Natural Sampling: Rationality without Base Rates

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The Bayesian classification of single cases into classes is investigated. The neglect of class base rates is usually considered to be a fundamental violation of the principles of rationality and, in human judgment, is called ‘the base rate fallacy’. This paper analyzes an important special sampling condition in which the base rates actually turn out to be irrelevant in estimating classification probabilities. It is shown that the base rates do not affect the precision of the estimates of classification probability. This precision is modeled by a second-order probability distribution. Implications for the design of artificial and for the modeling of natural knowledge systems are discussed.

I wish to thank Maximilian Thaler and Marianne Kardinal for their help. This research was supported by the Fonds zur Förderung der wissenschaftlichen Forschung, Vienna.