[EM] RE: Election-methods digest, Vol 1 #401 - 1 msg
nkklrp at hotmail.com
Fri Dec 26 22:10:01 PST 2003
>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
>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.
Yes, rejecting both would be most in keeping with the spirit of Eric's
tied-defeats solution, and would be most what people would expect.
Of course wording that covers that should be included. Maybe it could be
said in a way that covers all those possibilities inl one wording, without
separate mention of the special case where 2 or more tied-defeats
indivicuallly don't cycle with old-kept-defeats, but do so if boith are
I'm for whateve tied-defeats solution is briefest and simplest in public
If the wording foir Eric's briefer solution starts getting too long, by
having to cover that situation described above, then with its brevity
somewhat eroded, it could be worth considering this slightly more elaborate
solution that I named in a recent e-mail, for which that situation is
Slightly more elaborate and slightly better tied-defeats solution wording:
1. The equally strongest as-yet unconsidered defeats are called the
2. The defeats that were kept before any tied-defeats were kept are called
the "old defeats".
3. Any tied defeat that isn't in a cycle consisting only of it and some old
defeats is "qualified".
4. Keep any qualified defeat that isn't in a cycle each of whose members is
either qualified or old.
That's much longer than Eric's brief solution. Maybe when Eric's wording is
modified to cover the situation that Markus described, Eric's wording will
still be briefer and simpler than this one. Still, this one is worth
considering if the brief one loses too much of its brevity.
I'd like to add that the suggestion of looking at all q! possible
consideration-orderings of the tied defeats is completely unacceptable for a
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