People's beliefs sometimes diverge after observing the same information, which has been interpreted as evidence of irrationality. This behaviour has been proposed to result from people's limited cognitive resources and motivated reasoning, but how belief revision differs across these explanations has not been formalized or compared to a rational norm. Further, while people may be biased relative to a normative ideal, they may still make optimal choices given their limited cognitive resources, or rationally balance the utility of holding accurate beliefs with the belief's intrinsic utility. Across two studies, we develop and test a unified computational account of belief polarization under these proposed mechanisms, showing that people's performance on a belief updating task best fits a limited-resource Bayesian model; external motivations may contribute to divergence (or convergence) by determining what pre-existing information people consider relevant to a situation, rather than by changing how people evaluate new information in isolation.