# [EM] Ranked Pairs Description

Markus Schulze markus.schulze at alumni.tu-berlin.de
Fri Dec 26 07:13:01 PST 2003

```Dear Eric,

you wrote:

> If two or more pairwise defeats have an equal strength and the
> margins are also equal, they are considered to be equivalent.
> Starting with the strongest defeat, consider each defeat in
> sequence with previously kept defeats, if any. If two or more
> defeats are equivalent, those defeats are considered together
> with previously kept defeats, if any. If any defeat under
> consideration is apart of a cycle, it is rejected. If any defeat
> under consideration is not apart of a cycle, it is kept.

Suppose AB and CD have the same strength. Suppose (a) locking only
AB would not create a directed cycle with already locked pairwise
defeats, (b) locking only CD would not create a directed cycle with
already locked pairwise defeats, but (c) locking both AB and CD
simultaneously would create a directed cycle with already locked
pairwise defeats.

Then I fear that your formulation could mistakenly be interpreted
in such a manner as if both pairwise defeats were rejected.

Markus Schulze

```