A Definition and Graphical Representation for Causality

We present a precise definition of ca use and e ffect in terms of a f undamental notion called unresponsiveness. Our definition is based on Savage's (1954 ) form ulation of decision the­ ory and departs from the traditional view of ca usation in that o ur ca usal assertions are made relative to a set of decisions. An im­ portant conseq uence of this depart ure is that we can reason abo ut ca use locally, not re­ q uiring a ca usal explanation for every depen­ dency. S uch local reasoning can be beneficial beca use it may not be necessary to determine whether a partic ular dependency is ca usal to make a decision. Also in this paper, we ex­ amine the graphical encoding of ca usal rela­ tionships. We show that infl uence diagrams in canonical form are an acc urate and effi­ cient representation of ca usal relationships. In addition, we establish a correspondence between canonical form and Pearl's ca usal theory.