Bayesianism and wishful thinking are compatible.

Bayesian principles show up across many domains of human cognition, but wishful thinking-where beliefs are updated in the direction of desired outcomes rather than what the evidence implies-seems to threaten the universality of Bayesian approaches to the mind. In this Article, we show that Bayesian optimality and wishful thinking are, despite first appearances, compatible. The setting of opposing goals can cause two groups of people with identical prior beliefs to reach opposite conclusions about the same evidence through fully Bayesian calculations. We show that this is possible because, when people set goals, they receive privileged information in the form of affective experiences, and this information systematically supports goal-consistent conclusions. We ground this idea in a formal, Bayesian model in which affective prediction errors drive wishful thinking. We obtain empirical support for our model across five studies.