Inferring conjunctive probabilities from noisy samples: evidence for the configural weighted average model.

Judging whether multiple events will co-occur is an important aspect of everyday decision making. The underlying probabilities of occurrence are usually unknown and have to be inferred from experience. Using a rigorous, quantitative model comparison, we investigate how people judge the conjunctive probabilities of multiple events to co-occur. In 2 experiments, participants had to repeatedly choose between pairs of 2 conjunctive events (represented as 2 gambles). To estimate the probability that both events occur, they had access to a small sample of information. The 1st experiment consisted of a balanced set of gambles, whereas in the 2nd experiment, the gambles were constructed such that the models maximally differed in their predictions. A hierarchical Bayesian approach used for estimating the models' parameters and for testing the models against each other showed that the majority of participants were best described by the configural weighted average model. This model performed best in predicting people's choices, and it assumes that constituent probabilities are ranked by importance, weighted accordingly, and added up. The cognitive modeling approach provides an understanding of the cognitive processes underlying people's conjunctive probability judgments.