Instability occurs when the very fact of choosing one particular possible option rather than another affects the expected values of those possible options. In decision theory: An act is stable iff given that it is actually performed, its expected utility is maximal. When there is no stable choice available, the resulting instability can seem to pose a dilemma of practical rationality. A structurally very similar kind of instability, which occurs in cases of anti-expertise, can likewise seem to create dilemmas of epistemic rationality. One possible line of response to such cases of instability, suggested by both Jeffrey (1983) and Sorensen (1987), is to insist that a rational agent can simply refuse to accept that such instability applies to herself in the first place. According to this line of thought it can be rational for a subject to discount even very strong empirical evidence that the anti-expertise condition obtains. I present a new variety of anti-expertise condition where no particular empirical stage-setting is required, since the subject can deduce a priori that an anti-expertise condition obtains. This kind of antiexpertise case is therefore not amenable to the line of response that Jeffrey and Sorensen recommend. 1. Introduction: Instability and Anti-Expertise Instability is the general phenomenon that occurs when the very fact of choosing one particular possible option rather than another affects the expected values of those possible options. Such instability can crop up both when we are considering which action to perform and also when we are considering what to believe-so the affected values in question could either be utilities or truth-values (accuracy). The aim for this paper is to present a new case of instability of the latter kind, concerning whether or not to believe a proposition, one which creates, I will suggest, a novel kind of 'anti-expertise' dilemma for epistemic rationality. However, since the former kind of instability, concerning the expected utility of different possible actions, has been much more frequently discussed, let's begin by very briefly rehearsing one of the best-known examples in the decision theory literature: Gibbard & Harper's (1978) classic 'Death in Damascus' case 1. 1 "Death works from an appointment book which states time and place; a person dies if and only if the book correctly states in what city he will be at the stated time. The book is made up weeks in advance on the basis of highly reliable predictions. An appointment on the next day has been inscribed for him. Suppose, on this basis, the man would take his being in Damascus the next day as strong evidence that his appointment with Death is in Damascus, and would take his being in Aleppo the next day as strong evidence that his appointment is in Aleppo... If... he decides to go to Aleppo, he then has strong grounds for expecting that Aleppo is where Death already expects him to be, and hence it is rational for him to prefer staying in Damascus. Similarly, deciding to stay in Damascus would give him strong...