Causal Sufficiency and Actual Causation
This work provides a foundational re-evaluation of actual causation definitions for researchers in causality and AI, aiming to establish a more robust and intuitive formalization.
This paper addresses the lack of consensus in defining actual causation by revisiting Pearl's initial strategy of capturing the intuition that X=x causes Y=y if X=x is a Necessary Element of a Sufficient Set for Y=y. It proposes six formal definitions of causal sufficiency and two interpretations of necessity, leading to twelve new definitions of actual causation, with one emerging as superior.
Pearl opened the door to formally defining actual causation using causal models. His approach rests on two strategies: first, capturing the widespread intuition that X=x causes Y=y iff X=x is a Necessary Element of a Sufficient Set for Y=y, and second, showing that his definition gives intuitive answers on a wide set of problem cases. This inspired dozens of variations of his definition of actual causation, the most prominent of which are due to Halpern & Pearl. Yet all of them ignore Pearl's first strategy, and the second strategy taken by itself is unable to deliver a consensus. This paper offers a way out by going back to the first strategy: it offers six formal definitions of causal sufficiency and two interpretations of necessity. Combining the two gives twelve new definitions of actual causation. Several interesting results about these definitions and their relation to the various Halpern & Pearl definitions are presented. Afterwards the second strategy is evaluated as well. In order to maximize neutrality, the paper relies mostly on the examples and intuitions of Halpern & Pearl. One definition comes out as being superior to all others, and is therefore suggested as a new definition of actual causation.