A causal modeling perspective on decision theory

Decision theory is often fragmented, with competing schools like Evidential Decision Theory (EDT) and Causal Decision Theory (CDT) lacking a unified language. This ambiguity makes it difficult to compare theories, especially in controversial scenarios like Newcomb's problem. This paper proposes using Nonparametric Structural Equation Models (NPSEMs)—a standard tool in causal inference—as a formal foundation for decision theory. By representing agents as instantiations of error terms within an NPSEM, the author provides a rigorous way to define agents, counterfactuals, and causal relationships, moving beyond heuristic causal diagrams.

The author introduces Personal Decision Theory (PDT), which shifts the focus from maximizing population-level expected utility to maximizing an agent's own counterfactual utility. While EDT and CDT rely on population-level expectations, PDT leverages the agent's subjective model of their specific counterfactual outcomes. The paper argues that this approach is more intuitive, as it directly addresses the individual agent's goal of maximizing their own utility rather than an average across a population.

To evaluate competing theories, the paper proposes an objective performance metric based on hypothetical interventions: if a policy-maker were to enforce a specific decision theory across a population, which theory would yield the highest total expected utility? Under the assumptions that agents have correct subjective models and that the decision theory does not directly influence utility (e.g., through psychological stress), the author proves that PDT is optimal. This framework also allows for a formal analysis of Newcomb's problem, demonstrating that the relative performance of EDT and CDT depends on the causal influence the decision theory has on the predictor's accuracy.