# 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
consideration.
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
defeats:

-  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
A.

If there are defeats between options in the Schwartz set, we
drop the weakest such defeats from the list of pairwise

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 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.
----------------------------------------------------------------------
manoj

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