Dear Mike,
you wrote (28 Oct 2000):
> Markus wrote (28 Oct 2000):
> > Mike wrote (25 Oct 2000):
> > > Ok, Markus, but what would you say to a suggestion that
> > > we count the ballots by Tideman(wv) and by BeatpathWinner,
> > > and then hold a 2nd balloting so people can vote which of
> > > those 2 winners they prefer? That sounds democratic to me.
> > >
> > > 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.
> >
> > 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?
Example: (1) Candidate A is the Tideman winner and candidate B
is the Schulze winner. Candidate A pairwise beats candidate B.
Then the election method above chooses candidate A.
(2) Now some voters uprank candidate A. Since Tideman meets
monotonicity, candidate A stays the Tideman winner. But the
Schulze winner can be changed (without violating monotonicity!)
from candidate B to candidate C. If candidate C pairwise beats
candidate A then the election method above chooses candidate C
so that monotonicity is violated.
Could you please demonstrate that such a scenario isn't
possible? Obviously the fact that Tideman and Schulze meet
monotonicity isn't sufficient to demonstrate that also the
election method above meets monotonicity.
Markus Schulze
