Still not quite it.
BTW, an observation: if i want to maximize the distance at which the thrown stone lands, assuming constant initial speed and zero height, I work out the algebra - I have unknown, x, the shoot angle, and I have laws of physics that express distance as function of x, and I find best x. In newcomb's, I have x=my choice, I have been given rules of the world, whereby the payoff formula includes the x itself, i calculate best x, which is one-box (not surprisingly). The smoking lesion also works fine. Once you stop invoking your built-in decision theory on confusing cases, things are plain and clear.
At this point, how well you perform depends to what sort of axiom system you are using to solve for x, and by Godel's theorem, there will be some problem that is going to get ya, i.e. cause failure.
At this point, how well you perform depends to what sort of axiom system you are using to solve for x, and by Godel's theorem, there will be some problem that is going to get ya, i.e. cause failure.
This doesn't seem like something that needs to be solvable. You can you diagonalization to defeat any decision theory; just award some utility iff the agent chooses the option not recommended by that decision theory. A different decision theory can choose the other option, but that decision theory has acausal influence over the right answer that prevents it from winning.
In my recent post, I outlined 5 conditions that I'd like a decision theory to pass; TDT, UDT and ADT pass them, while CDT and EDT don't. I called decision theories that passed those conditions "advanced decision theories", but that's probably not an optimal name. Can I ask you to brainstorm some other suggestions for me? (I may be writing a follow-up soon.)
As usual, it's best to brainstorm on your own before reading any of the comments. You can write down your ideas, then check if any have already been suggested, then comment with the new ones.
Thanks!