The Faulty Signal Problem: counterfactual asymmetries in causal decision theory and rational deliberation

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 (Australas J Philos 591: 5-30, 1981a. doi: 10.1080/00048408112340011) and that of Sobel (Australas J Philos 64(4): 407437, 1986. doi: 10.1080/00048408612342621). As Rabinowicz (Philosophical essays dedicated to Lennart Aqvist on His Fiftieth Birthday, Department of Philosophy, Uppsala, 1982) 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.