Closed-Form Bounds for Probabilities of Causation in Multi-Valued Settings

A recent paper on arXiv (2505.15274) expands the understanding of probabilities of causation (PoCs) by applying it to multi-valued treatments and outcomes. The researchers establish closed-form bounds for a set of discrete PoCs within Structural Causal Models, utilizing both standard experimental and observational distributions. They propose equivalence classes of PoCs to streamline arbitrary discrete PoCs into this framework and introduce a replaceability principle for transferring bounds across different value arrangements. The soundness of these bounds is demonstrated across all dimensions, with empirical verification of tightness in lower-dimensional scenarios through Balke's linear programming approach. The authors hypothesize that tightness holds in all dimensions, with simulations indicating their closed-form bounds consistently improve upon recent recursive bounds. This research contributes to counterfactual analysis and personalized decision-making, important for AI and causal inference.