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Testing the limits of optimality: the effect of base rates in the Monty Hall dilemma

Learning & Behavior volume 42, pages 69–82 (2014)Cite this article

Abstract

The Monty Hall dilemma is a probability puzzle in which a player tries to guess which of three doors conceals a desirable prize. After an initial selection, one of the nonchosen doors is opened, revealing that it is not a winner, and the player is given the choice of staying with the initial selection or switching to the other remaining door. Pigeons and humans were tested on two variants of the Monty Hall dilemma, in which one of the three doors had either a higher or a lower chance of containing the prize than did the other two options. The optimal strategy in both cases was to initially choose the lowest-probability door available and then switch away from it. Whereas pigeons learned to approximate the optimal strategy, humans failed to do so on both accounts: They did not show a preference for low-probability options, and they did not consistently switch. An analysis of performance over the course of training indicated that pigeons learned to perform a sequence of responses on each trial, and that sequence was one that yielded the highest possible rate of reinforcement. Humans, in contrast, continued to vary their responses throughout the experiment, possibly in search of a more complex strategy that would exceed the maximum possible win rate.

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Notes

  1. All confidence intervals throughout the article are 95 % confidence intervals.

  2. Throughout the article, d is effect size, defined as the difference between the sample mean and the relevant comparison value, expressed in standard deviations.

  3. Theoretical comparison values are based on the unconditional probabilities from Table 1, because they produce a single value that is dependent solely on the birds’ (and not the host’s) behavior. One can still test the viability of other theoretical values by noting whether or not they fall within the specified 95 % confidence intervals.

  4. Although the proportions of sequences varied from bird to bird, each bird produced all of the possible sequences during the initial days of training, and no single sequence strongly predominated in any individual bird’s responses.

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Affiliations

  1. Whitman College, Walla Walla, WA, USA

    Walter T. Herbranson & Shanglun Wang

  2. Department of Psychology, Whitman College, 345 Boyer Avenue, Walla Walla, WA, 99362, USA

    Walter T. Herbranson

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  1. Walter T. Herbranson
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  2. Shanglun Wang
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Correspondence to Walter T. Herbranson.

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Herbranson, W.T., Wang, S. Testing the limits of optimality: the effect of base rates in the Monty Hall dilemma. Learn Behav 42, 69–82 (2014). https://doi.org/10.3758/s13420-013-0126-6

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  • DOI: https://doi.org/10.3758/s13420-013-0126-6

Keywords

  • Choice
  • Monty Hall dilemma
  • Optimality
  • Pigeons
  • Probability learning
  • Sequence learning