[EM] Fixing IRV
schulze at sol.physik.tu-berlin.de
Thu Aug 9 07:40:49 PDT 2001
you 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.
You wrote (8 Aug 2001):
> All voting systems that eliminate alternatives
> prior to selecting a winner violate monotonicity.
I guess that it will be very difficult to define "eliminating
alternatives prior to selecting a winner" without making
Riker's theorem trivial or even a tautology.
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