Ooh, and we can apply similar reasoning to the marble problem if we change it, in a seemingly isomorphic way, so that instead of making the trade based on all the responses of the people who saw a green marble, Psy-Kosh selects one of the green-marble-observers at random and considers that person's response (this should make no difference to the outcomes, assuming that the green-marblers can't give different responses due to no-spontaneous-symmetry-breaking and all that).

Then, conditioning on drawing a green marble, person A infers a 9/10 probability that the bucket contained 18 green and 2 red marbles. However, if the bucket contains 18 green marbles, person A has a 1/18 chance of being randomly selected given that she drew a green marble, whereas if the bucket contains 2 green marbles, she has a 1/2 chance of being selected. So, conditioning on her response being the one that matters as well as the green marble itself, she infers a (9:1) * (1/18)/(1/2) = (9:9) odds ratio, that is probability 1/2 the bucket contains 18 green marbles.

Which leaves us back at a kind of anthropic updating, except that this time it resolves the problem instead of introducing it!