AI summaryⓘ
The authors created a clear way to describe how decisions are made using a formal math tool called nonparametric structural equation models, which helps show causes and effects clearly. They used this tool to explain existing decision theories and introduced a new one they call personal decision theory, where agents try to maximize their own expected happiness based on their beliefs. They also made a way to measure how well a decision theory works when it influences many people, such as through teaching or rules, and found that under certain conditions, their new theory performs best. The authors used well-known puzzles, like the smoking lesion problem and Newcomb's problem, to show how their framework works. Overall, their work aims to make it easier to compare and improve decision theories by giving the field a solid, shared foundation.
decision theorynonparametric structural equation modelscausalitysubjective utilitycounterfactualsevidential decision theory (EDT)causal decision theory (CDT)personal decision theorysmoking lesion problemNewcomb's problem
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.