Appropriate Causal Models and the Stability of Causation

TL;DR

This paper examines the Halpern-Pearl causality definition, demonstrating how adding variables can clarify causality judgments and discussing the stability of causality answers under model modifications, especially considering normality assumptions.

Contribution

It shows that adding variables can resolve causality ambiguities in the HP framework and analyzes the stability of causality answers when models are extended conservatively.

Findings

Adding variables can disambiguate causality in models.

The HP definition yields intuitive causality judgments with added variables.

Normality assumptions limit the oscillation of causality answers.

Abstract

Causal models defined in terms of structural equations have proved to be quite a powerful way of representing knowledge regarding causality. However, a number of authors have given examples that seem to show that the Halpern-Pearl (HP) definition of causality gives intuitively unreasonable answers. Here it is shown that, for each of these examples, we can give two stories consistent with the description in the example, such that intuitions regarding causality are quite different for each story. 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. It is also shown that, by adding extra variables, a modification to the original HP definition made to deal with an example of Hopkins and Pearl may not be necessary. Given how much can be done by adding extra variables, there might be a concern that the notion of causality is somewhat unstable. Can adding extra variables in a "conservative" way (i.e., maintaining all the relations between the variables in the original model) cause the answer to the question "Is X=x a cause of Y=y" to alternate between "yes" and "no"? It is shown that we can have such alternation infinitely often, but if we take normality into consideration, we cannot. Indeed, under appropriate normality assumptions. adding an extra variable can change the answer from "yes" to "no", but after that, it cannot cannot change back to "yes".