[EM] Someone thinks that Approval should meet the Mutual Majority Criterion

[Michael Ossipoff]

Someone recently accused me of contriving the definition of sincere
voting so that Approval would fail MMC (which specifies sincere voting
in its premise).

One way to answer his objection is to ask him to compare Approval with
methods that meet MMC, and ask himself if he notices a difference.

The methods that I recommend for the Green scenario, IRV, but
especiallly Woodall or maybe Benham, also are free of chicken dilemma,
and so maybe comparing Approval with them would be unfair--because
we're only trying to show the benefit of MMC.

So then, let's compare Approval with a method that has chicken
dilemma, but passes MMC. Let's compare Approval with Beatpath:

The A voters and the B voters all prefer both A and B to C. The A
voters and the B voters are, together, a majority of the voters.

They are a mutual majority, and {A,B} is their MM-preferred set.

Let's assume that there is no chicken dilemma. The A voters and the B
votes are co-operative and amicable. None of them are inclinded to
defect against eachother. The A voters and the B voters have no
chicken dilemm need to not rank eachother's candidate.

So, voting sincerely, the voting looks like this:

A>B
B>A
C

Because the A voters and the B voters add up to a majority, C is defeated.

The A voters and the B voters succeeded in getting a winner from their
majority-preferred set by merely ranking sincerely.

If the A voters are more numerous than the B voters, then A will win
instead of B. The A voters can gain that, while still fully supporting
B againist C.

Can they do that in Approval?

MMC measures for something of practical importance that Beatpath, IRV,
Woodall, Benham, and Schwartz Woodall have, but  which Approval
doesn't have.

Michael Ossipoff