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

- Bruce Burns,
*University of Sydney*

## 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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