[EM] Of course MMT fails FBC. MTA-Optional-Conditional.

[MIKE OSSIPOFF]

Regarding the co-operation/defection problem, there are about 4 possibilities:
 
1. Just propose MTA and Keep the co-operation/defection problem.
 
That would be the easiest. But it would mean that the situation with respect
to an undeserving, but better than bottom, lesser-evil would be unchanged from
Plurality. Voters unwilling to help that lesser-evil against their favorite could
refuse to, casting a protest vote that, by not supporting the lesser-evil, will
result in four more years of greater-evil presidency. Of course, if that lesser-evil
loses, and the greater-evil wins due to their refusal of help, then they've taught
a lesson to the other opponents of the greater-evil, regarding the viability of
that lesser-evil.
 
But it would be good to avoid that, to be able help defeat greater evils without helping
a disliked lesser-evil against genuinely good candidates. That's why it would be
good to have a method that doesn't have the co-operation/defection problem.
 
2. Accept the potentially controversial nature of MMPO or MDDTR, caused by their
perceived excessive departures from Plurality...and the resulting vulnerability to opponents
creating a distraction about that.
 
3. Use a much more complicated method that meets FBC, Mono-Add-Plump, doesn't elect
C in Kevin's MMPO bad-example, and doesn't have the co-operation/defection problem.
 
4. Find a simpler method that has those advantages.
 
I've considered a few other possibilities for #4:
 
MTA Optional Conditional (MDDOC):
 
Like ordinary MTA, except that the voter has the option to make a middle rating "conditional".
 
The counting of conditional middle ratings is limited as follows:
 
For any two candidates x and y, an "x-only ballot" is one that top-rates x but not y 
(symmetrically likewise for "y-only ballots")
 
If the number of x ballots that middle-rate y is greater than the number of 
y ballots that middle-rate x, then delete either 1) enough of the x ballots' conditional
middle-rating of y so as to equalize those two numbers; or 2) all of the x
ballots' conditional middle-ratings of y--(whichever is fewer).
 
Do that for every pair of candidates.
 
Otherwise the count is the same as ordinary MTA.
 
[end of MDDOC definition]
 
I think that that method avoids all of the problems that I spoke of above. Well
it's a little more complicated than ordinary MTA, but the complication has obvious
and natural motivation.
-------------------------

I now mention a few things that at least sound like they could lead to a solution, but I only
mention them as tentative ideas that likely won't lead anywhere. Just two possible, long-shot
directions that occurred to me.

1. 
Have a rule that the middle-ratings given by a ballot don't count against that ballot's top-rated
candidate(s). In other words: If a top rated candidate on your ballot is 
in a top+middle tie or near-tie with a middle rated candidate
on your ballot, the middle-rating doesn't count.
 
I mention that even though I haven't looked at it enough to know if it's just another wording of some
previously-discussed pairwise-count method, or if it can really lead to a co-operation/defection solution. 
It sounds a little questionable, like something too good to be true, that won't really work as intended.
I don't claim to know what method it amounts to, or its consequences.

2.
Of course it occurred to me that, in MDDTR and MMPO, your middle rating for someone doesn't
really count as a vote _for hir_--but only as a vote _against_ your unrated candidates. So I asked
"Then why not just cast a vote against them, via negative Approval?". But of course negative
Approval is equivalent to ordinary Approval, and that's what MTA's top + middle count already is. So that
approach apparently doesn't change anything or lead to a solution to co-operation/defection.
 
Mike Ossipoff