A common explanation for biases in judgment and choice has been to postulate two separate processes in the brain: a “System 1” that generates judgments automatically, but using only a subset of the information available, and a “System 2” that uses the entire information set, but is only occasionally activated. This theory faces two important problems: that inconsistent judgments often persist even with high incentives, and that inconsistencies often disappear in within-subject studies. In this paper I argue that these behaviors are due to the existence of “implicit knowledge”, in the sense that our automatic judgments (System 1) incorporate information which is not directly available to our reflective system (System 2). System 2 therefore faces a signal extraction problem, and information will not always be efficiently aggregated. The model predicts that biases will exist whenever there is an interaction between the information private to System 1 and that private to System 2. Additionally it can explain other puzzling features of judgment: that judgments become consistent when they are made jointly, that biases diminish with experience, and that people are bad at predicting their own future judgments. Because System 1 and System 2 have perfectly aligned preferences, welfare is well-defined in this model, and it allows for a precise treatment of eliciting preferences in the presence of framing effects.