A few weeks ago at a Seattle LW meetup, we were discussing the Sleeping Beauty problem and the Doomsday argument. We talked about how framing Sleeping Beauty problem as a decision problem basically solves it and then got the idea of using same heuristic on the Doomsday problem. I think you would need to specify more about the Doomsday setup than is usually done to do this.
We didn't spend a lot of time on it, but it got me thinking: Are there papers on trying to gain insight into the Doomsday problem and other anthropic reasoning problems by framing them as decision problems? I'm surprised I haven't seen this approach talked about here before. The idea seems relatively simple, so perhaps there is some major problem that I'm not seeing.
EDIT: Expanded first point a bit.
Hm. One could try and fix it by splitting each point in time into different "worlds," like you suggest below. But the updating from time (let's assume there's no clock to look at, so the curves are smooth) would rely on the subjective probabilities, which you are avoiding. The update ratio is P(feels like 4 hours | heads) / P(feels like 4 hours). If P(feels like 4 hours | X) is 0.9 if X is heads and 0.8 if X is tails, then if the probabilities are 1/3 the ratio will be 1.08, while if the probabilities are 1/2, 1/4, 1/4 the update is a factor of 1.059.
This does lead to a case a bit more complicated than my original examples, though, because the people in different worlds will make different decisions. I'm not even sure how ADT would handle this situation, since it has to avoid the subjective probabilities - do you respond like an outside observer, and use 0.5, 0.5 for everything?
Yes, that would be reasonable.
Those only hold if things are simple. To say "these might prevent things from getting any more complicated" is to put the cart before the horse.
ADT does not avoid subjective probabilities - it only avoid anthropic probabilities. P(feels like 4 hours | heads) is perfectly fine. ADT only avoids probabilities that would change if you shifted from SIA to SSA or vice versa.