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Re: April 17th Draft of the Voting GR



On Sat, Apr 19, 2003 at 09:22:00AM +0200, Matthias Urlichs wrote:
> ... which is exactly why I am using the idea of a list. Nowhere does it say 
> (in my text) that you can re-add a defeat to that list, and indeed that is 
> never done, so
> 
> > If that's the case, perhaps it's worth adding a phrase such as "Once a
> > defeat is dropped, it remains dropped, even if a transitive defeat which
> > had caused it to be dropped is later eliminated."
> >
> ... a sentence like this one is superfluous.

Refering to the message with id <87smsf3ewg.fsf@glaurung.green-gryphon.com>,
you still have the potential ambiguity that "transitive defeat" is defined
in terms of "defeats" not in terms of "the list of undropped defeats".

Consider this ballot:

3 ABC
2 CAB
2 BCA

A:B 5:2
B:C 5:2
C:A 4:3

A transitively defeats B
A transitively defeats C
B transitively defeats A
B transitively defeats C
C transitively defeats A
C transitively defeats B

Drop C:A

A transitively defeats B
A transitively defeats C
B transitively defeats A
B transitively defeats C
C transitively defeats A
C transitively defeats B

Drop A:B, B:C

Tie between A, B, and C.
______________________________________________________________________

However, if transitive defeats are based on undropped defeats (as
opposed to all defeats, dropped or not), after you drop C:A you
have

A transitively defeats B
A transitively defeats C
B transitively defeats C

A wins.
______________________________________________________________________

Maybe it would make some people happier if we used the phrase
"uneliminated transitive defeat" instead of "transitive defeat", and if
we used the term "uneliminated schwartz set" in place of schwartz set?

Thanks,

-- 
Raul



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