A decision theory can be useful not only as a tool for determining which action, given your desires and beliefs, is most preferable, but also as a means for analyzing the nature of rational deliberation. In this paper, I turn to two classic proposals for a causal decision theory, that of Lewis and that of Sobel :407–437, 1986. doi: 10.1080/00048408612342621). As Rabinowicz revealed, Lewis’ proposal is unable to be applied to as broad a set of decision problems as a version (...) of CDT offered by Sobel, an account of decision theory that Lewis thought was equivalent to his own. Rabinowicz argued by offering a counterexample to Lewis’ account. In this essay, I build on that approach, offering a novel counterexample, the “Faulty Signal Problem,” which proves that Lewis’ theory fails to provide a recommendation in an even broader class decision problems than Rabinowicz recognized, particularly those that exhibit what I refer to as counterfactual asymmetries. The problem for Lewis, however, is not just a technicality. Lewis and Sobel’s theories, respectively, conceptualize rational deliberation in two different ways. Lewis’ proposal, which utilized conditionalization as its form of belief revision, shares with evidential decision theory the same underlying attitude toward the agent as evidence-maker. In contrast, Sobel’s theory, based on imaging, captures the idea that deliberation requires a distinctly suppositional attitude that respects the agent’s causal views. The Faulty Signal Problem not only gives reason to favor Sobel’s proposal over Lewis’; it also provides justification for seeing imaging as necessary for a genuinely causal decision theory. (shrink)

This paper argues that expected utility theory for actions in chancy environments should be formulated in terms of centered chances. The subjective expected utility of an option A may be seen as a weighted sum of the utilities of A in different possible worlds, with weights being the credences that the agent assigns to these worlds. The utility of A in a given world is then definable as a weighted sum of the values of A’s different possible outcomes, with weights (...) being the conditional chances of these outcomes if A were performed. On the centered-chance view, the chances to be used as weights in the definition of utility are centered. Unlike ordinary chances, centered chances depend not only on what happens prior to the agent’s choice but also on the events that occur after the choice. Thus, to give an example, suppose that the action under consideration results in a bad outcome due to some event whose ordinary chance of occurring was very low at the time of choice. Then the utility of that action in the actual world could be high on the non-centered view, but on the centered view that utility is negative, since the centered chance of the event in question given the action was one, given that it did actually take place. A precise definition of centered chances is not easy to frame, but the concept can be made intuitively clear. The resulting decision theory is, in my opinion, philosophically more satisfactory than the extant proposals, even though it doesn’t differ much in its practical recommendations, with the exception of some rather peculiar cases. (shrink)