Equiprobability principle or “no change” principle? Examining reasoning in the Monty Hall Dilemma using unequal probabilities

Abstract

The Monty Hall Dilemma (MHD) is a well-known cognitive illusion. It is often claimed that one reason for the incorrect answers is that people apply the equiprobability principle: they assume that the probability of the two remaining options must be equal. An alternative explanation for assigning the same probabilities to options is that they had the same prior probabilities and people perceive no significant change. Standard MHD versions do not distinguish these possibilities, but a version with unequal prior probabilities could. Participants were given an unequal probabilities version of MHD and told that either the high or low probability option had been eliminated. This affected participants’ choices and their posterior probabilities. Only 14% of participants’ responses were consistent with applying the equiprobability principle, but 51% were consistent with a “no change” principle. Participants were sensitive to the implications of the prior probabilities but did not appear to use Bayesian updating.


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