There seems to be an even more elegant way to define causal relationships between agents, or more generally between programs. Starting from a hypothesis Θ∈□(Γ×Φ), for Γ=ΣR, we consider its bridge transform B∈□(Γ×2Γ×Φ). Given some subset of programs Q⊆R we can define Δ:=ΣQ then project B to BΔ∈□(Γ×2Δ)[1]. We can then take bridge transform again to get some C∈□(Γ×2Γ×2Δ). The 2Γ factor now tells us which programs causally affect the manifestation of programs in Q. Notice that by Proposition 2.8 in the IBP article, when Q=R we just get all programs that are running, which makes sense.
Agreement Rules Out Mesa-Optimization
The version of PreDCA without any explicit malign hypothesis filtering might be immune to malign hypotheses, and here is why. It seems plausible that IBP admits an agreement theorem (analogous to Aumann's) which informally amounts to the following: Given two agents Alice and Bobcat that (i) share the same physical universe, (ii) have a sufficiently tight causal relationship (each can see what the other sees), (iii) have unprivileged locations inside the physical universe, (iv) start from similar/compatible priors and (v) [maybe needed?] similar utility functions, they converge to similar/compatible beliefs, regardless of the complexity of translation between their subjective viewpoints. This is plausible because (i) as opposed to the cartesian framework, different bridge rules don't lead to different probabilities and (ii) if Bobcat considers a simulation hypothesis plausible, and the simulation is sufficiently detailed to fool it indefinitely, then the simulation contains a detailed simulation of Alice and hence Alice must also consider this to be plausible hypothesis.
If the agreement conjecture is true, then the AI will converge to hypotheses that all contain the user, in a causal relationship with the AI that affirms them as the user. Moreover, those hypotheses will be compatible with the user's own posterior (i.e. the differences can be attributed the AIs superior reasoning). Therefore, the AI will act on the user's behalf, leaving no room for mesa-optimizers. Any would-be mesa-optimizer has to take the shape of a hypothesis that the user should also believe, within which the pointer-to-values still points to the right place.
Two nuances:
Maybe in practice there's still room for simulation hypotheses of the AI which contain coarse-grained simulations of the user. In this case, the user detection algorithm might need to allow for coarsely simulated agents.
If the agreement theorem needs condition v, we get a self-referential loop: if the AI and the user converge to the same utility function, the theorem guarantees them to converge to the same utility function, but otherwise it doesn't. This might make the entire thing a useless tautology, or there might be a way to favorably resolve the self-reference, vaguely analogously to how Loeb's theorem allows resolving the self-reference in prisoner dilemma games between FairBots.
There are actually two ways to do this, corresponding to the two natural mappings Γ×2Γ→Γ×2Δ. The first is just projecting the subset of Γ to a subset of Δ, the second is analogous to what's used in Proposition 2.16 of the IBP article. I'm not entirely sure what's correct here. ↩︎