It is commonly argued that the brain aggregates information in a hierarchical fashion. I will discuss how hierarchical aggregation of information gives rise to predictable imperfections in inference, consistent with well-known features of perceptual illusions and decision biases. I demonstrate the basic results in a setup with two modules: both seek to infer some unobserved value, and each has private information, but the second module additionally observes the first module’s posterior. As a whole this system will fail to aggregate information efficiently. In particular, it predicts two commonly observed features of decision-making: (1) the influence of irrelevant associations (framing effects), and (2) the avoidance of dominated options. I discuss experimental evidence for both features. This combination of properties is not predicted by either random utility or inattention.