Base Rates in Bayesian Inference: Signal Detection Analysis of the Cab Problem

Several investigators concluded that humans neglect base rate information when asked to solve Bayesian problems intuitively. This conclusion is based on a comparison between normative (calculated) and subjective (responses by naive judges) solutions to problems such as the cab problem. The present article shows that the previous normative analysis was incomplete. In particular, problems of this type require both a signal detection theory and a judgment theory for their proper Bayesian analysis. In Bayes' theorem, posterior odds equals prior odds times the likelihood ratio. Previous solutions have assumed that the likelihood ratio is independent of the base rate, whereas signal detection theory (backed up by data) implies that this ratio depends on base rate. Before the responses of humans are compared with a normative analysis, it seems desirable to be sure that the normative analysis is accurate.