We conduct a laboratory experiment using the Monty Hall problem to study how simplified examples improve learning behavior and correct irrational choices in probabilistic situations. In particular, we show that after experiencing a simplified version of the MHP, subjects perform better in the MHP, compared to the control group who only experienced the 3-door version. Our results suggest that simplified examples strongly induces learning.

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. (...) We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point. (shrink)

The framework of elementary probabilistic operations (EPO) explains the structure of elementary probabilistic reasoning tasks as well as people’s performance on these tasks. The framework comprises three components: (a) Three types of probabilities: joint, marginal, and conditional probabilities; (b) three elementary probabilistic operations: combination, marginalization, and conditioning, and (c) quantitative inference schemas implementing the EPO. The formal part of the EPO framework is a computational level theory that provides a problem space representation and a classification of elementary probabilistic problems based (...) on computational requirements for solving a problem. According to the EPO framework, current methods for improving probabilistic reasoning are of two kinds: First, reduction of Bayesian problems to a type of probabilistic problems requiring less conceptual and procedural competencies. Second, enhancing people’s utilization competence by fostering the application of quantitative inference schemas. The approach suggests new applications, including the teaching of probabilistic reasoning, using analogical problem solving in probabilistic reasoning, and new methods for analyzing errors in probabilistic problem solving. (shrink)

The Monty-Hall Problem ($MHP$) has been used to argue against a subjectivist view of Bayesianism in two ways. First, psychologists have used it to illustrate that people do not revise their degrees of belief in line with experimenters' application of Bayes' rule. Second, philosophers view $MHP$ and its two-player extension ($MHP2$) as evidence that probabilities cannot be applied to single cases. Both arguments neglect the Bayesian standpoint, which requires that $MHP2$ (studied here) be described in different terms than usually applied (...) and that the initial set of possibilities be stable (i.e., a focusing situation). This article corrects these errors and reasserts the Bayesian standpoint; namely, that the subjective probability of an event is always conditional on a belief reviser's specific current state of knowledge. (shrink)