Cheating Death in Damascus

Evidential and Causal Decision Theory are the leading contenders as theories of rational action, but both face fatal counterexamples. We present some new counterexamples, including one in which the optimal action is causally dominated. We also present a novel decision theory, Functional Decision Theory (fdt), which simultaneously solves both sets of counterexamples. Instead of considering which physical action of theirs would give rise to the best outcomes, fdt agents consider which output of their decision function would give rise to the best outcome. This theory relies on a notion of subjunctive dependence, where multiple implementations of the same mathematical function are considered (even counterfactually) to have identical results for logical rather than causal reasons. Taking these subjunctive dependencies into account allows fdt agents to outperform cdt and edt agents in, e.g., the presence of accurate predictors. While not necessary for considering classic decision theory problems, we note that a full specification of fdt will require a non-trivial theory of logical counterfactuals and algorithmic similarity.