[EM] Tideman and GMC

[Markus Schulze]

Dear Steve,

you 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 don't remember that Mike posted an example where the Schulze
method chose a Pareto inferior candidate.

******

You wrote (11 May 2000):
> As I wrote in February, criteria such as this one suggest that 
> the Schulze criterion is too strong.

What do you mean with "Schulze criterion"?

******

You wrote (11 May 2000):
> Markus wrote (10 May 2000):
> > _Every_ Condorcet method can be manipulated by burying
> > [=lower a candidate with respect to sincere placement in the
> > hopes of defeating it] and compromising [=raise a candidate
> > with respect to sincere placement in the hopes of electing
> > it]. Actually, the Condorcet methods don't differ in how
> > much they are vulnerable by burying and compromising.
>
> How is that vulnerability measured?

Blake Cretney introduced "burying" and "compromising" and
claimed that he can measure the vulnerability. I asked him for
further details but he didn't answer.

******

You wrote (11 May 2000):
> The example above shows that Schulze can be manipulated too.

Every acceptable election method can be manipulated.

******

You wrote (11 May 2000):
> Markus' argument reminds me of Don Saari's argument that all
> criteria failed by Borda, including manipulability, are failed
> by other voting methods, so Borda is better because Borda
> satisfies participation and reinforcement.

Why does everybody believe that I promote the Borda method? It
is true that I introduced the participation criterion to this
list. It is true that I introduced to this list Moulin's proof
that the Condorcet criterion and the participation criterion
are incompatible. But the unique reason why I did this is that
if you are in a public discussion outside the internet then you
will have to know what to answer when you are confronted with
Moulin's proof.

Condorcet is not a cult. It is not blasphemy to say that
Condorcet methods are not perfect. Is it?

******

You 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 Schulze
schulze at sol.physik.tu-berlin.de
schulze at math.tu-berlin.de
markusschulze at planet-interkom.de