We derive a new cost of information in rational inattention problems, the neighborhood-based cost functions, starting from the observation that many settings involve exogenous states with a topological structure. These cost functions are uniformly posterior separable and capture notions of perceptual distance. This second property ensures that neighborhood-based costs, unlike mutual information, make accurate predictions about behavior in perceptual experiments. We compare the implications of our neighborhood-based cost functions with those of the mutual information in a series of applications: perceptual judgments, the general environment of binary choice, regime-change games, and linear-quadratic-Gaussian settings.

Observed choices between risky lotteries are difficult to reconcile with expected utility maximization, both because subjects appear to be too risk averse with regard to small gambles for this to be explained by diminishing marginal utility of wealth, as stressed by Rabin (2000), and because subjects’ responses involve a random element. We propose a unified explanation for both anomalies, similar to the explanation given for related phenomena in the case of perceptual judgments: they result from judgments based on imprecise (and noisy) mental representations of the decision situation. In this model, risk aversion results from a sort of perceptual bias—but one that represents an optimal decision rule, given the limitations of the mental representation of the situation. We propose a quantitative model of the noisy mental representation of simple lotteries, based on other evidence regarding numerical cognition, and test its ability to explain the choice frequencies that we observe in a laboratory experiment.