Causality: a decision theoretic approach

We propose a decision theoretic framework that allows a decision maker to express its causal model of the world. We extend the model of Savage (1972) by allowing the decision maker (DM) to choose policy interventions prior to choosing acts over the nonintervened variables. We define what it means for the DM's choices to express the DM's belief that the relation between some variables is causal. We provide axioms characterizing when the DM's causal model, as expressed through the DM's choices, is represented as a directed acyclic graph. A final axiom characterizes when the DM's causal model has a representation like the one in Pearl (1995). Consequently, under this additional axiom one can apply Pearl's results to identify the DM's causal model from the DM's probabilistic model.