The collider principle in causal reasoning: Why the Monty Hall dilemma is so hard. Burns, B. D & Wieth, M. J Exp Psychol Gen, 133(3):434-49, 2004.
doi  abstract   bibtex   
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?
@Article{Burns2004,
  author   = {Bruce D Burns and Mareike Wieth},
  journal  = {J Exp Psychol Gen},
  title    = {The collider principle in causal reasoning: {W}hy the {M}onty {H}all dilemma is so hard.},
  year     = {2004},
  number   = {3},
  pages    = {434-49},
  volume   = {133},
  abstract = {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?},
  doi      = {10.1037/0096-3445.133.3.434},
  keywords = {Causality, Choice Behavior, Humans, Logic, Michigan, Probability, Problem Solving, 15355148},
}

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