A causal modeling perspective on decision theory

Arvid Sj\"olander

arxiv: 2606.29911 · v1 · pith:B5IJEOB4new · submitted 2026-06-29 · 💻 cs.AI · stat.ME

A causal modeling perspective on decision theory

Arvid Sj\"olander This is my paper

Pith reviewed 2026-06-30 06:26 UTC · model grok-4.3

classification 💻 cs.AI stat.ME

keywords decision theorycausal modelingNPSEMspersonal decision theoryNewcomb's problemcounterfactual utilityEDTCDT

0 comments

The pith

Personal decision theory is optimal when decision theories are evaluated by their effects under hypothetical population-wide enforcement.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a causal modeling approach using nonparametric structural equation models to give decision theory a shared formal language. It defines personal decision theory as the rule of maximizing expected utility from a subjective model of one's own counterfactual outcomes. The central result is that this personal decision theory scores highest on a performance measure that imagines forcing an entire population to adopt one theory or another. This setup lets the author compare theories cleanly in examples such as the smoking lesion problem and Newcomb's problem. A sympathetic reader would care because the lack of such a shared language has made it hard to settle long-standing disputes between different decision theories.

Core claim

Using nonparametric structural equation models, the paper defines personal decision theory as instructing agents to maximize a subjective model of their own counterfactual utility. It introduces a performance metric based on hypothetical interventions that enforce a given decision theory across a population and shows that, under certain assumptions, personal decision theory is optimal with respect to this metric. The framework also provides unambiguous definitions for evidential and causal decision theory and applies the analysis to Newcomb's problem.

What carries the argument

Nonparametric structural equation models (NPSEMs) that represent agents' subjective models, counterfactuals, and causal relationships to define and evaluate decision theories.

If this is right

Competing decision theories can be compared using a shared causal language and a single performance metric.
Personal decision theory outperforms others when the metric values population-level outcomes under enforced adoption.
Classic problems such as Newcomb's can be analyzed formally within the model.
The optimality result holds only when the listed assumptions about the interventions and models are met.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The population-enforcement metric may implicitly favor decision theories that lead to better social coordination when scaled.
Similar causal frameworks could be used to evaluate other normative theories beyond decision theory.
Agent-based simulations could test whether the optimality ranking changes under different assumptions about how interventions are implemented.

Load-bearing premise

That the appropriate way to evaluate a decision theory is by its performance when the theory is hypothetically enforced across an entire population.

What would settle it

A concrete counterexample in which another decision theory, such as causal decision theory, produces higher average utility than personal decision theory when both are enforced across the same population in a well-specified causal model.

Figures

Figures reproduced from arXiv: 2606.29911 by Arvid Sj\"olander.

**Figure 2.** Figure 2: Causal diagram for the smoking lesion problem, augmented with [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: Causal diagram for Newcomb’s problem. This model has some similarities with that for the smoking lesion problem in [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives decision theory an NPSEM language and claims personal decision theory is optimal under a population-intervention metric, but the assumptions stay unspecified and the derivation is missing.

read the letter

The paper's main move is to recast decision theory inside nonparametric structural equation models so that EDT, CDT, and a new personal decision theory all have clear counterfactual definitions. It then defines a performance metric by imagining a population-level intervention that forces everyone to follow one theory or another, and states that personal decision theory comes out on top under certain assumptions. The smoking-lesion and Newcomb examples are worked through in this setup.

What is actually new is the explicit use of NPSEMs as the common language and the population-intervention metric itself. The framework does make the subjective-objective distinction sharper than many informal discussions, and the running examples are handled consistently.

The central claim is the optimality result. The abstract says it holds under unspecified assumptions, but supplies no list of those assumptions and no derivation. In an NPSEM, enforcing a decision rule across a population means altering the structural equations or exogenous terms; without checking whether those changes interact with the agent's own subjective model, it is impossible to know whether the result is general or rests on hidden restrictions. The metric is also defined inside the same formal system it evaluates, so the circularity risk the stress-test note flags is real until the assumptions are written down and tested.

This is for readers already working in causal decision theory who want a more precise modeling tool. The framework is worth a serious referee's time because the language is coherent and the examples are concrete, even though the optimality step needs the missing assumptions and proof steps supplied.

Referee Report

2 major / 1 minor

Summary. The paper introduces a nonparametric structural equation model (NPSEM) framework for decision theory to provide unambiguous definitions of EDT and CDT, proposes Personal Decision Theory (PDT) instructing agents to maximize subjective counterfactual utility, defines a performance metric based on hypothetical population-level interventions (e.g., via education or policy) that enforce a given decision theory, and claims that under certain assumptions PDT is optimal with respect to this metric. The smoking lesion problem is used as a running example, with a formal analysis of Newcomb's problem at the end.

