Representation and integration of prior beliefs in a probabilistic reasoning task

Bayes’ theorem offers a normative prescription for how people should combine their original beliefs (i.e. their priors) in light of new evidence. The question of whether people reason about probabilities in accordance with Bayes’ theorem has long been a subject of fierce debate: some researchers suggests that priors are largely ignored (e.g., Bar-Hillel, 1980); others suggest that they are overweighted and people are conservative (e.g., Edwards, 1968); others suggest that Bayesian models predict performance quite well, but only at the aggregate population level (e.g., Mozer et al. 2008). Yet much of this previous work does not measure each person’s full prior distribution, making it difficult to determine exactly what the participants were doing. Over the course of two experiments, we elicited people’s full prior distributions for a simple probability task. We found that (a) people disregarded the prior and determined the posterior directly from the likelihood (which is mathematically equivalent to using a uniform prior) and (b) when estimating the posterior, people weighted evidence accurately only in the aggregate, with almost all individuals either overweighting or underweighting evidence relative to the normative standards of Bayes’ theorem. This work helps clarify to what extent Bayes’ theorem describes people’s actual probability estimates.