[EM] Fwd: Two MMV definiions (brief, and ordered-procedure)

[Anders Kaseorg]

On 12/09/2013 08:15 AM, Michael Ossipoff wrote:
> Keep every defeat that doesn't contradict a set of kept stronger defeats.
>
> Then, among the kept defeats, un-keep each defeat that contradicts a
> set consisting of defeats equal to it, and of kept defeats stronger
> than it is.

So this is different from my fix: you’re dividing the process into two 
stages such that defeats in an equal-strength cycle can still be used to 
reject strictly weaker contradicting defeats in stage 1, before being 
discarded themselves in stage 2.  That makes sense.  It does seem to 
avoid the monotonicity failure cases discussed before.

I’ll abandon my earlier fix in favor of this one.

> Maybe there should be a 3rd stage that discards any set of equal
> defeats that contradict only eachother.

No, that would introduce a new monotonicity failure in the case of 
multiple overlapping cycles.  Suppose there are equally strong defeats

A > B, B > C, C > A, B > D, D > A

Then the extra stage rejects the equal-strength cycles A > B > C > A and 
A > B > D > A.  However, if support for C > A were increased, then the 
extra stage would no longer be able to reject the first cycle, which 
means B > C and C > A would be affirmed, harming C.

Anders