[EM] Fixing IRV
schulze at sol.physik.tu-berlin.de
Fri Aug 10 04:59:33 PDT 2001
you wrote (9 Aug 2001):
> Markus wrote (9 Aug 2001):
> > Richard wrote (8 Aug 2001):
> > > Markus wrote (8 Aug 2001):
> > > > Richard wrote (7 Aug 2001):
> > > > > Actually, IIRC, there is a proof somewhere in the literature
> > > > > that elimination methods are not monotonic. Does anyone
> > > > > recall the theorem I mentioned above about elimination and
> > > > > monotonicity?
> > > >
> > > > Some elimination methods are monotonic (e.g. Ranked Pairs). Some
> > > > methods are not monotonic although they don't use eliminations
> > > > (e.g. Dodgson).
> > >
> > > Granted, but disproving the converse doesn't disprove the
> > > original statement.
> > The negation of "No elimination method is monotonic." is: "There
> > is a monotonic elimination method." And of course proving the
> > negation is the same as disproving the original statement.
> But, the *converse* of "All elimination methods are
> non-monotonic" is "All non-monotonic methods are elimination
> methods". You cited Dodgson as a counter-example of the
> converse, as a method that is non-monotonic but not an
> elimination method. And as I said, disproving the converse
> does not disprove the original statement.
Granted, but RP _is_ as an example of the negation. And as I said,
proving the negation _does_ disprove the original statement.
You wrote (9 Aug 2001):
> However, I see your point that "eliminating alternatives
> prior to selecting a winner" could be subject to
> interpretation (English can be a slippery thing). But to me
> it's pretty clear that this phrase would apply IRV (for
> example) but not to RP. Without the "prior" phrase, any
> method might be considered an elimination method, since all
> election methods eliminate alternatives.
Suppose, that Tideman didn't propose RP but RP-elimination
and that it didn't occurred to him that RP-elimination = RP.
How do you want to check whether a given elimination method can
also be defined as a method that doesn't "eliminate alternatives
prior to selecting a winner"?
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