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

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?