🤖 AI Summary
Existing decision theories lack a unified formal language, and key concepts—such as the distinction between subjective and objective perspectives and criteria for evaluating theoretical superiority—remain ambiguous, impeding rigorous comparison. This work addresses these limitations by constructing a unified decision-theoretic framework grounded in nonparametric structural equation models (NPSEMs), which precisely characterizes agents, causal relationships, and counterfactuals, and formally defines evidential decision theory (EDT) and causal decision theory (CDT). Building on this foundation, the paper proposes a personal decision theory that aims to maximize an individual’s subjective counterfactual utility and introduces a performance evaluation metric based on population-level interventions, proving its optimality under specific conditions. The framework enables formal analyses of Newcomb’s paradox and the smoking lesion problem, offering a clear modeling language and a comparable benchmark for decision theories.
📝 Abstract
Decision theory provides a formal framework for how agents should make choices under uncertainty, drawing on ideas from philosophy, probability, and causality. Despite significant progress, the field still lacks a unified modeling language, and key concepts - such as the distinction between subjective and objective elements, or what it means for a decision theory to perform well - are often left implicit. This can make it difficult to evaluate and compare competing theories, particularly in controversial cases. In this paper, we address these issues by introducing a formal framework for decision theory based on nonparametric structural equation models (NPSEMs), a well-established tool in causal inference. NPSEMs provide a unified foundation for representing agents, counterfactuals, and causal relationships, allowing for unambiguous definitions of EDT and CDT. Building on this foundation, we propose a novel decision theory - personal decision theory - which instructs agents to maximize a subjective model of their own counterfactual utility. We introduce a formal performance metric based on hypothetical interventions that enforce a given decision theory across a population - such as might be achieved through education or policy -- and show that, under certain assumptions, personal decision theory is optimal with respect to this metric. Throughout, we use the smoking lesion problem as a running example and conclude with a formal analysis of Newcomb's problem. Our aim is to provide decision theory with a clearer modeling language and firmer evaluative ground, thereby enabling more rigorous comparisons and facilitating conceptual progress in the field.