“A Representation Theorem for Causal Decision Theory”, 1999 ():
Having come to grips with the concept of a conditional belief, we now return to the problem of proving a representation theorem for causal decision theory. No decision theory is complete until it has been supplemented with a representation theorem that shows how its “global” requirement to maximize expected utility theory will be reflected at the “local” level as constraints on individual beliefs and desires. The main foundational shortcoming of causal decision theory has always been its lack of an adequate representation result.
Evidential decision theory can be underwritten by Bolker’s theorem and the generalization of it that was established at the end of Ch4. This seems to militate strongly in favor of the evidential approach.
In this chapter I remove this apparent advantage by proving a Bolker-styled representation result for an abstract conditional decision theory whose two primitives are probability under a supposition and preference under a supposition.
This theorem is, I believe, the most widely applicable and intuitively satisfying representation result yet attained. We will see that, with proper qualifications, it can be used as a common foundation for both causal decision theory and evidential decision theory. Its existence cements one of the basic theses of this work. It was claimed in Ch5 that evidential and causal decision theories should not be seen as offering competing theories of value, but as disagreeing about the epistemic perspective from which actions are to be evaluated. The fact that both theories can be underwritten by the same representation result shows that this is indeed the case.