Counterfactual Realizability
Arvind Raghavan, Elias Bareinboim
TL;DR
Counterfactual Realizability introduces a formal notion of realizability for Layer-$\mathcal{L}_3$ counterfactuals and a complete algorithm, CTF-REALIZE, to decide whether a given counterfactual distribution can be physically sampled under fundamental constraints. By extending Fisherian experimentation with counterfactual randomization and counterfactual mediators, the authors show how certain $\mathcal{L}_3$-quantities can be directly estimated, and provide a graphical criterion (counterfactual-ancestor condition) and maximal action set $\mathbb{A}^\dag(\mathcal{G})$ for realizability. They prove the approach is complete and demonstrate its practical impact in causal fairness and causal RL, where counterfactual strategies can dominate traditional $\mathcal{L}_1$ and $\mathcal{L}_2$ baselines. The work lays a foundation for novel experiment designs that enable direct estimation of otherwise nonidentifiable quantities, with implications for personalized decision-making and interpretability. The framework also clarifies limitations and suggests directions for integrating partial identification and sequential decision-making under known causal structure.
Abstract
It is commonly believed that, in a real-world environment, samples can only be drawn from observational and interventional distributions, corresponding to Layers 1 and 2 of the Pearl Causal Hierarchy. Layer 3, representing counterfactual distributions, is believed to be inaccessible by definition. However, Bareinboim, Forney, and Pearl (2015) introduced a procedure that allows an agent to sample directly from a counterfactual distribution, leaving open the question of what other counterfactual quantities can be estimated directly via physical experimentation. We resolve this by introducing a formal definition of realizability, the ability to draw samples from a distribution, and then developing a complete algorithm to determine whether an arbitrary counterfactual distribution is realizable given fundamental physical constraints, such as the inability to go back in time and subject the same unit to a different experimental condition. We illustrate the implications of this new framework for counterfactual data collection using motivating examples from causal fairness and causal reinforcement learning. While the baseline approach in these motivating settings typically follows an interventional or observational strategy, we show that a counterfactual strategy provably dominates both.