Bayes’ Theorem: Can A Theory of Judgment and Inference Do Without It?
This chapter suggests a biological justification for subjective expected utility (SEU) theory generally, which might be extended to T. Bayes’ theorem. It shows how hypotheses generated from earlier studies of probability estimation might be rephrased in terms applicable to a decision task, with some useful results. The chapter describes several other ways in which subjective probabilities can be studied through reference to the decision process. It also shows how decisions can be used to measure parameters of subjective probability distributions for continuous quantities. Bayes’ theorem as a rule for the revision of beliefs is a theorem derivable from the axioms of probability theory, which are an integral part of SEU theory. An entirely separate source of interest in the external application of Bayes’ theorem stems from an interest in helping those whose business it is to make decisions. The primary task for one group was a standard decision task, while the other group was given a relative frequency-judgment task.