# [EM] Ranked Pairs Description

Eric Gorr eric at ericgorr.net
Fri Dec 26 08:46:12 PST 2003

```At 4:11 PM +0100 12/26/03, Markus Schulze wrote:
>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.

They should both be rejected as one could not determine which defeat
should be kept, unless one would choose randomly between them, but
then this would not be a 'deterministic' method.

--
== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
"Therefore the considerations of the intelligent always include both
benefit and harm." - Sun Tzu
== Insults, like violence, are the last refuge of the incompetent... ===

```