Imaging Maximizes Expected Modal Accuracy

Proofs that conditionalization (uniquely) maximizes expected accuracy by any (strictly) proper scoring rule are often taken as underwriting an accuracy-based argument for conditionalization as a plan, that is, for conditionalizing on the supposition that one learns that E, rather than after actually learning that E. But, it is well-known that there are two essentially different kinds of supposition: indicative and counterfactual. So if conditionalization, as is also often acknowledged, maps to the former, what about the expected accuracy of whatever update procedure maps to the latter? This paper proposes a reply, if that procedure is imaging. The simple insight is that the counterfactual supposition of E calls for maximizing expected modal accuracy, evaluated not at the actual world but at the closest E-world(s). We prove that three sorts of imaging from the literature, Stalnakerian, Laplacian, and Joycean, each uniquely maximize expected modal accuracy, in three different ways, by any strictly proper scoring rule. We argue for favouring the Joycean way.