[EM] sequential dropping

[Markus Schulze]

Dear James Green-Armytage,

> > > Am I correct in thinking that minimax chooses E in this
> > > example, ranked pairs chooses D, and river chooses F?
> >
> > > Oops. Minimax chooses D, not E... is that right?
> >
> > MinMax chooses A.
>
> Yes, indeed it does. I'm quite embarrassed. Did I get the
> others right, at least?

Yes, you got the others right.

By the way: "Sequential dropping" (SD) also violates
independence of clones.

Example: Suppose the defeats are (sorted according to
their strengths in a decreasing order):

   B > C
   D > B
   A > B
   A > C
   C > D
   D > A

SD chooses A. (MinMax chooses A. Tideman chooses D.
Schulze chooses A.)

Suppose A is replaced by (A1,A2,A3). Suppose the
defeats are (sorted according to their strengths
in a decreasing order):

   A1 > A2
   A2 > A3
   A3 > A1
   B > C
   D > B
   A1 > B, A2 > B, A3 > B
   A1 > C, A2 > C, A3 > C
   C > D
   D > A1, D > A2, D > A3

Now, SD chooses D. (MinMax chooses D. Tideman
chooses D. Schulze chooses A1.)

Markus Schulze