These three causal graphs cannot be distinguished by the observational statistics. The causal information given in the problem is an essential part of its statement, and no decision theory which ignores causation can solve it.
I think this isn’t actually compatible with the thought experiment. Our hypothetical agent knows that it is an agent. I can’t yet formalize what I mean by this, but I think that it requires probability distributions corresponding to a certain causal structure, which would allow us to distinguish it from the other graphs. I don’t know how to write down a probability distribution that contains myself as I write it, but it seems that such a thing would encode the interventional information about the system that I am interacting with on a purely probabilistic level. If this is correct, you wouldn’t need a separate representation of causality to decide correctly.
Our hypothetical agent knows that it is an agent. I can’t yet formalize what I mean by this, but I think that it requires probability distributions corresponding to a certain causal structure, which would allow us to distinguish it from the other graphs
How about: an agent, relative to a given situation described by a causal graph G, is an entity that can perform do-actions on G.
No, that’s not what I meant at all. In what you said, the agent needs to be separate from the system in order to preform do-actions. I want an agent that knows it’s an agent, so it has to have a self-model and, in particular, has to be inside the system that is modelled by our causal graph.
One of the guiding heuristics in FAI theory is that an agent should model itself the same way it models other things. Roughly, the agent isn’t actually tagged as different from nonagent things in reality, so any desired behaviour that depends on correctly making this distinction cannot be regulated with evidence as to whether it is actually making the distinction the way we want it to. A common example of this is the distinction between self-modification and creating a successor AI; an FAI should not need to distinguish these, since they’re functionally the same. These sorts of ideas are why I want the agent to be modelled within its own causal graph.
I think this isn’t actually compatible with the thought experiment. Our hypothetical agent knows that it is an agent. I can’t yet formalize what I mean by this, but I think that it requires probability distributions corresponding to a certain causal structure, which would allow us to distinguish it from the other graphs. I don’t know how to write down a probability distribution that contains myself as I write it, but it seems that such a thing would encode the interventional information about the system that I am interacting with on a purely probabilistic level. If this is correct, you wouldn’t need a separate representation of causality to decide correctly.
How about: an agent, relative to a given situation described by a causal graph G, is an entity that can perform do-actions on G.
No, that’s not what I meant at all. In what you said, the agent needs to be separate from the system in order to preform do-actions. I want an agent that knows it’s an agent, so it has to have a self-model and, in particular, has to be inside the system that is modelled by our causal graph.
One of the guiding heuristics in FAI theory is that an agent should model itself the same way it models other things. Roughly, the agent isn’t actually tagged as different from nonagent things in reality, so any desired behaviour that depends on correctly making this distinction cannot be regulated with evidence as to whether it is actually making the distinction the way we want it to. A common example of this is the distinction between self-modification and creating a successor AI; an FAI should not need to distinguish these, since they’re functionally the same. These sorts of ideas are why I want the agent to be modelled within its own causal graph.