I'd said:
> > If EM ever needs to vote on something, a good system might be
> > to count the ballots by BeatpathWinner and by Tideman(wv), and
> > choose the winner that pairwise-beats the other.
Markus said:
>Could you please demonstrate that your proposal meets
>monotonicity?
I don't have a demonstration about that, but that may not mean anything.
If a method fails a criterion then there's always a failure example.
If a method meets a criterion then we have the more difficult task of
proving that there can't be a failure example. As you know, there are
true but unprovable propositions, and there may be cases where
a method has no failure examples for some criterion, but that's
unprovable.
For that reason, it seems to make more sense to say that voting
systems are innocent till proven guilty of violating a criterion.
If you can't prove that the proposal I described violates Monotonicity,
do you have a good reason for believing that it is likely to?
In any case, as I said, it's a moot point anyway, since EM doesn't
vote. If we did, and it were felt or proved that the procedure that
I described violates Monotonicity, then I'd only suggest it, or
Voter's Choice, for the purpose of choosing a voting system for use
in subsequent votes.
More likely, though, if it were just a choice
between Tideman(wv) & BeatpathWinner, it would be better to just
take a vote between those 2. Otherwise, if there are more methods
proposed, I'd suggest Voter's Choice, even though it's nonmonotonic.
Probably Tideman(wv) and BeatpathWinner have more 1st choice advocates
than other voting systems for the purpose of voting on EM, but it
may be better not to assume that.
>
>You wrote (28 Oct 2000):
> > Of course saying that that would violate monotonicity and
> > demonstrating it aren't quite the same thing, are they?
>
>Of course proposing a method and demonstrating that it meets
>monotonicity aren't quite the same thing either, are they?
No, and demonstrating criterion failure, which always has an example
if it's true, and demonstrating criterion nonfailure, which may
be unprovable--those aren't the same thing either, are they? That's
why it makes more sense to assume that a method passes a criterion
unless it's demonstrated to fail it, or unless there's good reason
to expect that it has a failure example, even if one hasn't been
found or demonstrated to exist.
Mike Ossipoff
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