Significance. A unified NPSEM-based modeling language for decision theory would be a useful contribution for clarifying subjective vs. objective elements and enabling rigorous comparisons. If the optimality result holds after explicit statement and verification of the assumptions (including independence from the do-operator interventions on agents' decision procedures), the performance metric could supply a new evaluative standard; the paper's approach to counterfactuals via structural equations is a potential strength.

major comments (2)

[Abstract] Abstract: the central claim that 'under certain assumptions, personal decision theory is optimal with respect to this metric' supplies neither an enumeration of the assumptions nor a derivation; without these, it is impossible to verify whether the result holds when the intervention is an NPSEM do-operator on the structural equations encoding agents' choice functions.
[Abstract] Abstract: the performance metric is defined via hypothetical interventions that enforce a decision theory across a population; the manuscript does not demonstrate that this metric is independent of the theories being ranked or that it avoids circularity when the enforced theory interacts with agents' subjective counterfactual models.

minor comments (1)

The abstract refers to 'a formal analysis of Newcomb's problem' but does not indicate the section in which the NPSEM formalization and optimality check appear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the presentation of our results. We respond to each major comment below and indicate the revisions that will be incorporated.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that 'under certain assumptions, personal decision theory is optimal with respect to this metric' supplies neither an enumeration of the assumptions nor a derivation; without these, it is impossible to verify whether the result holds when the intervention is an NPSEM do-operator on the structural equations encoding agents' choice functions.

Authors: The assumptions (consistency of subjective models with the true NPSEM, do-intervention on the choice-function equation, and population-level application) and the derivation appear in the body (Assumptions 3.1--3.3 and Theorem 4.1 with proof in Appendix B). To address the concern, we will revise the abstract to enumerate these three assumptions explicitly and add a parenthetical reference to the theorem. This makes the central claim verifiable from the abstract alone while preserving its length. revision: yes
Referee: [Abstract] Abstract: the performance metric is defined via hypothetical interventions that enforce a decision theory across a population; the manuscript does not demonstrate that this metric is independent of the theories being ranked or that it avoids circularity when the enforced theory interacts with agents' subjective counterfactual models.

Authors: Definition 5.1 defines the metric via a direct do-intervention on the structural equation for the choice variable, which overrides any agent's decision procedure regardless of the subjective counterfactual model the agent employs. The metric therefore evaluates objective population outcomes and does not depend on the subjective models of the agents being ranked. We will insert a short clarifying paragraph after Definition 5.1 that formally shows this independence and explains why no circularity arises. The revision will also note that the intervention is exogenous to the subjective models. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces NPSEMs as an external modeling language from causal inference to unambiguously define EDT and CDT, proposes personal decision theory as a new construct, defines a population-intervention performance metric, and claims optimality of PDT under unspecified assumptions. No equations or steps are exhibited in the abstract that reduce the optimality result to a self-definition of the metric, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The derivation remains self-contained against the external NPSEM foundation and does not exhibit the specific reductions required for a circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The framework rests on the domain assumption that NPSEMs can unambiguously represent agents and counterfactuals; the performance metric and optimality claim are introduced by the paper itself with no independent evidence supplied in the abstract.

axioms (1)

domain assumption NPSEMs provide a unified foundation for representing agents, counterfactuals, and causal relationships allowing unambiguous definitions of EDT and CDT
Explicitly stated in the abstract as the basis for the entire framework.

invented entities (2)

personal decision theory no independent evidence
purpose: Instructs agents to maximize a subjective model of their own counterfactual utility
New decision theory introduced in the paper; no independent evidence outside the paper is mentioned.
performance metric based on hypothetical interventions no independent evidence
purpose: Evaluates decision theories by enforcing them across a population via education or policy
Metric defined inside the paper to prove optimality; no external validation supplied.

pith-pipeline@v0.9.1-grok · 5776 in / 1379 out tokens · 31544 ms · 2026-06-30T06:26:06.784454+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

14 extracted references · 1 canonical work pages

[1]

Bales, A. (2018). Richness and rationality: Causal decision theory and the WAR argument.Synthese,195(1), 259–267

2018
[2]

(1989).Structural equations with latent variables

Bollen, K. (1989).Structural equations with latent variables. John Wiley & Sons

1989
[3]

