Development and implications of the studies concerning the “problem of three prisoners”

Abstract

The “problem of three prisoners”is a vigorous example of counter-intuitive problems to estimate posterior probability. It is so counter-intuitive that a lot of people have a difficulty in accepting the normative estimate based on Bayes’theorem. We proposed a modified version of the original problem by changing prior probabilities given in the problem text. It would lead to different estimates depending on the cognitive strategy taken, and the Bayesian estimate is even more counter-intuitive than that of original version. Factors that contribute to its difficulty were examined through mathematical analyses and psychological experiments. Multiple factors are identified, among which an intermediate-level representation of the problem structure was emphasized. We also proposed a “roulette representation” which is a mathematically isomorphic, visual model to facilitate more intuitive understanding of the Bayesian solution. The naïve schemas and heuristics underlying subjective estimation of posterior probability are discussed. Significance and implications of our studies are further discussed in the context of recent related studies.View full abstract