[EM] RE: Election-methods digest, Vol 1 #401 - 1 msg

[MIKE OSSIPOFF]

>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.

I reply:

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 
kept.

I'm for whateve tied-defeats solution is briefest and simplest in public 
proposals.

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 
already covered:

Slightly more elaborate and slightly better tied-defeats solution wording:

1. The equally strongest as-yet unconsidered defeats are called the 
"tied-defeats".

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 
publc proposal.

Mike Ossipoff

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