Gerd Gigerenzer and Ulrich Hoffrage argue that Bayesian reasoning can be improved by using frequency formats instead of probability formats. They show that Bayesian algorithms are computationally simpler in frequency formats, which correspond to the way information is naturally acquired through sequential sampling. By analyzing thousands of solutions to Bayesian problems, they found that when information was presented in frequency formats, statistically naive participants derived up to 50% of all inferences using Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. The authors challenge the notion that the human mind is predisposed against Bayesian inference. They argue that the issue lies in the information format, not the cognitive algorithms themselves. They propose that cognitive algorithms are designed for specific information formats, and that frequency formats are more natural for humans, as they align with how information is acquired through natural sampling. This is supported by examples from animals to neural networks, where systems learn through sequential encoding and updating of event frequencies. The authors present two studies showing that frequency formats lead to more Bayesian reasoning than probability formats. They also show that Bayesian algorithms are computationally simpler in frequency formats, as they require fewer operations and can be performed on natural numbers rather than fractions. They further argue that frequency formats allow for more accurate Bayesian inference because they carry more information about sample sizes, enabling the computation of posterior distributions and confidence intervals. The authors distinguish between information format and information menu. The standard probability format has a standard menu with three pieces of information, while the frequency format has a short menu with only two pieces of information. They show that Bayesian algorithms are simpler in the short menu, and that frequency formats allow for the same Bayesian computations as probability formats. The authors also present several shortcuts that simplify Bayesian computations in both probability and frequency formats. These include the rare-event shortcut, the big hit-rate shortcut, and the comparison shortcut. These shortcuts are particularly effective in cases where the base rate is rare or the hit rate is high. The authors conclude that frequency formats lead to more Bayesian reasoning than probability formats, and that the cognitive algorithms underlying Bayesian inference include both standard Bayesian algorithms and shortcuts that approximate Bayesian inference. They propose three classes of cognitive algorithms: (a) algorithms that satisfy Equations 1 through 3; (b) pictorial analogs that work with operations such as "cutting" instead of multiplying; and (c) three shortcuts that approximate Bayesian inference well when certain conditions hold. They also propose several predictions based on these findings, including that frequency formats elicit a higher proportion of Bayesian algorithms than probability formats, and that Bayesian algorithms are simpler in the short menu.Gerd Gigerenzer and Ulrich Hoffrage argue that Bayesian reasoning can be improved by using frequency formats instead of probability formats. They show that Bayesian algorithms are computationally simpler in frequency formats, which correspond to the way information is naturally acquired through sequential sampling. By analyzing thousands of solutions to Bayesian problems, they found that when information was presented in frequency formats, statistically naive participants derived up to 50% of all inferences using Bayesian algorithms. Non-Bayesian algorithms included simple versions of Fisherian and Neyman-Pearsonian inference. The authors challenge the notion that the human mind is predisposed against Bayesian inference. They argue that the issue lies in the information format, not the cognitive algorithms themselves. They propose that cognitive algorithms are designed for specific information formats, and that frequency formats are more natural for humans, as they align with how information is acquired through natural sampling. This is supported by examples from animals to neural networks, where systems learn through sequential encoding and updating of event frequencies. The authors present two studies showing that frequency formats lead to more Bayesian reasoning than probability formats. They also show that Bayesian algorithms are computationally simpler in frequency formats, as they require fewer operations and can be performed on natural numbers rather than fractions. They further argue that frequency formats allow for more accurate Bayesian inference because they carry more information about sample sizes, enabling the computation of posterior distributions and confidence intervals. The authors distinguish between information format and information menu. The standard probability format has a standard menu with three pieces of information, while the frequency format has a short menu with only two pieces of information. They show that Bayesian algorithms are simpler in the short menu, and that frequency formats allow for the same Bayesian computations as probability formats. The authors also present several shortcuts that simplify Bayesian computations in both probability and frequency formats. These include the rare-event shortcut, the big hit-rate shortcut, and the comparison shortcut. These shortcuts are particularly effective in cases where the base rate is rare or the hit rate is high. The authors conclude that frequency formats lead to more Bayesian reasoning than probability formats, and that the cognitive algorithms underlying Bayesian inference include both standard Bayesian algorithms and shortcuts that approximate Bayesian inference. They propose three classes of cognitive algorithms: (a) algorithms that satisfy Equations 1 through 3; (b) pictorial analogs that work with operations such as "cutting" instead of multiplying; and (c) three shortcuts that approximate Bayesian inference well when certain conditions hold. They also propose several predictions based on these findings, including that frequency formats elicit a higher proportion of Bayesian algorithms than probability formats, and that Bayesian algorithms are simpler in the short menu.