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arxiv: 1907.11752 · v6 · submitted 2019-07-26 · 💻 cs.AI · stat.ME

Choosing with unknown causal information: Action-outcome probabilities for decision making can be grounded in causal models

Mauricio Gonzalez Soto , David Danks , Hugo J. Escalante Balderas , L. Enrique Sucar This is my paper

Pith reviewed 2026-05-24 15:31 UTC · model grok-4.3

classification 💻 cs.AI stat.ME
keywords causal decision makinginterventionsunknown causal modelsNash equilibriumexpected utilityaction-outcome probabilitiesrational choice
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The pith

Decision-making probabilities can be grounded in causal models whether the mechanisms are known or unknown.

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

The paper establishes that action-outcome probabilities used in rational decision making can be derived from causal models by treating actions as interventions. This grounding holds both when the full causal model is known and when only some parts are unknown to the decision maker. A sympathetic reader would care because it provides a way to use causal information for better decisions even with incomplete knowledge, extending beyond purely probabilistic approaches. It also applies this to game theory by generalizing Nash equilibrium.

Core claim

In decision problems where actions and consequences are causally connected, actions are regarded as interventions over a causal model. The previous result for known causal models is extended to unknown causal mechanisms. This grounds action-outcome probabilities in causal models for both cases. As an application, Nash Equilibrium is extended to strategic games where players consider causal information.

What carries the argument

Treating actions as interventions over a causal model to derive action-outcome probabilities.

If this is right

  • Action-outcome probabilities for expected utility calculations are obtained from interventions on the causal model when known.
  • The derivation extends directly to cases where the causal mechanism is unknown to the decision maker.
  • Strategic games have equilibria defined using causal information from player interventions.
  • Rational decision making remains possible under uncertainty with causally grounded probabilities in both settings.

Where Pith is reading between the lines

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

  • AI decision systems might benefit from maintaining possible causal models to compute intervention effects rather than relying solely on observed correlations.
  • Human experiments could test whether people naturally use causal intervention reasoning in unknown-mechanism choice tasks.
  • This approach could generalize to multi-agent settings beyond games, such as cooperative planning with uncertain causal links.
  • Further work might derive bounds on decision quality when only approximate causal models are available.

Load-bearing premise

Actions can be treated as interventions on an underlying causal model even when the decision maker does not know the precise causal mechanism that controls the environment.

What would settle it

Finding a rational decision problem with unknown causality where no set of action-outcome probabilities can be consistently derived from any causal intervention model would disprove the extension.

read the original abstract

Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using associative information: maximize expected utility. There is an ongoing debate around the origin of probabilities involved in such calculation. In this work, we will show how the probabilities for decision-making can be grounded in causal models by considering decision problems in which the available actions and consequences are causally connected. In this setting, actions are regarded as an intervention over a causal model. Then, we extend a previous causal decision-making result, which relies on a known causal model, to the case in which the causal mechanism that controls some environment is unknown to a rational decision-maker. In this way, action-outcome probabilities can be grounded in causal models in known and unknown cases. Finally, as an application, we extend the well-known concept of Nash Equilibrium to the case in which the players of a strategic game consider causal information.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that action-outcome probabilities in decision problems can be grounded in causal models (via the do-operator on an underlying graph) both when the causal mechanism is known and when it is unknown to the decision maker; it extends a prior known-model result to the unknown case and applies the framework to extend Nash equilibrium to strategic games that incorporate causal information.

Significance. If the central extension is rigorously derived, the work would strengthen the link between causal semantics and expected-utility calculations in settings where the decision maker lacks an explicit mechanism, with potential implications for causal decision theory and game-theoretic solution concepts.

major comments (2)
  1. [Section 4] Section 4 (the extension to unknown mechanisms): the manuscript asserts that interventional probabilities remain available without an explicit graph, yet supplies neither a formal statement of the unknown-mechanism setting nor the derivation steps that obtain the same interventional probabilities from a distribution over mechanisms; without these steps it is impossible to verify that the grounding claim survives the extension.
  2. [Section 4] Section 4, paragraph on the unknown-case probabilities: the argument appears to rely on an implicit mixture over possible causal graphs, but no independent justification is given that this mixture preserves the intervention semantics rather than reducing to observational conditioning; this step is load-bearing for the claim that the probabilities are still 'grounded in causal models' when the mechanism is unknown.
minor comments (1)
  1. [Abstract] The abstract states the extension is possible but contains no equations or formal definitions; a one-sentence formal statement of the unknown-mechanism case would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on Section 4. We agree that the presentation of the unknown-mechanism case requires additional formalization to make the extension fully rigorous and verifiable.

read point-by-point responses

  1. Referee: [Section 4] Section 4 (the extension to unknown mechanisms): the manuscript asserts that interventional probabilities remain available without an explicit graph, yet supplies neither a formal statement of the unknown-mechanism setting nor the derivation steps that obtain the same interventional probabilities from a distribution over mechanisms; without these steps it is impossible to verify that the grounding claim survives the extension.

    Authors: We acknowledge that the current text does not contain an explicit formal definition of the unknown-mechanism setting or the full derivation. In the revised manuscript we will add a subsection that (i) defines the decision maker's information as a probability distribution over a class of causal mechanisms consistent with the observed data, and (ii) derives the interventional probability by first applying the do-operator inside each mechanism and then integrating with respect to the distribution over mechanisms. This will make the claim that the same interventional probabilities are recovered fully explicit. revision: yes

  2. Referee: [Section 4] Section 4, paragraph on the unknown-case probabilities: the argument appears to rely on an implicit mixture over possible causal graphs, but no independent justification is given that this mixture preserves the intervention semantics rather than reducing to observational conditioning; this step is load-bearing for the claim that the probabilities are still 'grounded in causal models' when the mechanism is unknown.

    Authors: We agree that an explicit justification is required. In the revision we will insert a paragraph showing that the mixture is taken after the intervention: the quantity is defined as the expectation, over the posterior on mechanisms, of P(Y | do(X), M), where each term uses the causal semantics of its own mechanism M. Because the do-operator is applied inside the integral rather than outside, the resulting probability does not coincide with ordinary conditioning on the observational distribution; we will include a short proof that the two expressions differ in general. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The provided abstract and context describe an extension of a prior causal decision-making result to unknown mechanisms, grounding action-outcome probabilities in causal models via interventions. No equations, fitted parameters, or self-citations are quoted that reduce any claimed probability or equilibrium to the input by construction. The central claim relies on treating actions as interventions, which is an independent modeling choice rather than a definitional loop or renamed empirical pattern. Without load-bearing self-citation chains or ansatzes smuggled via prior work by the same authors, the derivation does not reduce to its inputs. This is the expected honest non-finding for a high-level conceptual extension paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract only; the paper relies on the standard assumption that actions are interventions in a causal model, with no free parameters, new entities, or additional axioms stated.

axioms (1)
  • domain assumption Actions are regarded as an intervention over a causal model
    Explicitly stated in the abstract as the modeling choice that allows grounding of probabilities.

pith-pipeline@v0.9.0 · 5736 in / 1199 out tokens · 47422 ms · 2026-05-24T15:31:54.761776+00:00 · methodology

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Reference graph

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