I think defect is the right answer in your AI problem and therefore that NDT gets it right
That's surprising to me. Imagine that the situation is "prisoner's dilemma with shared source code", and that the AIs inspect each other's source code and verify that (by some logical but non-causal miracle) they have exactly identical source code. Do you still think they do better to defect? I wouldn't want to build an agent that defects in that situation :-p
The paper that jessicat linked in the parent post is a decent introduction to the notion of logical counterfactuals. See also the "Idealized Decision Theory" section of this annotated bibliography, and perhaps also this short sequence I wrote a while back.
An AI should certainly cooperate if it discovered that by chance its opposing AI had identical source code.
I read your paper and the two posts in your short sequence. Thanks for the links. I still think it's very unlikely that one of the AIs in your original hypothetical (when they don't examine each other's source code) would do better by defecting.
I accept that if an opposing AI had a model of you that was just decent but not great, then there is some amount of logical connection there. What I haven't seen is any argument about the shape of the graph o...
I've recently read the decision theory FAQ, as well as Eliezer's TDT paper. When reading the TDT paper, a simple decision procedure occurred to me which as far as I can tell gets the correct answer to every tricky decision problem I've seen. As discussed in the FAQ above, evidential decision theory get's the chewing gum problem wrong, causal decision theory gets Newcomb's problem wrong, and TDT gets counterfactual mugging wrong.
In the TDT paper, Eliezer postulates an agent named Gloria (page 29), who is defined as an agent who maximizes decision-determined problems. He describes how a CDT-agent named Reena would want to transform herself into Gloria. Eliezer writes
Eliezer then later goes on the develop TDT, which is supposed to construct Gloria as a byproduct.
Why can't we instead construct Gloria directly, using the idea of the thing that CDT agents wished they were? Obviously we can't just postulate a decision algorithm that we don't know how to execute, and then note that a CDT agent would wish they had that decision algorithm, and pretend we had solved the problem. We need to be able to describe the ideal decision algorithm to a level of detail that we could theoretically program into an AI.
Consider this decision algorithm, which I'll temporarily call Nameless Decision Theory (NDT) until I get feedback about whether it deserves a name: you should always make the decision that a CDT-agent would have wished he had pre-committed to, if he had previously known he'd be in his current situation and had the opportunity to precommit to a decision.
In effect, you are making an general precommittment to behave as if you made all specific precommitments that would ever be advantageous to you.
NDT is so simple, and Eliezer comes so close to stating it in his discussion of Gloria, that I assume there is some flaw with it that I'm not seeing. Perhaps NDT does not count as a "real"/"well defined" decision procedure, or can't be formalized for some reason? Even so, it does seem like it'd be possible to program an AI to behave in this way.
Can someone give an example of a decision problem for which this decision procedure fails? Or for which there are multiple possible precommitments that you would have wished you'd made and it's not clear which one is best?
EDIT: I now think this definition of NDT better captures what I was trying to express: You should always make the decision that a CDT-agent would have wished he had precommitted to, if he had previously considered the possibility of his current situation and had the opportunity to costlessly precommit to a decision.