The original third wave scholars favor an evolutionary account that posits human brain adaptation to natural frequency processing. However, they do not agree on why this is so. Most scholars now agree that natural frequency representations do facilitate Bayesian reasoning. Although Kahneman and Tversky had already noted the advantages of frequency representations, it was the third wave scholars who pushed the prescriptive agenda, arguing that there are feasible and effective methods for improving belief revision. In the 1990s, a third wave of research spurred by Leda Cosmides and John Tooby and by Gerd Gigerenzer and Ulrich Hoffrage showed that people can reason more like a Bayesian if only the information provided takes the form of (non-relativized) natural frequencies.
A second wave, spearheaded by Daniel Kahneman and Amos Tversky, showed that people often ignored prior probabilities or base rates, where the priors had a frequentist interpretation, and hence were not Bayesians at all. The first wave of psychological research, pioneered by Ward Edwards, revealed that people were overly conservative in updating their posterior probabilities (i.e., P(D|H)).
Bayes' theorem, named after English statistician, philosopher, and Presbyterian minister, Thomas Bayes, offers a method for updating one’s prior probability of an hypothesis H on the basis of new data D such that P(H|D) = P(D|H)P(H)/P(D). What have we learnt from over a half-century of research and theory on this topic that could explain why people are often non-Bayesian? Can Bayesian reasoning be facilitated, and if so why? These are the questions that motivate this Frontiers in Psychology Research Topic. Rather, it is the typical individual whose reasoning and judgments often fall short of the Bayesian ideal who is the focus of improvement. Bayesian reasoning is a normative approach to probabilistic belief revision and, as such, it is in need of no improvement. We confess that the first part of our title is somewhat of a misnomer.
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