Okay, I have a question: what will you call the decision theory where x is the action, I write down f(x) which is the pay-off, like in applied mathematics, and then I solve it for maximum f(x) using regular school algebra? I use that a lot when writing AIs for the computer game, really (when I want to find the direction in which to shoot, for instance, or want to turn minimizing the 3rd derivative)
Then I don't need to go into any recursion what so ever if i have conditionals on x inside the pay-offs (as in newcomb). I don't do some update cycle to solve the x=x , i know it doesn't fix x, and i don't recurse if i find x=1+x/2
BTW, an observation on the newcomb's problem: it seems to me that one boxing people write payoff function as
f(1)=box1(1)
f(2)=box2(2)+box1(2)
box1(1)=1000000
box1(2)=0
box2(1)=1000
box2(2)=1000
and one-box, other people write it as:
f(1)=box1
f(2)=box2+box1
box1>=0
box2>=0
and ignore the fact about prediction (boxes as function of x) altogether because they trust a world model where this is forbidden more than they trust the problem statement, which is kind of silly thing to do when you're solving a hypothetical anyway. Or maybe because they listen harder to 'the contents of boxes are fixed' than to 'prediction'. In any case to me the 1-boxing vs 2-boxing now looks like a trivial case of 'people can disagree how to transform verbal sentence into a model' . Given that there's as many versions of English as there are people speaking English, it's not very interesting. One can postulate the both boxes being transparent to make even more nonsensical version.
Basically, all of the decision theories are just deducing payoffs and calculating argmax, but there's a subtle complication with regard to the deduction of payoffs. I'm almost done with the post that explains it.
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!