The application of information theory to decision making connects Shannon's framework to the economics of choice under uncertainty. Christopher Sims (2003), drawing on Shannon's channel capacity concept, proposed rational inattention theory: the idea that decision makers have a finite capacity to process information, measured in bits, and that observed departures from optimal behavior can be explained as consequences of this information-processing constraint rather than irrationality.
Rational Inattention
Subject to: I(θ; a) ≤ κ (channel capacity constraint)
I(θ; a) = mutual information between state θ and action a
κ = information processing capacity (bits)
λ = shadow cost of information (Lagrange multiplier)
In Sims' framework, a decision maker observes a noisy signal about the state of the world θ and chooses action a to maximize expected utility. The key constraint is that the mutual information between θ and the chosen action a cannot exceed the decision maker's channel capacity κ. This constraint produces optimal "inattention" — the decision maker rationally ignores fine distinctions in the state space because discriminating them would exceed processing capacity. The resulting behavior exhibits discrete choices, stochastic choice, and apparent biases that arise not from preferences but from information-processing costs.
Value of Information
Information-theoretic decision theory formalizes the value of acquiring information before making a decision. The value of information (VOI) is the difference in expected utility between deciding with and without the additional information. For a Bayesian decision maker, VOI equals the expected reduction in posterior uncertainty weighted by the decision stakes. Information gain — the expected KL divergence between posterior and prior — provides an information-theoretic measure of how much a signal reduces uncertainty, independent of the particular decision problem.
Rational inattention theory provides a formal explanation for "choice overload" — the observation that too many options can impair decision quality and satisfaction (Iyengar & Lepper, 2000). As the number of options increases, the information required to identify the best option grows logarithmically, eventually exceeding the decision maker's channel capacity. The theory predicts that decision makers will simplify large choice sets by categorizing options into coarse groups — a prediction consistent with observed heuristic strategies and with Miller's chunking principle.
Applications in Psychology
Information-theoretic models of decision making have been applied to a range of psychological phenomena. In perceptual decision making, the drift diffusion model can be reinterpreted as a sequential channel that accumulates information about the stimulus at a rate determined by signal strength. The decision bound — the amount of evidence needed to commit to a choice — can be derived from an optimal tradeoff between accuracy and the time cost of acquiring additional information.
In experimental design, optimal designs maximize the expected information gain about the parameter of interest — a principle that connects to active learning and adaptive experimentation. In foraging theory, animals must decide when to leave a depleted patch, a decision that can be analyzed as an information-seeking problem: the animal gathers samples from the current patch and switches when the expected information gain from continuing to sample falls below the opportunity cost of moving to a new patch. These diverse applications demonstrate the generality of the information-theoretic approach to decision making.