Rational ignoring with unbounded cognitive capacity
In canonical decision problems with standard assumptions, we demonstrate that inversely related payoffs and probabilities can produce expected-payoff-maximizing decisions that are independent of payoff-relevant information. This phenomenon of rational ignoring, where expected-payoff maximizers ignore costless and genuinely predictive information, arises because the conditioning effects of such signals disappear on average (i.e., under the expectations operator) even though they exert non-trivial effects on payoffs and probabilities considered in isolation (i.e., before integrating). Thus, rational ignoring requires no decision costs, cognitive constraints, or other forms of bounded rationality. This implies that simple decision rules relying on small subsets of the available information can, depending on the environment in which they are used, achieve high payoffs. Ignoring information is therefore rationalizable solely as a consequence of the shape of the stochastic payoff distribution.
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