Priors and desires

This paper offers a simple but powerful model of wishful thinking, cognitive dissonance, and related biases. Choices maximize subjective expected utility, but beliefs depend on the decision maker's interests as well as on relevant information. Simplifying assumptions yield a representation in which the payoff in an event affects beliefs as if it were part of the evidence about its likelihood. A single parameter determines both the direction and weight of this `evidence', with positive values corresponding to optimism and negative values to pessimism. Changes to a person's interests amount to new `evidence', and can alter beliefs even in the absence of new information. The magnitude of the bias increases with the degree of uncertainty and the strength of the decision maker's interests. High stakes can reduce the bias indirectly by increasing incentives to acquire information, but are otherwise consistent with substantial bias. Exploring applications, I show that wishful thinking can lead investors to become progressively more exposed to risk, and that while improved policing unambiguously deters crime, increased punishment may have little or no deterrent value.