Fuzzy universality of probability judgment.

Probability judgment is essential to navigating through life, from understanding risks to making decisions under uncertainty. However, probability theory is relatively recent. How has humanity managed to get along before this development? In PNAS, Fontanari et al. (1) provide exciting new evidence of probabilistic cognition among Mayan indigenous groups, both adults and children, whose performance was generally indistinguishable from that of Western adults. On their face, these findings clash with the extensive literature on biases in probability judgment in which Westerners’ judgments violate elementary rules of probability theory (2). Even statisticians who are familiar with the probability calculus systematically violate its rules (3). Nevertheless, Mayans without formal education succeeded at tasks such as judging proportions, combining probabilities, and updating beliefs that college-educated people fail. That failure occurs in simple choice tasks that require neither numerical estimates nor computation. The mystery deepens when we consider the developmental origins of probability judgment: paradoxically, Fontanari et al. claim that infants make accurate probabilistic predictions in tasks that closely resemble those that older preschoolers fail. Why are infants so smart and statisticians so dumb? Order can be brought to this seeming chaos by considering successive generations of theories of the development of probability judgment, which have each ruled out compelling misconceptions. Many studies show that young children pass “probability-judgment” tasks that only require discrimination of greater-or-lesser magnitude, have clear and memorable instructions, and do not require memory for problem information (i.e., they use external stores) (4–6). Early studies often had confounded tasks that made them easier to pass. These tasks could be passed without understanding probability by simply picking whichever option had more of the winning color or tokens, a relative-magnitude judgment. Although understanding ratios is not the only criterion for understanding probability, it has long been considered an essential criterion (7, 8). Only the tasks shown in the right panel of figure 3 B and C of Fontanari et al. satisfy this criterion: a larger ratio but smaller number of winning tokens is pitted against a smaller ratio but larger number. Choosing 9/12 over 12/48 reflects understanding the importance of both numerator and denominator in probability judgments, a harder test to pass than relative-magnitude judgments. Thus, substituting relative magnitude for true probability judgments presumably accounts for high performance in some tasks in Fontanari et al. However, the posterior and updating tasks go beyond simple magnitude judgments because they involve responding to changes. Educated Westerners and even professionals fall prey to well-known errors in judging posterior and updated probabilities. For example, told that 10% of patients have a disease (the prior) and a patient tested positive for the A