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.
So do you think it’s worth writing up, or getting someone to do so?
Yeah. I’ve been feeling a bit guilty so I started another attempt at a writeup, in a week or two we’ll see if it goes anywhere.
I think the second thing to do is to list all the problems, and what the correct answer is/what answer the algorithms give.
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.