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orthonormal comments on Decision Theories: A Semi-Formal Analysis, Part I - Less Wrong
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But everyone's source code is communicated at each round to everyone. What do you mean, "in advance"? What for?
This is very speculative. While an agent can make predictions about itself as long as it wishes, thus making a natural counterfactual inference performed by the other agent longer, that makes the spurious counterfactuals longer as well. Wei asks in another thread:
Unless an agent sabotages itself by deciding arbitrarily, and then observes spurious inferences from that decision, I don't see how to push spurious inferences in front of the natural ones.
I think this part of the post should be rephrased, so that it says that we don't know how to prove that even such bizarre exploitation strategy is impossible, instead of the current assertion (unless you have background knowledge or a new result that suggests that this conjecture is reasonable).
Edit: Turns out this is indeed possible, if X can be tricked into checking a specifically contrived proof out of order. Here's a post describing the setup.
It's easier for me to imagine a programmer writing a program specifically to exploit mine than it is to imagine a program that's able to recognize an opportunity for such exploitation in general. Just as a Nash equilibrium strategy can't be exploited even if it's publicly known in advance, we'd like our decision theories to be secure from exploitation even if their source code were publicly known.
I agree; I just thought of it as I was writing the post, and in retrospect I should have asked the decision-theory mailing list before putting it in. But my intuition is that this sort of malice could be possible, using the equivalent of a Henkin sentence. I'll edit to make it clearer that this is speculation, though.
This sounds like a way of making a natural proof, not a spurious one... Could you explain in more detail?
I had the intuition that one could both "push X away from genuine counterfactuals" using diagonalization and "pull X toward particular spurious counterfactuals" using specially constructed explicit Henkin sentences (which the inference module will find). But I'm more confident that the first half makes sense than that the second half does.
Right, but sentences where? Why does our agent believe them? Can you give a sketch of an analogous example?
The inference module of X will at some point start trying to prove sub-problems about the code of Y if it doesn't find an easily proved counterfactual. In the source code of Y, in a place where X will apply its inference module, the programmer has included an explicit Henkin sentence (i.e. contains the ingredients for its own proof) such that when X applies its inference module, it quickly proves "if X!=a then U=-1000", which happens to be the sort of thing the NDT agent was looking for. This section of code doesn't affect Y's decision except when Y is playing a game of this sort against X.
Again, highly speculative.
I still don't understand what you're saying. What's the nature of this "Henkin sentence", that is in what way is it "included" in Y's source code? Is it written in the comments or something? What does it mean for X to "apply its inference module"? My only guess is that you are talking about X starting to enumerate proofs in order other than their length, checking the proofs that happen to be lying around in Y's code just in case, so that including something in Y's code might push X to consider a proof that Y wants it to consider earlier than some other proof. Is it what you mean?
How would "if X!=a then U=-1000" follow from a Henkin sentence (it obviously can't make anything it likes true)?
The mental image of an inference module that I'm trying to trick is something like a chess program, performing a heuristically biased depth-first search on the space of proofs, based on the source code of the round. If the first path it takes is a garden path to an easy but spurious counterfactual proof, and if the genuine counterfactual is unreachable at the same level (by some diagonalization of X's proof method), then X should be fooled. The question is whether, knowing X's source code, there's a Y which leads X's heuristics down that garden path.
Since in the end we'll achieve X=a, the statement "if X!=a then U=-1000" is true, and it should be provable by NDT if it finds the right path, so there should be some way of helping NDT find the proof more quickly.
I don't have a strong intuition for how to fool the "enumerate and check all proofs up to length N" inference module.
Okay. Let's say we write an X that will start from checking any proof given to it (and accepting its conclusion). How can we construct a proof of X=a that X can read then? It looks like the more X reads, the longer the proof must be, and so there doesn't exist a proof that X can also read. I don't see how to construct a counterexample to this property without corrupting X's inference system, though I imagine some quining trick might work...
Right. That's why I acknowledge that this is speculative.
If it turns out there's really no need to worry about spurious counterfactuals for a reasonable inference module, then hooray! But mathematical logic is perverse enough that I expect there's room for malice if you leave the front door unlocked.