Predictable Poverty in Sequential Decision Problems

Wells (forthcoming) has an really nice example of a sequential decision problem in which an evidential decision theorist will end up predictably poorer than a causal decision theorist. Wells thinks that this case shows that we should reject evidential decision theory. I agree that we should reject evidential decision theory, but I don’t think that a proponent of CDT should use Wells’s case to argue for this conclusion.

The reason is that there are sequential decision problems in which a causal decision theorist will end up predictably poorer than an evidential decision theorist, even when both the causal decision theorist and the evidential decision theorist face this decision problem in the same circumstances. If predictable relative poverty like this gives a sufficient reason to reject EDT, then it likewise gives a sufficient reason to reject CDT. (I think we should tollens—though I won’t be making that case here.)

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The Role of Interventions in Causal Decision Theory

Causal Bayes Nets provide a nice formal representation of the world’s causal and probabilistic structure, and so it is natural to want formulate causal decision theory (CDT) in terms of causal Bayes nets. Lots of good work has been done on this front—see, in particular, Meek and Glymour (1994), Pearl (2000, chapter 4), Hitchcock (2016), and Stern (2017). Central to these formulations of CDT is the distinction between a probability function which has been conditioned on an act A’s performance and a probability function which has been updated on an intervention bringing about A’s performance.

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Singular causation and model reduction

In my previous post I tried to get clear about when variables could be safely removed from a causal model without affecting what the model is capable of telling us about singular causal relations. There, I endorsed two principles stating when causal models may be reduced by excising variables in a particular way. If we endorse these principles, and we want to give a theory of singular causation formulated in terms of correct causal models, then we should want that theory to give the very same verdicts before and after model reduction. The point of today’s post is that there is a wide family of theories of causation which run afoul of this constraint. Those theories will say that two variable values are causally related in one model, but reverse this judgment when the model is reduced.

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