Doesn't this boil down to being able to "put yourself in another's shoes"? Are mirror neurons what are necessary to carry out moral reasoning?

This kind of solves the pie division problem. If you are capable of putting yourself in the other guy's shoes and still sincerely believing you should get the whole pie, perhaps there is some information about your internal state that you can communicate to the others to convince them?

IS the essence of morality that you should believe in the same division no matter which position you occupy?