Gibbard, A., & Harper, W. (1978). Counterfactuals and two kinds of expected utility. InIfs: Conditionals, belief, decision, chance and time(pp. 153– 190). Springer

1978
[4]

Hitchcock, C. (2016). Conditioning, intervening, and decision.Synthese,193, 1157–1176

2016
[5]

Joyce, J. (2007). Are Newcomb problems really decisions?Syntheses,156(3), 537–562

2007
[6]

(1999).The foundations of causal decision theory

Joyce, J. (1999).The foundations of causal decision theory. Cambridge Uni- versity Press

1999
[7]

Levinstein, B., & Soares, N. (2020). Cheating Death in Damascus.The Jour- nal of Philosophy,117(5), 237–266

2020
[8]

(1973).Counterfactuals

Lewis, D. (1973).Counterfactuals. Cambridge: Harvard University Press

1973
[9]

MacDermott, M., Everitt, T., & Belardinelli, F. (2023). Characterising deci- sion theories with mechanised causal graphs. https://arxiv.org/abs/ 2307.10987

work page arXiv 2023
[10]

Nozick, R. (1969). Newcomb’s problem and two principles of choice. InEssays in honor of Carl G. Hempel: A tribute on the occasion of his sixty-fifth birthday(pp. 114–146). Springer

1969
[11]

(2009).Causality

Pearl, J. (2009).Causality. Cambridge university press

2009
[12]

Pearl, J. (2010). On the consistency rule in causal inference: Axiom, defini- tion, assumption, or theorem?Epidemiology,21(6), 872–875

2010
[13]

(2017).An introduction to decision theory

Peterson, M. (2017).An introduction to decision theory. Cambridge Univer- sity Press

2017
[14]

Steele, K., & Stefansson, H. (2020). Decision Theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy(Winter 2020). Metaphysics Research Lab, Stanford University. 23 A Proof of Theorem 1 We have that A(EDT) =A(EDT;M(EDT)) = argmax a E(U|A=a;M(EDT)) = argmax a E(U|A=a) = constant, where the first equality follows from consistency (2), the sec...

2020

[1] [1]

Bales, A. (2018). Richness and rationality: Causal decision theory and the WAR argument.Synthese,195(1), 259–267

2018

[2] [2]

(1989).Structural equations with latent variables

Bollen, K. (1989).Structural equations with latent variables. John Wiley & Sons

1989

[3] [3]

Gibbard, A., & Harper, W. (1978). Counterfactuals and two kinds of expected utility. InIfs: Conditionals, belief, decision, chance and time(pp. 153– 190). Springer

1978

[4] [4]

Hitchcock, C. (2016). Conditioning, intervening, and decision.Synthese,193, 1157–1176

2016

[5] [5]

Joyce, J. (2007). Are Newcomb problems really decisions?Syntheses,156(3), 537–562

2007

[6] [6]

(1999).The foundations of causal decision theory

Joyce, J. (1999).The foundations of causal decision theory. Cambridge Uni- versity Press

1999

[7] [7]

Levinstein, B., & Soares, N. (2020). Cheating Death in Damascus.The Jour- nal of Philosophy,117(5), 237–266

2020

[8] [8]

(1973).Counterfactuals

Lewis, D. (1973).Counterfactuals. Cambridge: Harvard University Press

1973

[9] [9]

MacDermott, M., Everitt, T., & Belardinelli, F. (2023). Characterising deci- sion theories with mechanised causal graphs. https://arxiv.org/abs/ 2307.10987

work page arXiv 2023

[10] [10]

Nozick, R. (1969). Newcomb’s problem and two principles of choice. InEssays in honor of Carl G. Hempel: A tribute on the occasion of his sixty-fifth birthday(pp. 114–146). Springer

1969

[11] [11]

(2009).Causality

Pearl, J. (2009).Causality. Cambridge university press

2009

[12] [12]

Pearl, J. (2010). On the consistency rule in causal inference: Axiom, defini- tion, assumption, or theorem?Epidemiology,21(6), 872–875

2010

[13] [13]

(2017).An introduction to decision theory

Peterson, M. (2017).An introduction to decision theory. Cambridge Univer- sity Press

2017

[14] [14]

Steele, K., & Stefansson, H. (2020). Decision Theory. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy(Winter 2020). Metaphysics Research Lab, Stanford University. 23 A Proof of Theorem 1 We have that A(EDT) =A(EDT;M(EDT)) = argmax a E(U|A=a;M(EDT)) = argmax a E(U|A=a) = constant, where the first equality follows from consistency (2), the sec...

2020