Appropriate Causal Models and Stability of Causation

ABSTRACT. Causal models defined in terms structural equations have proved to be quite a powerful way of representing knowledge regarding causality. However, a number of authors have designed examples where it seems that the Halpern-Pearl (HP) definition of causality gives intuitively unreasonable answers. As has been pointed out by many authors, what gets counted as a cause is quite dependent on the choice of variables in the model. Here it is shown that in all the counterexamples suggested, there are two possible stories consistent with the counterexample, where intuitions regarding causality are quite different. By adding additional variables, we can disambiguate the stories; moreover, in the resulting causal models, the HP definition of causality gives the intuitively correct answer. The examples not only give insight into the modeling process, they also highlight some aspects of the definition of causality itself. Specifically, by extending one of the examples, it can be shown that a modification to the original HP definition made to deal with an example by Hopkins and Pearl may not be necessary. By extending another definition, a sequence of models can be constructed, each one a conservative extension of the one before, where the question of whether X=x is cause of Y=y alternates between being true and false.