A New Bayesian Decision Theory

One algorithm for strategic dominance, one algorithm for utility maximization

Two weeks ago I wrote an introduction to normative decision theory, yet I haven’t made clear what decision algorithm should be used. Before that, I’d like to give some preliminaries.

Generally speaking, Newcomb's Problem and the Smoking Lesion Problem represent counterexamples to CDT and EDT and show where they differ. But if causal chains and conditional probabilities consider one another then CDT and EDT are equivalent, causing one to choose the dominance principle (assuming probabilities are held constant) and thus two-boxing and smoking.

However, if probabilities update based on the agent's actions, such as in the meta-Newcomb's problem and Parfit's Hitchhiker, then CDT=EDT would recommend the maximization of expected utility and thus one-boxing and paying up respectively.

I don't think defining CDT = EDT is useful, so coming up with a new decision theory may be optimal. Without regard to labels or choosing a specific decision theory, I think one should choose the dominance principle if probabilities are held constant and thus choose smoking, two-boxing, etc.

But if probabilities aren’t constant, then one should pre-commit to an action that does not necessarily dominate (assuming constant probabilities) in exchange for an outcome that is (second?) best, e.g. pre-committing to pay Parfit’s biker.

This would be the kind of decision theory that recommends that one invoke EDT or FDT when probabilities can be updated by the agent, and invoke CDT otherwise. This would be the kind of decision theory that smokes, one-boxes, and doesn’t pay the biker ex-post, but “chooses to pay the biker ex-ante.” In other words, this would be the kind of decision theory that recommends decisions that maximize expected utility.

Of course, ideas are more important than labels, but labels still remain useful, and if I were to choose a label for such a decision procedure, given its relation to whether probabilities remain constant or update based on decisions, I would choose the name Bayesian Decision Theory (BDT).

Further thoughts and comments on decision theory are welcome.