Are People Naïve Probability Theorists? A Further Examination of the Probability Theory + Variation Model

Abstract

ABSTRACTTwo experiments tested predictions derived from the Probability Theory + Variation (PTV) model. PTV model assumes that judgments follow probability theory, but systematic errors arise from noise in the judgments. Experiment 1 compared the PTV model to a configural weighted averaging model in joint probability judgment and found more support for the PTV model in diagnostic cases. Specifically, noise was negatively correlated with semantic coherence and conjunction and disjunction fallacies increased when order effects produced more noise in conjunctions and disjunctions. Consistent with both models, judgments adhered stochastically to the addition law. Contrary to the integration rules of the PTV model, we failed to find increased noise in disjunctions compared to conjunctions. Experiment 2 tested predictions of the PTV model for conditional probability judgment. Consistent with the PTV model, noise was negatively correlated with semantic coherence in conditional probabilities and judgments adhered stochastically to Bayes' theorem. Conversion errors were generally more prevalent than conditional reversals, a finding that is not fully consistent with the PTV model. In general, the quantitative fit of the PTV model was relatively better for overlapping and subset problems compared to identical, independent and mutually exclusive problems, especially for semantic coherence. Copyright © 2014 John Wiley & Sons, Ltd.