IIRC, in “Good and Real” Gary Drescher suggests to first consider a modified version of Newcomb’s Problem, where both boxes are transparent. He then goes on to propose a solution in which agent precommits to one-box before being presented with the problem in a first place. This way, as I understand, causal diagram would first feature a node where agent chooses to precommit, and it both deterministically causes their later action to one-box, and Omega’s action to put $1000000 in larger box. This initial node for choosing to precommit does look like an agent’s abstract model of their and Omega’s actions.
Alternatively, in this paper, “Unboxing the Concepts in Newcomb’s Paradox: Causation, Prediction, Decision in Causal Knowledge Patterns”, Roland Poellinger suggests to augment ordinary causal networks with new type of undirected edge, he calls an “epistemic contour”. In his setup, this edge connects agent’s action to select either one or two boxes and Omega’s prediction. This edge is not cut when performing do(A) operation on the causal graph, but the information is passed backwards in time, thus formalizing the notion of “prediction”.
Great post, lot of food for thought, thanks!
IIRC, in “Good and Real” Gary Drescher suggests to first consider a modified version of Newcomb’s Problem, where both boxes are transparent. He then goes on to propose a solution in which agent precommits to one-box before being presented with the problem in a first place. This way, as I understand, causal diagram would first feature a node where agent chooses to precommit, and it both deterministically causes their later action to one-box, and Omega’s action to put $1000000 in larger box. This initial node for choosing to precommit does look like an agent’s abstract model of their and Omega’s actions.
Alternatively, in this paper, “Unboxing the Concepts in Newcomb’s Paradox: Causation, Prediction, Decision in Causal Knowledge Patterns”, Roland Poellinger suggests to augment ordinary causal networks with new type of undirected edge, he calls an “epistemic contour”. In his setup, this edge connects agent’s action to select either one or two boxes and Omega’s prediction. This edge is not cut when performing do(A) operation on the causal graph, but the
information is passed backwards in time, thus formalizing the notion of “prediction”.