Does non-correlation imply non-causation?

Abstract

The Markov condition describes the conditional independence relations present in a causal model that are consequent to its graphical structure, whereas the faithfulness assumption presumes that there are no other independencies in the model. Cartwright argues that causal inference methods have limited applicability because the Markov condition cannot always be applied to domains, and gives an example of its incorrect application. Cartwright also argues that both humans and Nature, fairly commonly, design objects that violate the faithfulness assumption. Because both arguments suggest that data is not likely to be ideal, we suggest that problems of the theory be separated from problems of the data. As regards the Markov condition, conflicted intuitions about conditional independence relationships in certain complex domains can be explained in terms of measurement and of proxy selection. As regards faithfulness, we show that violations of this assumption do not affect the predictive powers of causal models. More generally, the criticisms of causal models, taken constructively, reveal the subtlety of the ideal, while clarifying the source of problems in data.