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J Exp Psychol Gen. 2004 Sep;133(3):434-49.

The collider principle in causal reasoning: why the Monty Hall dilemma is so hard.

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Department of Psychology, Michigan State University, East Lansing, MI 48824-1117, USA.


The authors tested the thesis that people find the Monty Hall dilemma (MHD) hard because they fail to understand the implications of its causal structure, a collider structure in which 2 independent causal factors influence a single outcome. In 4 experiments, participants performed better in versions of the MHD involving competition, which emphasizes causality. This manipulation resulted in more correct responses to questions about the process in the MHD and a counterfactual that changed its causal structure. Correct responses to these questions were associated with solving the MHD regardless of condition. In addition, training on the collider principle transferred to a standard version of the MHD. The MHD taps a deeper question: When is knowing about one thing informative about another?

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