[EM] Fw: IBCM, Tideman, Schulze

[Markus Schulze]

Dear Steve,

you wrote (3 Jun 2000):
> Markus wrote (3 Jun 2000):
> > Steve wrote (2 Jun 2000):
> > > If RandomVoterHierarchy is the tie-breaker, aren't IBCM and
> > > MTM completely independent from clones, in whatever "strong"
> > > formulation Norm referred to?
> > 
> > Of course, you can use RandomBallot.
>
> Markus appears to agree with me that Norm erred when he 
> criticized Tideman as being worse than Schulze on independence 
> of clones.
>
> Markus wrote (3 Jun 2000):
> > But then your claim that "IBCM and MTM are more decisive than
> > Schulze or Path Voting" (26 Feb 2000) becomes false. 
>
> IBCM is more decisive than Schulze or path voting.  Markus might 
> want people to mistakenly believe it's not, but it is.  For 
> instance, consider the scenario "AB52,BC51,CA51" where IBCM 
> chooses C and Schulze chooses C&A.  Of course, IBCM's edge in 
> decisiveness would only matter in small committees, not in large 
> public elections.

I don't want anybody to "mistakenly believe" anything.
I only want to know on which presumptions your claim that the
IBCM method is more decisive than the Schulze method is based.

It is clear that it is possible to create situations where the
IBCM winner is unique and the Schulze winner is not unique. And
it is clear that it is possible to create situations where the
Schulze winner is unique and the IBCM winner is not unique.
Example: AB51,BC51,CA51,AD60,BD60,CD60,DE61,EA52,EB53,EC54.
Candidate A is the unique Schulze winner while the IBCM method
is indecisive between A, B and C.

Therefore my question is: How do you measure the decisiveness
of a method? Which presumptions do you use to justify your claim
that the IBCM method is more decisive than the Schulze method?

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