Noisy Retrieval of Experienced Probabilities Underlies Rational Judgment of Uncertain Multiple Events

Learning the probabilities of multiple events from the environment is an important core competency of any organism. In our within-participant experiment, participants experienced samples from two distributions, or prospects, each comprised of two to four events, and were required to provide simultaneous, rather than sequential, judgment of the likelihood of the complete set of observed events. Empirical calibration curves that map experienced probabilities to subjective probabilities reveal that the degree of underextremity (overestimation of low likelihood events and underestimation of high likelihood events) is strongly conditional on the number of judged events. We uncover two regularities conditional on the number of events that modify (a) the crossover points of the calibration curves with the identity line and (b) the gradient or sensitivity of probability judgments. We present a process model of elicited (subjective) probabilities that captures these empirical regularities. Experienced events recalled from memory may be erroneously attributed to the wrong events based on the similarity of event outcomes. We conclude that the observed miscalibration of probability judgments can be attributed to the noisy retrieval component of a rational process-based decision model. We discuss the implications of our model for the conflicting empirical findings of overweighting and underweighting in the decisions from experience literature. Finally, we show that reliance on small samples can be an ecologically rational strategy for a bounded rational decision-maker (subject to noisy recall), as aggregated subjective probabilities are closer to the ecological probabilities than the experienced (or sampled) probabilities are.