Rational ignoring with unbounded cognitive capacity

In a canonical decision problem with standard assumptions, we demonstrate that payoffs and probabilities may interact in such a way that expected-payoffmaximizing decisions do not depend on payoff-relevant information. This result holds without decision costs, cognitive constraints, or other forms of bounded rationality. Instances in which information-frugal decision rules achieve high levels of performance arise solely as a consequence of the stochastic payoff distribution and its covariation with predictive signals in the environment. Formalized as independence of expectedpayoff-maximizing decision rules from payoff-relevant predictors, the phenomenon of rational ignoring is shown to require inversely related payoffs and probabilities.