Probabilities of Causation �

This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical deenitions of the probabilities of necessary or suucient cau-sation (or both), we show h o w to optimally bound these quantities from data obtained in experimental and observational studies, making minimal assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by weakening the data-generation assumptions and deriving theoretically sharp bounds on the probabilities of causation. These results delineate precisely how empirical data can be used both in settling questions of attribution and in solving attribution-related problems of decision making.