[EM] Tideman and GMC

[MIKE OSSIPOFF]

>The aim of my reply was to give you the possibility to
>withdraw your polemic accusation without losing your
>honour. Unfortunately, you didn't observe this.

I suggest that it's best not to involve honor with any of this.
For instance, I've been mistaken too often, but I don't have
a concept of honor that says I've lost honor thereby--maybe
just a little credibility, when making an initial statement about
a complex subject. Maybe what would be dishonorable would be
to intentionally deceive.

Historically or course many unnecessary fights have been about
honor.

Mike Ossipoff



>
>******
>
>You wrote (13 May 2000):
> > Markus wrote (12 May 2000):
> > > Steve wrote (11 May 2000):
> > > > Markus wrote (10 May 2000):
> > > > > But it is more difficult to argue why -in the Tideman
> > > > > method- the winner should be changed from candidate C to
> > > > > candidate A when some voters uprank B ahead of D or
> > > > > downrank D behind B.
> > > >
> > > > It's another one of the paradoxes of voting, to which we
> > > > should be accustomed, but which are hard to explain to the
> > > > lay public.
> > >
> > > That's not true. There are acceptable election methods that
> > > cannot be manipulated by this strategy. Example: The MinMax
> > > winner cannot be changed from candidate A to candidate B
> > > by changing the strength of the pairwise defeat between two
> > > completely different candidates X:Y. The MinMax method is a
> > > very good method because it meets Condorcet, Monotonicity,
> > > Positive Involvement and No Show. (Unfortunately, on the
> > > other side the MinMax method violates Local Independence
> > > from Irrelevant Alternatives, Independence from Clones and
> > > Reversal Symmetry.)
> >
> > Markus misunderstood my point.  I didn't mean that any
> > particular paradox can occur in every method.  I just meant
> > that every method has at least one paradox which may be hard
> > to explain to voters.
>
>A "paradox of voting" is an unwanted property that every
>acceptable election method has.
>
>******
>
>You wrote (13 May 2000):
> > It appears to me that Markus has failed to offer any
> > substantive criticism of my argument that Schulze appears
> > at least as manipulable as methods like MTM and IBCM. His
> > only argument still standing is that it may be harder to
> > explain MTM or IBCM to the public than Schulze.
>
>I don't remember that I said that the Schulze method was
>less difficult to explain to the public.
>
>******
>
>You wrote (13 May 2000):
> > Many people in this maillist have commented on how complex
> > and abstract the Schulze definition may seem to the lay public.
> > (I think it was Norm who wrote about a month ago that a simpler
> > wording of Schulze had been posted, but I haven't seen it.  If
> > there's a simpler wording, please let me know how to find it in
> > my EM archive.)
>
>The unique reason why I defined and analysed the Schulze method
>in great detail is that I wanted to give every participant
>of this list the possibility to implement this method and to
>make computer simulations (e.g. with randomly generated voter
>rankings).
>
>You have to admit that (if you want to calculate the Tideman
>winner in a polynomial time) the exact algorithm to calculate
>the Tideman winner is also very long and abstract.
>
>******
>
>You wrote (13 May 2000):
> > When MTM (or IBCM) and Schulze are both decisive but disagree
> > on the winner, the MTM (or IBCM) winner beats pairwise the
> > Schulze winner more often than vice versa.  (And the IBCM
> > winner beats the MTM winner more often than vice versa,
> > suggesting IBCM is best of the three.)  These claims are
> > based on computer simulations using randomly generated voter
> > rankings.
>
>This argument is problematic because it can be cyclic.
>
>Suppose that somebody else would propose a new election method
>and would demonstrate that the winner of his election method
>beats pairwise the MTM winner more often than vice versa and
>that the Schulze winner beats the winner of his election method
>more often than vice versa. What would you conclude?
>
>******
>
>You wrote (13 May 2000):
> > I think more people will accept the (vaguely worded)
> > criterion that when x beats y pairwise, y shouldn't
> > "unnecessarily" finish ahead of x, sooner than they will accept
> > the (vaguely worded) criterion that the choice between x and y
> > shouldn't "unnecessarily" depend on pairings between two other
> > alternatives.
>
>The main justification of the Schulze method is beat path GMC.
>I don't agree with you that beat path GMC is "vaguely worded."
>
>******
>
>You wrote (13 May 2000):
> > Markus wrote (13 May 2000):
> > > Steve wrote (11 May 2000):
> > > > The older "Tideman fails GMC" example posted by Mike O was even
> > > > more extreme, showing the Schulze method preferred a candidate
> > > > even though no voter preferred it to the Tideman winner which
> > > > beat it pairwise.
> > >
> > > I couldn't find in the archives Mike's example where the Schulze
> > > method chooses a Pareto inferior candidate. Could you please
> > > repost this example?
> >
> > I didn't make that claim about Mike's example. See another
> > message I just posted for the example in question.
>
>There are two definitions of "Pareto inferior": a strong one and a
>weak one.
>
>"Candidate X is strongly Pareto inferior to candidate Y" means:
>Every voter strictly prefers candidate Y to candidate X.
>
>"Candidate X is weakly Pareto inferior to candidate Y" means:
>No voter strictly prefers candidate X to candidate Y and at
>least one voter strictly prefers candidate Y to candidate X.
>
>You wrote that no voter preferred the Schulze winner to the
>Tideman winner and that the Tideman winner beat the Schulze
>winner pairwise. Therefore you wrote that the Schulze method
>chose a weakly Pareto inferior candidate.
>
>Markus Schulze
>schulze at sol.physik.tu-berlin.de
>schulze at math.tu-berlin.de
>markusschulze at planet-interkom.de
>
>

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