[EM] True, the SD example is possible.

[Markus Schulze]

Dear Norman,
dear Mike,

Norman wrote (8 July 2000):
> I tried to modify Blake's 9-candidate example to one having
> fewer candidates but exhibiting the same problem, but was
> unsuccessful. Therefore, I think that SD's violation would
> be extremely rare in practice.

Mike wrote (11 July 2000):
> But imagine that academic up at the blackboard, with his
> arrow diagram of 36 defeats, each arrow with its magnitude-label.
> One has to question the effectiveness of a criticism that requires
> that kind of proof. How would it stand up against a reply
> that the guy is reaching pretty far to find a problem scenario, for
> a method that has some powerful advantages--which are much more
> likely to have effect. How patient would the audience be with his
> proof?
>
> ...
>
> Again, I just mention that consideration, in case it turned out
> that SD were the easiest BC complying method to get acceptance
> for. When you're talking to someone, whether a friend or someone
> walking up on the sidewalk, or a legislataor, you're going
> to be worring more about how that person will react to your
> method definition than about an academic coming to town with
> a 36-defeat digram to show people.

After Blake had explained how to create examples showing SD
violates monotonicity it was possible to create significantly
simpler examples than Blake's 9-candidate 13-defeat example.
Consider the following 7-candidate 9-defeat example:

Act I:

   AB 18
   BC 14
   CD 12
   DE 19
   EF 15
   FG 16
   GA 11
   DB 13
   GE 17

   SD chooses candidate A.

Act II:

   If "DE 19" is changed to "DE 10" then SD chooses
   candidate D. Therefore SD violates monotonicity.

In Act I, only one of the 9 defeats has to be dropped.
In Act II, two of the 9 defeats have to be dropped.
Therefore it wouldn't take very long to explain this
example to the audience.

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