400,
>> Raul Miller <moth@magenta.com> said: 

 > Here's A.6.4 rephrased with an explicit definition for "defeat",
 > the noun.

 > 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.

	I think we should separate the definition of terminology of
 defeats from the details of constructions of the Schwartz set. 

	Let me see if I can incorporate your working into mine:

 > I've also introduced a possible precedence ambiguity by splitting
 > the definition of "transitive defeat" into two parallel rules.

	Hmm.  I think that the defeat is still a defeat, whether or
 not we are dropping consideration of that defeat in the calculation
 of the Schwartz set. So, how about the below, which incorporates your
 definition of the noun and the verb (gerund?):
Replace A.6 with:

   A.6 Vote Counting

     1. Each voter's ballot ranks the options being voted on.  Not all
        options need be ranked.  Ranked options are considered
        preferred to all unranked options.  Voters may rank options
        equally.  Unranked options are considered to be ranked equally
        with one another.  Details of how ballots may be filled out
        will be included in the Call For Votes.
     2. If the ballot has a quorum requirement R any options other
        than the default option which do not receive at least R votes
        ranking that option above the default option are dropped from
     3. Any (non-default) option which does not defeat the default option
        by its required majority ratio is dropped from consideration.
        a. Given two options A and B, V(A,B) is the number of voters
           who prefer option A over option B.
        b. An option A defeats the default option D by a majority
           ratio N, if V(A,D) is strictly greater than N * V(D,A).
        c. If a supermajority of S:1 is required for A, its majority ratio
           is S; otherwise, its majority ratio is 1.
     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). 
        b. (A,B) is a defeat of option B if option A defeats option B.
        c. 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.
     5. We construct the Schwartz set from the list of pairwise

         -  An option A is in the Schwartz set if for all options B,
            considering only the undropped defeats, either A
            transitively defeats B, or B does not transitively defeat

        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
           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 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.  

I've got a bad feeling about this.
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

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