Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural sampling, from animal foraging to neural networks. By analyzing several thousand solutions to Bayesian problems, the authors found that when information was presented in frequency formats, statistically naive participants derived up to 50% of all inferences by Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference.

Research on people's confidence in their general knowledge has to date produced two fairly stable effects, many inconsistent results, and no comprehensive theory. We propose such a comprehensive framework, the theory of probabilistic mental models (PMM theory). The theory (a) explains both the overconfidence effect (mean confidence is higher than percentage of answers correct) and the hard-easy effect (overconfidence increases with item difficulty) reported in the literature and (b) predicts conditions under which both effects appear, disappear, or invert. In addition, (c) it predicts a new phenomenon, the confidence-frequency effect, a systematic difference between a judgment of confidence in a single event (i.e., that any given answer is correct) and a judgment of the frequency of correct answers in the long run. Two experiments are reported that support PMM theory by confirming these predictions, and several apparent anomalies reported in the literature are explained and integrated into the present framework.Do people think they know more than they really do? In the last 15 years, cognitive psychologists have amassed a large and apparently damning body of experimental evidence on overconfidence in knowledge, evidence that is in turn part of an even larger and more damning literature on so-called cognitive biases. The cognitive bias research claims that people are naturally prone to making mistakes in reasoning and memory, including the mistake of overestimating their knowledge. In this article, we propose a new theoretical model for confidence in knowledge based on the more charitable assumption that people are good judges of the reliability of their knowledge, provided that the knowledge is representatively sampled from a specified reference class. We claim that this model both predicts new experimental results (that we have tested) and explains a wide range of extant experimental findings on confidence, including some perplexing inconsistencies.Moreover, it is the first theoretical framework to integrate the two most striking and stable effects that have emerged from confidence studies-the overconfidence effect and the hardeasy effect-and to specify the conditions under which these effects can be made to appear, disappear, and even invert. In most recent studies (including our own, reported herein), subThis article was written while Gerd Gigerenzer was a fellow at the Center for Advanced Study in the Behavioral Sciences, Stanford, California. We are grateful for financial support provided by the Spencer Foundation and the Deutsche Foischungsgemeinschaft (DFG 170/2-1).We thank Leda Cosmides, Lorraine Daston, Baruch FischhofF, Jennifer Freyd, Kenneth Hammond, Wolfgang Hell, Sarah Licmenstein, Kathleen Much, John Tooby, Amos Tversky, and an anonymous reviewer for helpful comments on earlier versions of this article.Correspondence concerning this article should be addressed to Gerd Gigerenzer, who is now at the Institut fur Psychologic, Hellbrunnerstrasse 34, Universitat Salzburg, A-5020 Salzburg, Austria.

Most people, experts included, have difficulties understanding and combining statistical information effectively. Hoffrage et al. demonstrate that these difficulties can be considerably reduced by communicating the information in terms of natural frequencies rather than in terms of probabilities. Several applications in medicine, legal decision-making, and education are discussed.

Egon Brunswik argued that psychological processes are adapted to environmental properties. He proposed the method of representative design to capture these processes and advocated that psychology be a science of organism-environment relations. Representative design involves randomly sampling stimuli from the environment or creating stimuli in which environmental properties are preserved. This departs from systematic design. The authors review the development of representative design, examine its use in judgment and decision-making research, and demonstrate the effect of design on research findings. They suggest that some of the practical difficulties associated with representative design may be overcome with modern technologies. The importance of representative design in psychology and the implications of this method for ecological approaches to cognition are discussed.

Representing information in natural frequencies is a fast and effective way of facilitating diagnosis insight, which in turn helps physicians to better communicate risks to patients, and patients to better understand these risks.