Identification of Probabilities of Causation: A Complete Characterization
This addresses a foundational gap in causality-based decision-making, which is incremental as it extends prior work on binary cases to multi-valued scenarios.
The paper tackled the unresolved problem of characterizing probabilities of causation for multi-valued treatments and outcomes, and it resolved this by proposing a complete set of representative probabilities and deriving tight bounds for them.
Probabilities of causation are fundamental to modern decision-making. Pearl first introduced three binary probabilities of causation, and Tian and Pearl later derived tight bounds for them using Balke's linear programming. The theoretical characterization of probabilities of causation with multi-valued treatments and outcomes has remained unresolved for decades, limiting the scope of causality-based decision-making. In this paper, we resolve this foundational gap by proposing a complete set of representative probabilities of causation and proving that they are sufficient to characterize all possible probabilities of causation within the framework of Structural Causal Models (SCMs). We then formally derive tight bounds for these representative quantities using formal mathematical proofs. Finally, we demonstrate the practical relevance of our results through illustrative toy examples.