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People believe that, even in very large samples, proportions of binary signals might depart significantly from the population mean. We model this "non-belief in the Law of Large Numbers" by assuming that a person believes that proportions in any given sample might be determined by a rate different than the true rate. In prediction, a non-believer expects the distribution of signals will have fat tails. In inference, a non-believer remains uncertain and influenced by priors even after observing an arbitrarily large sample. We explore implications for beliefs and behavior in a variety of economic settings.

In this paper, we ask whether variation in preference anomalies is related to variation in cognitive ability. Evidence from a new laboratory study of Chilean high-school students with similar schooling backgrounds shows that small-stakes risk aversion and short-run discounting are less common among those with higher standardized test scores. The relationship with test scores survives controls for parental education and wealth. We find some evidence that elementary-school GPA is predictive of preferences measured at the end of high school. Two laboratory interventions provide suggestive evidence of a possible causal impact of cognitive resources on expressed preferences. (JEL: J24, D14, C91).