This article summarizes a conceptual framework and simple mathematical methods of estimating the probability that one event was a necessary cause of another, as interpreted by lawmakers. We show that the fusion of observational and experimental data can yield informative bounds that, under...

Abstract The paradox described below aims to clarify the principles by which empirical data are harnessed to guide decision making. It is motivated by the practical question of whether empirical assessments of the effect of treatment on the treated (ETT) can be useful for either policy...

Abstract This paper reviews concepts, principles, and tools that have led to a coherent mathematical theory that unifies the graphical, structural, and potential outcome approaches to causal inference. The theory provides solutions to a number of pending problems in causal analysis, including...

Abstract Augmenting the graphoid axioms with three additional rules enables us to handle independencies among observed as well as counterfactual variables. The augmented set of axioms facilitates the derivation of testable implications and ignorability conditions whenever modeling assumptions...

Abstract In this issue of the Causal, Casual, and Curious column, I compare several ways of extracting information from post-treatment variables and call attention to some peculiar relationships among them. In particular, I contrast do -calculus conditioning with counterfactual conditioning and...

Abstract The structural interpretation of counterfactuals as formulated in Balke and Pearl (1994a,b) [ 1 , 2 ] excludes disjunctive conditionals, such as “had $X$ been $x_1~\mbox{or}~x_2$ ,” as well as disjunctive actions such as $do(X=x_1~\mbox{or}~X=x_2)$ . In contrast, the closest-world...

Abstract Non-manipulable factors, such as gender or race have posed conceptual and practical challenges to causal analysts. On the one hand these factors do have consequences, and on the other hand, they do not fit into the experimentalist conception of causation. This paper addresses this...