[EM] Tideman and GMC

[Markus Schulze]

Dear Blake,

you wrote (11 Mar 2000):
> Markus Schulze wrote (29 Feb 2000):
> > Blake Cretney wrote (24 Feb 2000):
> > > Markus Schulze wrote (3 Feb 2000):
> > > > The intention of beat path GMC is that a voter should rather be
> > > > punished than rewarded for truncating his votes. In your example,
> > > > beat path GMC does exactly what it was designed to do. Those 35
> > > > voters whose sincere opinion is B > A > D > C truncate their votes
> > > > and change the winner from candidate A to candidate D. Thus the
> > > > truncators are punished. In so far as beat path GMC does exactly
> > > > what is was designed to do, your example cannot be interpreted as
> > > > a criticism of beat path GMC.
> > >
> > > But in your bad example for Tideman, the truncators were punished
> > > as well.  It does seem, however, that Schulze converts some
> > > situations where truncators are punished into situations where
> > > they have no effect.  This may well be a positive effect.
> > > I do, therefore, now see the rationale for favouring Schulze
> > > (winning-votes) over Tideman (winning-votes) as being slightly
> > > less likely to be affected by truncation.  This doesn't mean that
> > > truncation is a more useful strategy in Tideman (winning-votes),
> > > in fact it is worse.
> >
> > You'll have to rephrase this, because I have no idea what you mean.
> > What do you mean when you say that Schulze was less likely to be affected
> > by strategical truncation but that didn't mean that truncation is a more
> > useful strategy in Tideman?
>
> I mean that Schulze and Tideman are equivalent for reward, but Tideman is
> more likely to punish.

You'll have to rephrase this, because I still have no idea what you mean.

The comment above (3 Feb 2000) is about the following example (31 Jan 2000):

   25 A D B C
   35 B A D C -> B
   30 D C A B
   4  A D C B
   6  C A D B
               winning-votes
   A->D 35-30   35
   A->B 65-35   65
   C->A 36-29   36
   B->C 60-40   60
   D->B 65-35   65
   D->C 59-6    59

In this example, the Tideman winner before truncation is candidate A.
The Tideman winner after truncation is candidate A. Therefore the
truncators don't change the Tideman winner.

The Schulze winner before truncation is candidate A. The Schulze
winner after truncation is candidate D. In so far as the truncators
prefer candidate A to candidate D, the truncators are punished
by the Schulze method.

What do you mean when you say that this example demonstrates that
"Schulze converts some situations where truncators are punished into
situations where they have no effect" and that "Schulze and Tideman
are equivalent for reward, but Tideman is more likely to punish"?

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