Causality and Reasoning: The Monty Hall Dilemma
Bruce D. Burns, Mareike B. Wieth · eScholarship (California Digital Library) · 2003
In the Monty Hall Dilemma (MHD) contestants try to choose which of three doors conceals a prize.After selecting a door, one of the other doors is opened by a host who knows where the prize is, but always reveals a dud.Contestants are then asked if they want to stay with their first choice, or switch to the other unopened door?Switching yields a two-thirds chance of winning, but most people have difficulty accepting this answer.Glymour ( 2001) points out that central to the MHD is a particular causal structure, the collider principle.We hypothesized that an isomorphic version of the MHD that would help participants understand its causal structure would improve their performance.Making the MHD a form of competition should be one way to achieve this.We confirmed this by showing that in a competition version of the MHD participants were much more likely to solve the problem, and more likely to answer a counterfactual question indicating a correct understanding of the problem's causal structure.Furthermore, regardless of MHD version, participants who solved the problem were more likely to also answer the counterfactual correctly.Thus the MHD can be seen as an example of people's difficulties with understanding even relative simple causal structures.