Whoohoo! I just figured out the correct way to handle this problem, that renders the global and egocentric/internal reflections consistent.

We will see if my solution makes sense in the morning, but the upshot is that there was/is nothing wrong with the green roomer's posterior, as many people have been correctly defending. The green roomer who computed an EV of $5.60 modeled the money pay-off scheme wrong.

In the incorrect calculation that yields $5.6 EV, the green roomer models himself as winning (getting the favorable +$12) when he is right and losing (paying the -$52) when he is wrong. But no, not exactly. The green roomer doesn't win every time he's right -- even though certainly he's right every time he's right.

The green roomer wins 1 out of every 18 times that he's right, because 17 copies of himself that were also right do not get their own independent winnings, and he loses 1 out of every 2 times he's wrong, because there are 2 of him that are wrong in the room that pays $52.

So it is Bostrom's division-of-responsibility, with the justification. It is probably more apt to name it division-of-reward.

Here's is the correct green roomer calculation:

EV = P(heads)(payoff given heads)(rate of payoff given heads)+ P(tails)(payoff given tails)(rate of payoff given tails)

=.9($12)(1/18)+.1(-$52)(1/2) = -2

(By the way, this doesn't modify what I said about pointers, but I must admit I don't understand at the moment how the two perspectives are related. Yet; some thoughts.)