Abstract
There are simple mechanical systems that elude causal representation. We describe one that cannot be represented in a single directed acyclic graph. Our case suggests limitations on the use of causal graphs for causal inference and makes salient the point that causal relations among variables depend upon details of causal setups, including values of variables.
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Notes
See also Woodward (2003, p. 234).
The possibility that some systems cannot be represented in any single causal graph is implied by an example Glymour considers (2010, p. 202).
Below we consider the possibility that there are arrows going in both directions between P and V.
Korb et al. (2004) model interventions in such a way that they do not necessarily wipe out a variable’s relationship to its prior causes, but might merely alter its probability distribution. But even interventions of this sort are incapable of rendering some of a variable’s causes inactive while activating others. See also Eberhardt and Scheines (2007).
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Acknowledgments
We would like to thank Elliott Sober and Jim Woodward for helpful discussion. We are grateful to several anonymous reviewers for their valuable feedback.
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Hausman, D.M., Stern, R. & Weinberger, N. Systems without a graphical causal representation. Synthese 191, 1925–1930 (2014). https://doi.org/10.1007/s11229-013-0380-3
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DOI: https://doi.org/10.1007/s11229-013-0380-3