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Subjective Causality

Joseph Y. Halpern, Evan Piermont

TL;DR

This work addresses how to recover a decision maker's subjective causal judgments from her preferences over interventions. By adopting Pearl's structural equations framework, it shows that, under a set of axioms, one can represent preferences with a causal model $M$, a context distribution $p$ over exogenous factors, and a utility $u$ over outcomes, such that actions are ranked by their expected utility after accounting for interventions via the do-operator. It further identifies conditions under which the causal model is unique and provides a construction that connects Lewis-style counterfactual semantics with causal models. The results enable testing whether observed behavior is consistent with a causal model and offer a method to identify causal judgments from actions, with implications for modeling causal decision making in economics and related fields. The discussion highlights connections to prior work and points to future work on sequential decisions and dynamic consistency.

Abstract

We show that it is possible to understand and identify a decision maker's subjective causal judgements by observing her preferences over interventions. Following Pearl [2000], we represent causality using causal models (also called structural equations models), where the world is described by a collection of variables, related by equations. We show that if a preference relation over interventions satisfies certain axioms (related to standard axioms regarding counterfactuals), then we can define (i) a causal model, (ii) a probability capturing the decision-maker's uncertainty regarding the external factors in the world and (iii) a utility on outcomes such that each intervention is associated with an expected utility and such that intervention $A$ is preferred to $B$ iff the expected utility of $A$ is greater than that of $B$. In addition, we characterize when the causal model is unique. Thus, our results allow a modeler to test the hypothesis that a decision maker's preferences are consistent with some causal model and to identify causal judgements from observed behavior.

Subjective Causality

TL;DR

This work addresses how to recover a decision maker's subjective causal judgments from her preferences over interventions. By adopting Pearl's structural equations framework, it shows that, under a set of axioms, one can represent preferences with a causal model , a context distribution over exogenous factors, and a utility over outcomes, such that actions are ranked by their expected utility after accounting for interventions via the do-operator. It further identifies conditions under which the causal model is unique and provides a construction that connects Lewis-style counterfactual semantics with causal models. The results enable testing whether observed behavior is consistent with a causal model and offer a method to identify causal judgments from actions, with implications for modeling causal decision making in economics and related fields. The discussion highlights connections to prior work and points to future work on sequential decisions and dynamic consistency.

Abstract

We show that it is possible to understand and identify a decision maker's subjective causal judgements by observing her preferences over interventions. Following Pearl [2000], we represent causality using causal models (also called structural equations models), where the world is described by a collection of variables, related by equations. We show that if a preference relation over interventions satisfies certain axioms (related to standard axioms regarding counterfactuals), then we can define (i) a causal model, (ii) a probability capturing the decision-maker's uncertainty regarding the external factors in the world and (iii) a utility on outcomes such that each intervention is associated with an expected utility and such that intervention is preferred to iff the expected utility of is greater than that of . In addition, we characterize when the causal model is unique. Thus, our results allow a modeler to test the hypothesis that a decision maker's preferences are consistent with some causal model and to identify causal judgements from observed behavior.
Paper Structure (8 sections, 6 theorems, 30 equations)

This paper contains 8 sections, 6 theorems, 30 equations.

Table of Contents

  1. Introduction
  2. Causal Models
  3. Syntax and Semantics
  4. Decision Environment
  5. Representation
  6. Axioms
  7. Proof of Theorems \ref{['thm:representation']} and \ref{['thm:uniq']}
  8. Discussion

Key Result

Theorem 1

The preference order $\succsim_\mathcal{S}$ satisfies Axioms Aax:canc--Aax:rec if and only if it has a subjective causal expected utility representation $(M,\textup{p},\textup{u})$. Moreover, if $\succsim_\mathcal{S}$ satisfies Axiom Aax:defp$^*$, then $M$ is unique over the set of non-null contexts

Theorems & Definitions (12)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Theorem 2
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • ...and 2 more