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

[Michael Ossipoff]

On Tue, Dec 10, 2013 at 12:23 AM, Anders Kaseorg <andersk at mit.edu> wrote:
> 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.
>
> 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.

That's what stage 3 would do, in the 3-stage version, if cycle AEDA
still remained in stage 3.

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

The only defeats qalified for defeat in step 2 are CD and DA, because
they contradict eachother (equal defeats) and AB & BC  (stronger
defeats) in the a cycle ABCDA.

A wins.

After the change in votes, the same things happen, and A still wins.

Even though AB and BC are now unequal, CA is still weaker than both.

MIchael Ossipoff






> 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
>