Re: April 17th Draft of the Voting GR
On Sat, Apr 19, 2003 at 11:28:06AM -0500, Manoj Srivastava wrote:
> How does the version in the message with Message-ID:
> <[🔎] 87fzof1m69.fsf@glaurung.green-gryphon.com> look?
Hmm... focussing on this issue of "dropped defeats" and
"transitive defeats":
< 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.*2
Ok, so we have a list of defeats (non are dropped) and a corresponding
set of transtive defeats.
< 5. We construct the Schwartz set from (a subset of) the list of
< pairwise defeats.*1
Hmm... we construct the Schwartz set from the transitive defeats which
we construct from the list of defeats, so technically this is correct,
however:
< - If (A,C) is an undropped defeat then option A
< unconditionally defeats option C.
< - If (A,B) is an undropped defeat, and option B
< unconditionally defeats option C, then option A
< unconditionally defeats option C.
< - An option A is in the Schwartz set if for all options B,
< considering only the undropped defeats, either A
< unconditionally defeats B, or B does not unconditionally
< defeat A.
No mention of the transitive defeats at all. Instead, "unconditionally
defeats" seems to be defined to mean essentially the same thing.
Is it wise to introduce a new way of saying "transitively defeats"?
If so, why aren't we using this term consistently throughout?
Why not just eliminate the term "transitively" if we're going to use
"unconditional" in its place?
[Personally, I'm a bit uncomfortable with this new term, since
"unconditional" carries a meaning which doesn't seem to help explain
what's going on here.]
--
Raul
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