Abstract
As a framework for analyzing the effects of task structures in problem solving, a probabilistic model of problem solving is formulated by introducing “probabilities of using problem representations.” The effects of “undermining hypotheses by data (or evidence)” in probability updating tasks are experimentally examined by measuring the probabilities of using problem representations. “Undermining” here means both “direct undermining by data” and “indirect undermining via the likelihood function of which value is zero.” The experimental analysis shows that (1) undermining is a strong obstacle to the Bayesian solutions of the probability updating tasks, and (2) there exist differences between the direct and the indirect undermining effects. A mathematical model, named “Probability Flow Model,” is made which expresses how the probabilities of using problem representations depend upon the general tendencies of human information use. This Probability Flow Model is experimentally validated. The differences between the direct and the indirect undermining effects are examined on the basis of the Probability Flow Model. The analysis shows that the differences are due to the differences in the degree of realization of the general tendencies of human information use. An interpretation of the differences in the degree of realization of the general tendencies is given from the viewpoint of how to relate a datum to hypotheses in solving the probability updating tasks. A new approach to human inductive reasoning, in which there has been no theoretical progress during the last two decades, is also suggested from the viewpoint of belief fixation and belief perseverance. It is an old custom that the classical statistics in Neyman-Pearson school is used in psychological data analyses, although its application to them is unreasonable. In this paper, Bayesian statistics is adopted because of its appropriateness to psychological data.
