Tideman and GMC

[DEMOREP1 at aol.com]

> Markus Schulze wrote (3 Feb 2000):
> > Example:
> > 
> >    26 voters vote C > A > B > D.
> >    20 voters vote B > D > A > C.
> >    18 voters vote A > D > C > B.
> >    14 voters vote C > B > A > D.
> >    08 voters vote B > D > C > A.
> >    07 voters vote D > A > C > B.
> >    07 voters vote B > D > A = C.
> > 
> > Then the matrix of pairwise defeats looks as follows:
> > 
> >    A:B=51:49
> >    A:C=45:48
> >    A:D=58:42
> >    B:C=35:65
> >    B:D=75:25
> >    C:D=40:60
> > 
> > Tideman:
> > 
> >    Tideman would
> >    1) lock B > D,
> >    2) lock C > B,
> >    3) skip D > C because it would create a directed cycle
> >       with the other already locked pairwise defeats,
> >    4) lock A > D,
> >    5) lock A > B,
> >    6) lock C > A.
> > 
> >    Thus the Tideman ranking is C > A > B > D and the Tideman
> >    winner is candidate C.
> > 
> > Schulze:
> > 
> >    A has 58 votes against B via the beat path A > D > C > B.
> >    A has 58 votes against C via the beat path A > D > C.
> >    A has 58 votes against D via the beat path A > D.
> > 
> >    B has 48 votes against A via the beat path B > D > C > A.
> >    B has 60 votes against C via the beat path B > D > C.
> >    B has 75 votes against D via the beat path B > D.
> > 
> >    C has 48 votes against A via the beat path C > A.
> >    C has 65 votes against B via the beat path C > B.
> >    C has 65 votes against D via the beat path C > B > D.
> > 
> >    D has 48 votes against A via the beat path D > C > A.
> >    D has 60 votes against B via the beat path D > C > B.
> >    D has 60 votes against C via the beat path D > C.
> > 
> >    Candidate A is the Schulze winner because candidate A defeats
> >    every other candidate via beat paths.
> > 
> > In the Schulze Method, the strength of the pairwise defeat B:D
> > has no influence on the final winner; even if we set B:D=100:0
> > or B:D=0:100, candidate A stays the Schulze winner. On the other
> > hand, if we set B:D=59:41 then the Tideman winner is changed from
> > candidate C to candidate A.
----
Clone removal method-

75 BD 25
65 CB 35
60 DC 40
58 AD 42
51 AB 49
48 (51.5) CA 45 (48.5)  () using half votes in ties

D is removed (note the 61 BD combinations)

65 CB 35
51 AB 49
48 (51.5) CA 45 (48.5)  () using half votes in ties

C beats B and A
C wins