Psychological, political, cultural, and sociological factors shape how people form and revise their beliefs. An established finding across these fields is that people are motivated to hold onto their beliefs even in the face of evidence by ignoring or reinterpreting information in a way that supports what they think. Although these and similar findings are compelling, the predominantly qualitative theories which guide research in this domain, and the often implicit definitions of motivation that accompany these theories, come at the cost of obscuring the cognitive mechanisms that produce motivated reasoning. Here, we introduce a new Bayesian decision-theoretic framework which describes three key factors necessary for distinguishing between cases of practically rational behavior and motivated reasoning. We demonstrate how the framework works in a series of simulations and argue that it provides guidance about what psychologists need to measure to determine where the errors in people's reasoning are occurring when they fail to revise their beliefs in light of new evidence. We then propose that this framework provides guidance for thinking about the development of interventions aimed at correcting misconceptions.