Prefrontal cortex has long been implicated in tasks involving higher order inference in which decisions must be rendered, not only about which stimulus is currently rewarded, but also which stimulus dimensions are currently relevant. However, the precise computational mechanisms used to solve such tasks have remained unclear. We scanned human participants with functional MRI, while they performed a hierarchical intradimensional/extradimensional shift task to investigate what strategy subjects use while solving higher order decision problems. By using a computational model-based analysis, we found behavioral and neural evidence that humans solve such problems not by occasionally shifting focus from one to the other dimension, but by considering multiple explanations simultaneously. Activity in human prefrontal cortex was better accounted for by a model that integrates over all available evidences than by a model in which attention is selectively gated. Importantly, our model provides an explanation for how the brain determines integration weights, according to which it could distribute its attention. Our results demonstrate that, at the point of choice, the human brain and the prefrontal cortex in particular are capable of a weighted integration of information across multiple evidences.