Causal Inference of Ambiguous Manipulations

Over the last two decades, philosophers, statisticians, and computer scientists have converged on the fundamental outline of a theory of causal representation and causal inference (Spirtes, Glymour, and Scheines, 2000; Pearl, 2000). Some conditions and assumptions under which reliable inference about the effects of manipulations is possible have been precisely characterized; other conditions and assumptions under which reliable inference about the effects of manipulation is impossible have also been characterized. However, the theory of inference about the effects of manipulations that has been developed does not consider the problem of “defined variables”. In causal modeling, sometimes variables are deliberately introduced as defined functions of others variables. More interestingly, sometimes two or more measured variables are deterministic functions of one another, not deliberately, but because of redundant measurements. In these cases, manipulation of an observed defined variable may actually be an ambiguous description of a manipulation of some underlying variables, although the manipulator does not know that this is the case. In this article we revisit the question of precisely characterizing conditions and assumption under which reliable inference about the effects of manipulations is possible, even when the possibility of “ambiguous manipulations” is allowed.