Between non communicating copies of your decision algorithm, it's forced that every instance comes to the same answers/distributions to all questions, as otherwise Eliezer can make money betting between different instances of the algorithm. It's not really a categorical imperative, beyond demanding consistency.

The crux of the OP is asking for a probability assessment of the world, not whether the DT functions.

I'm not postulating 1/n allocation of responsibility; I'm stating that the source of the confusion is over: P(A random individual is in a world of class Ai | Data) with P(A random world is of class Ai | Data) And that these are not equal if the number of individuals with access to Data are different in distinct classes of world.

Hence in this case, there are 2 classes of world, A1 with 18 Green rooms and 2 Reds, and A2 with 2 Green rooms and 18 Reds.

P(Random individual is in the A1 class | Woke up in a green room) = 0.9 by anthropic update. P(Random world is in the A1 class | Some individual woke up in a green room) = 0.5

Why? Because in A1 there 18/20 individuals fit the description "Woke up in a green room", but in A2 only 2/20 do.

The crux of the OP is that neither a 90/10 nor 50/50 split seem acceptable, if betting on "Which world-class an individual in a Green room is in" and "Which world-class the (set of all individuals in Green rooms which contains this individual) is in" are identical. I assert that they are not. The first case is 0.9/0.1 A1/A2, the second is 0.5/0.5 A1/A2.

Consider a similar question where a random Green room will be asked. If you're in that room, you update both on (Green walls) and (I'm being asked) and recover the 0.5/0.5, correctly. This is close to the OP as if we wildly assert that you and only you have free will and force the others, then you are special. Equally in cases where everyone is asked and plays separately, you have 18 or 2 times the benefits depending on whether you're in A1 or A2.

If each individual Green room played separately, then you update on (Green walls), but P(I'm being asked|Green) = 1 in either case. This is betting on whether there are 18 people in green rooms or 2, and you get the correct 0.9/0.1 split. To reproduce the OP the offers would need to be +1/18 to Greens and -3/18 from Reds in A1, and +1/2 to Greens and -3/2 from Reds in A2, and then you'd refuse to play, correctly.