How to improve Bayesian reasoning: Comment on Gigerenzer and Hoffrage (1995)

G. Gigerenzer and U. Hoffrage (1995) claimed that Bayesian inference problems, which have been notoriously difficult for laypeople to solve using base rates, hit rates, and false-alarm rates, become computationally simpler when information is presented with frequencies based on natural sampling. They made an evolutionary argument for the improved performance. The authors of the present article show that performance can improve with either probabilities or frequencies, depending on the rareness of the events and the type of information presented. When events are rare, probabilities are more difficult to understand than frequencies (i.e., 5 out of 1,000 vs. .005.). Furthermore, when the information is presented as joint and marginal events, nested sets become more apparent. Frequencies based on natural sampling have these desirable properties. The authors agree with Gigerenzer and Hoffrage that frequencies can improve Bayesian reasoning, but they attribute that improvement to the use of mental models that involve elements of nested sets.