[EM] MMV and resolvability

[Markus Schulze]

Hallo,

here is another example to illustrate MMV's violation
of monotonicity.

Situation 1:

   A>B, B>C, C>D, D>A, D>E, E>A each have the same
   strength and are stronger than every other pairwise
   defeat.

   The other pairwise defeats are (sorted by their strength
   in a decreasing order):

   A>C

   C>E

   E>B

   B>D

   MMV skips A>B, B>C, C>D, D>A, D>E, and E>A, since they
   form a directed cycle.

   Then it locks A>C,C>E,E>B, and B>D, so that A is the
   unique winner.

Situation 2:

   Some voters rank candidate A higher (relatively to
   candidate D), so that the pairwise defeat D>A becomes
   weaker.

   A>B, B>C, C>D, D>E, E>A each have the same
   strength and are stronger than every other pairwise
   defeat.

   The other pairwise defeats are (sorted by their strength
   in a decreasing order):

   A>C

   C>E

   E>B

   D>A

   B>D

   MMV skips A>B, B>C, C>D, D>E, and E>A, since they
   form a directed cycle.

   Then it locks A>C,C>E,E>B, and D>A, so that D is the
   unique winner.

Thus, by ranking candidate A higher candidate A is changed
from a winner to a loser.

Markus Schulze