Frequency vs. Probability Formats: Framing the Three Doors Problem

Instead of subscribing to the view that people are unable to perform Bayesian probabilistic inference, recent research suggests that the algorithms people naturally use to perform Bayesian inference are better adapted for information presented in a natural frequency format than in the common probability format. We tested this hypothesis on the notoriously difficult three doors problem, inducing subjects to consider the likelihoods involved in terms of natural frequencies or in terms of probabilities. We then examined their ability to perform the mathematics underlying the problem, a stronger indication of Bayesian inferential performance than merely whether they gave the correct answer to the problem. With a robustness that may surprise people unfamiliar with the effects of information formats, the natural frequency group demonstrated dramatically greater normative mathematical performance than the probability group. This supports the importance of information formats in a more complex context than in previous studies