Expected utility is the probability-weighted average utility of outcomes produced by an action, policy, or intervention. A decision rule chooses the action with the highest expected utility, while a policy applies the same idea in automated decision-making. section 12.2.2
For causal decisions, evaluate the utility distribution under an intervention: E(U(Yₓ)). This differs from the observational quantity E(U(Y) | X=x), which conditions on actions that occurred rather than forcing them. section 12.2.2 section 12.2.4
Investment choice
An investment model compares debt and equity under bear and bull markets. Initially, debt has observational expected utility of $57,000 versus $37,000 for equity, while interventional expectations are $39,000 and $34,000. After changing one outcome probability, the preferred action can diverge, showing why causal expectations matter for robust policy selection. section 12.2.4
Newcomb’s paradox
With a predictor that is 95% accurate, choosing both boxes yields $51,000 expected utility, while choosing only box B yields $950,000. The example exposes tension between conditioning on predicted choices and evaluating causal consequences. section 12.2.5
