Rational Inattention: A Bayesian Predictive Approach

We recast rational inattention as a Bayesian predictive decision problem in which the agent reports a predictive distribution and is evaluated by a proper local scoring rule. This yields a direct link to rate-distortion theory and shows that Shannon entropy emerges endogenously as the honest local utility for predictive refinement. Bernardo's characterization of proper local scoring rules together with Shannon's amalgamation invariance imply that the logarithmic score, and hence mutual information, is the unique information measure consistent with coherent prediction under refinement of the state space. Information costs, therefore, need not be assumed: they arise as expected predictive utility. Within this framework we establish a supported complete-class result: the optimal policies are Gibbs-Boltzmann channels, with the classical rational-inattention family recovered as a special case. Canonical models appear as geometric specializations of the same structure, including multinomial logit (and IIA) under entropic regularization, James-Stein shrinkage as optimal capacity allocation in Gaussian learning, and linear-quadratic-Gaussian control as the capacity-optimal Gaussian channel. Overall, the Bayesian predictive formulation reframes bounded rationality as an optimal design principle: finite information capacity is an endogenous solution to a well-posed predictive problem, and behaviors often attributed to cognitive frictions, soft choice, regularization, sparsity, and screening arise as rational responses to the geometry of predictive refinement.