Rational agents should update their beliefs in the light of new evidence. Equally, changes in belief should depend only on the quality of the evidence, and not on factors such as the order in which the evidence is acquired, or whether intermediate judgements are requested during evidence acquisition. In contrast we show that requests for intermediate judgments can inhibit belief updating for real decision makers, which represents a new type of decision making fallacy. This behaviour is paradoxical from the point of view of classical Bayesian models, but we show that it is consistent with an a priori, parameter free prediction of a cognitive model based on quantum theory.