[EM] approval vs. IRV: false claim about MMC examples?

[James Green-Armytage]

Mike Ossipoff wrote:
>As I was saying before, I often call MMC the "Fortuitous Special Case 
>Criterion), because it only applies in what, for a certain set of voters,
>is 
>a fortuitous special case. But that case isn't so fortuitous for other 
>voters, and every example of that type leads to an IRV failure example
>for 
>WDSC & FBC.

Mike Ossipoff also wrote:
>every MMC example is an IRV failure example in wihch IRV fails FBC & WDSC

	I don't think that this is actually true. I think that not all examples
where there is a mutual majority provide an incentive for order reversal.
	First, let's say that you can consider a straightforward one-candidate
majority to be a special type of mutual majority. Then you can have
example where approval fails MMC and regular MC, but where there is no way
that any of the voters can benefit from order reversal in IRV. 
	Here is such an example. These are the sincere preferences, and the >>
marks represent the approval cutoffs (rather than marking a stronger
preference, which is what I usually use them for). 

42: A>B>>C
10: A>>B>C
2: B>>A>C
2: B>>C>A
44: C>B>>A

approval score
A: 52
B: 58
C: 42

	So, A is a straight majority winner, the first choice of a clear
majority. A would win with IRV, of course, if people voted sincerely.
Also, the voters who prefer B or C can reverse the order of their
preferences all they want but they still won't be able to change the
outcome. So there is no FBC or WDSC failure in this particular example.
	Of course, what approval fans will say is, "why would 10 of the ABC
voters be so dumb as to approve B?" Well, I can give you a plausible
scenario at least. Let's say that no one knew that A would actually have a
majority. Let's say that the A voters were worried about C winning, and
some of them saw B as the compromise candidate, and went ahead and
approved B. Sure, it's a bad calculation on their part, but it's not
unthinkable that they could make it. And it's really quite a damaging
example for approval, in my opinion, because the candidate who is the
first choice of a majority isn't elected.
	But this isn't the main point of this e-mail. I'm trying to keep it
simple, so what I'm saying is that not all examples where approval fails
mutual majority give incentive for order reversal in IRV.
	Okay, okay, you're not satisfied that a straight majority qualifies as a
mutual majority? Fine, it doesn't even have to be a straight majority, as
long as the dominant majority candidate (dominant from an IRV point of
view) is preferred to the other majority candidate(s) by voters outside
the majority. For example:

sincere preferences, plus approval cutoffs
10: X>A>B>>C
32: A>X>B>>C
10: A>X>>B>C
2: B>>A>X>C
2: B>>C>A>X
44: C>B>>A>X

approval score:
A: 52
X: 52
B: 58
C: 42

IRV tally:
A	X	B	C
42	10	4	44
+2		-4	+2
44	10		46
+10	-10
54			46

	So, now, A and X form a mutual majority. (They're also clones but I'm not
worried about that right now.) A is a clear Condorcet winner, and also
wins using IRV, as above. And yet once again B can win in approval, as
above. (And this example illustrates another screwed-up thing about
approval: A and X have identical approval scores, even though 90% of the
voters prefer A to X. But I digress...) 
	Assuming an IRV tally, can anyone show me how any of the voters here can
reverse a preference or otherwise vote insincerely in order to get a
result that they prefer?
	I really don't see a way. I'm sure that someone will point it out if
there is one.
	But unless there is a way, I think that Mike's statement is inaccurate.
	
James