My paper "Anthropic decision theory for self-locating beliefs", based on posts here on Less Wrong, has been published as a Future of Humanity Institute tech report. Abstract:
This paper sets out to resolve how agents ought to act in the Sleeping Beauty problem and various related anthropic (self-locating belief) problems, not through the calculation of anthropic probabilities, but through finding the correct decision to make. It creates an anthropic decision theory (ADT) that decides these problems from a small set of principles. By doing so, it demonstrates that the attitude of agents with regards to each other (selfish or altruistic) changes the decisions they reach, and that it is very important to take this into account. To illustrate ADT, it is then applied to two major anthropic problems and paradoxes, the Presumptuous Philosopher and Doomsday problems, thus resolving some issues about the probability of human extinction.
Most of these ideas are also explained in this video.
To situate Anthropic Decision Theory within the UDT/TDT family: it's basically a piece of UDT applied to anthropic problems, where the UDT approach can be justified by using generally fewer, and more natural, assumptions than UDT does.
My current outline of UDT is organized by levels:
1) Indexical uncertainty, which is solved by converting to single player games with imperfect information. This level is basically playing with graphs. Absent-Minded Driver, Wei's coordination problem, Psy-Kosh's problem. Interpreting anthropic problems as choosing the right game, like in your work.
2) Cartesian uncertainty, where your copies aren't delineated in the world and you need to find them first, then reduce the problem to level 1. This level is where self-referential sentences come in. Symmetric PD, Newcomb's Problem, Counterfactual Mugging. Models based on halting oracles, Peano arithmetic, modal logic.
3) Logical uncertainty, where you can't do level 2 crisply because your power is limited. This level is about approximations and bounds. Proof searchers, spurious counterfactuals, logical inductors, logical updatelessness.
4) Full on game theory, where even level 3 isn't enough because there are other powerful agents around. This level is pretty much warfare and chaos. Bargaining, blackmail, modal combat, agent simulates predictor.
At this point I feel that we have definitively solved levels 1 and 2, are making progress on level 3, and have a few glimpses of level 4. But even on the first two levels, writing good exposition is a challenge. I'll send you drafts as I go.
Good decomposition, though I am sceptical that there is much clean at level 4.