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

[Anders Kaseorg]

On 12/09/2013 08:29 PM, Anders Kaseorg wrote:
> 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.

Oh, but here’s a new monotonicity failure.

Defeats (strong to weak):
• A > E, C > D, D > A, E > D
• A > B, B > C
• C > A
The first stage discards C > A; the second stage discards A > E, D > A, 
E > D, and affirms C > D, A > B, B > C.

Now suppose support for A > B is increased slightly.
• A > E, C > D, D > A, E > D
• A > B
• B > C
• C > A
The first stage instead discards B > C; the second stage discards A > E, 
D > A, E > D, and affirms C > D, A > B, C > A.  This has harmed A.

(Empirically, this failure seems much rarer than failures with original 
MMV.  Still, argh.)

Anders