A Note on the Correctness of the Causal Ordering Algorithm

In this paper we examine in detail the algorithm of Simon [1953], called the causal ordering algorithm (COA), used for constructing the “causal ordering ” of a system given a complete specification of the system in terms of a set of “structural ” equa-tions that govern the variables in the system. This algorithm constructs a graphical characterization of the model in the form of a directed cluster graph. Simon argued in [Simon, 1953] and subsequent papers that a graph so generated explicates causal structure among variables in the model. We further formalize this claim and prove a theorem which justifies it. In particular, we prove that given a set of equations E satisfying certain conditions, any directed causal graph that is imposed on the variables consistent with E must be consistent with the graph generated by COA