[EM] Fwd: MMV and resolvability

[Anders Kaseorg]

On 12/07/2013 12:49 PM, Michael Ossipoff wrote:>   Two things:
> 2. It isn't just by my own wording, that MMV doesn't have the probem
> that you (Anders Kaseorg) described. Prabhakar's wording, it seems to
> me, doesn't have that problem either. Here is what Prabhakar said:
>
> [quote]
> (i) If a matchup later in the list conflicts with the
> previously-determined order, the latter matchup is superseded
> (ignored).
>
> (ii) In the even unlikelier case where several matchups with
> same-size majorities conflict with each other, all such conflicting
> matchups are ignored (though any non-conflicting matchups of that
> size are still included).
> [/quote]

This could be interpreted either way, depending on whether operations 
(i) and (ii) are supposed to happen simultaneously or sequentially.  It 
would be clearer if (ii) was written “…several _remaining_ matchups with 
same-size majorities…”.

On 12/07/2013 07:56 PM, Michael Ossipoff wrote:
> Better brief definition of MMV (which I formerly called DED-RP):
>
> Keep every defeat that doesn't contradict (by being in a cycle with
> them) a set of defeats that are all at least as strong as it.
>
> [end of brief MMV definition]

This brief definition seems too brief.  In my example
   5/2: A > C, B > C, C > D
   4/3: A > B, B > D, D > A
the defeat A > B is in a cycle with a set of defeats that are at least 
as strong as it (A > B > D > A).  But it sounds like you agree that we 
want to affirm A > B.  In order to do that, we need to disqualify D > A 
_before_ checking whether to affirm A > B.  Perhaps you think that this 
order of operations is somehow implicit, but given that Eric Gorr’s 
calculator works differently, I think it’s important to be unambiguous:

“Affirm every defeat that doesn’t contradict the set of strictly 
stronger affirmed defeats and equally strong ‘admissible’ defeats, where 
a defeat is ‘admissible’ if it doesn’t contradict the set of strictly 
stronger affirmed defeats.”

Anders