Functional Decision Theory: A New Theory of Instrumental Rationality

TL;DR

The paper introduces functional decision theory (FDT), a normative framework that selects the output of a fixed decision function rather than a physical action, and argues it yields higher expected utility than CDT or EDT in a range of classic dilemmas. By formalizing subjunctive dependence and extending Pearl-style causal reasoning to include logical dependencies, the authors show how FDT can coherently handle predictors, twins, and other Newcomblike scenarios without ad hoc precommitments. Through detailed analyses of Newcomb's problem, the smoking lesion, Parfit's hitchhiker, and related variants, FDT is shown to outperform both CDT and EDT on “fair” problems, offering a unified approach to decision theory and game theory. While acknowledging open challenges (notably deriving subjunctive structures from observation and assessing universal optimality), the paper argues that FDT provides a promising general-purpose normative theory of rational choice with broad practical relevance, including AI and coordination problems.

Abstract

This paper describes and motivates a new decision theory known as functional decision theory (FDT), as distinct from causal decision theory and evidential decision theory. Functional decision theorists hold that the normative principle for action is to treat one's decision as the output of a fixed mathematical function that answers the question, "Which output of this very function would yield the best outcome?" Adhering to this principle delivers a number of benefits, including the ability to maximize wealth in an array of traditional decision-theoretic and game-theoretic problems where CDT and EDT perform poorly. Using one simple and coherent decision rule, functional decision theorists (for example) achieve more utility than CDT on Newcomb's problem, more utility than EDT on the smoking lesion problem, and more utility than both in Parfit's hitchhiker problem. In this paper, we define FDT, explore its prescriptions in a number of different decision problems, compare it to CDT and EDT, and give philosophical justifications for FDT as a normative theory of decision-making.

Figures (4)

• Figure 1: A causal graph for CDT agents facing Newcomb's problem. The agent observes the double-bordered node (which is, in this case, unused), intervenes on the rectangular node, and calculates utility using the diamond node.
• Figure 2: A Bayesian network for Newcomb's problem. The only stochastic nodes are Act and Accurate; all the other nodes are deterministic. As you may verify, the results below continue to hold if we add more stochasticity, e.g., by making Predisposition strongly but imperfectly correlated with Act. The prior probabilities on Act are left as a free parameter. This graph is more verbose than necessary: we could collapse V and Outcome into a single node, and collapse Prediction and Box B into a single node. Note that this is not a causal graph; the arrow from Act to Predisposition describes a correlation in the agent's beliefs but does not represent causation.
• Figure 3: Fiona's graph $G^\mathit{F}$ for the smoking lesion problem. In the case where she has the lesion, the point of intervention will be $\text{fdt}(\underline{P^\mathit{F}_S}, \underline{G^\mathit{F}})$, as illustrated. In the case where she does not have the lesion, the point of intervention will instead be $\text{fdt}(\underline{P^\mathit{F}_R}, \underline{G^\mathit{F}})$. In either case, Fiona does not have introspective access to the point of intervention, and computes her action under ignorance about her own preferences.
• Figure 4: A graph $G^\mathit{F}$ for Fiona in the mechanical blackmail problem. The point of intervention is drawn for the case where she observes the blackmail. Blackmailer determines whether $\text{fdt}(\underline{P^\mathit{F}}, \underline{G^\mathit{F}}, \text{blackmail})$ or $\text{fdt}(\underline{P^\mathit{F}}, \underline{G^\mathit{F}}, \text{$\emptyset$})$ gets to set Act.