[EM] Fixing IRV
rmoore4 at home.com
Thu Aug 9 20:25:58 PDT 2001
Markus Schulze wrote:
>>>Some elimination methods are monotonic (e.g. Ranked Pairs). Some
>>>methods are not monotonic although they don't use eliminations
>>Granted, but disproving the converse doesn't disprove the
> 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.
> 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.
I for one don't see a tautology, but since tautologies are
true by definition then if it were one we wouldn't even need
to see a proof.
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.
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