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

[Anders Kaseorg]

On 12/10/2013 01:04 PM, Michael Ossipoff wrote:
> Stage 2 says:
>
> 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.
>
> AE and DA, by virtue of cycle jAEDA, contradict only equal defeats, so
> that doesn't qualify them for un-keeping (discard) in step 2l

Based on this comment, it sounds like what you really meant to say in 
stage 2 was:

“Then, among the kept defeats, un-keep each defeat that contradicts a 
set consisting of equal defeats and kept stronger defeats, _without 
contradicting any set of only equal defeats_.”?

That extra constraint adds much simpler monotonicity failures.  Defeats 
(strongest to weakest):
• B > C, C > D, D > B
• A > D, C > A
Stage 1 does nothing, then stage 2 keeps B > C, C > D, D > B and 
discards A > D, C > A, leading to a four-way tie.

Now increase support for D > B.  Defeats (strongest to weakest):
• D > B
• B > C, C > D
• A > D, C > A
Stage 1 does nothing, then stage 2 keeps D > B, discards B > C, C > D, 
and keeps A > D, C > A, leading to C > A > D > B, where D has been harmed.

Anders