Compact Representations of Extended Causal Models

One of Judea Pearl's many, many important contributions to the study of causality was the first attempt to use the mathematical tools of causal modeling to give an account of "actual causation", a notion that has been of considerable interest among philosophers and legal theorists (Pearl, 2000, Chapter 10). Pearl later revised his account of actual causation in joint work with Halpern (Halpern & Pearl, 2005). A number of authors (Hall, 2007; Halpern, 2008; Hitchcock, 2007; Menzies, 2004) have suggested that an account of actual causation must be sensitive to considerations of normality, as well as to causal structure. In (Halpern & Hitchcock, 2011), we suggest a way of incorporating considerations of normality into the Halpern-Pearl theory, and show how to extend the account to illuminate features of the psychology of causal judgment, as well as features of causal reasoning in the law. Our account of actual causation makes use of "extended causal models", which include both structural equations among a set of variables, and a partial preorder on possible worlds, which represents the relative "normality" of those worlds. We actually want to think of people as working with the structural equations and normality order to evaluate actual causation. However, consideration of even simple examples immediately suggests a problem. A direct representation of the equations and normality order is too cumbersome for cognitively limited agents to use effectively. If our account of actual causation is to be at all realistic as a model of human causal judgment, some form of compact representation will be needed.