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Learning & Behavior

, Volume 42, Issue 1, pp 69–82 | Cite as

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

  • Walter T. Herbranson
  • Shanglun Wang
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.

Keywords

Choice Monty Hall dilemma Optimality Pigeons Probability learning Sequence learning 

References

  1. Brown, P. L., & Jenkins, H. J. (1968). Autoshaping of the pigeon’s keypeck. Journal of the Experimental Analysis of Behavior, 11, 1–8.PubMedCentralPubMedCrossRefGoogle Scholar
  2. Burns, B. D., & Wieth, M. (2004). The collider principle in causal reasoning: Why the Monty Hall dilemma is so hard. Journal of Experimental Psychology: General, 133, 434–449.CrossRefGoogle Scholar
  3. De Neys, W. (2007). Developmental trends in decision making: The case of the Monty Hall Dilemma. In J. A. Elsworth (Ed.), Psychology of decision making in education, behavior, and high risk situations (pp. 271–281). Hauppauge, NY: Nova Science.Google Scholar
  4. Edwards, W. (1961). Probability learning in 1000 trials. Journal of Experimental Psychology, 62, 385–394.PubMedCrossRefGoogle Scholar
  5. Fantino, E., & Esfandiari, A. (2002). Probability matching: Encouraging optimal responding in humans. Canadian Journal of Experimental Psychology, 56, 58–63. doi: 10.1037/h0087385 PubMedCrossRefGoogle Scholar
  6. Gardner, R. A. (1957). Probability-learning with two and three choices. American Journal of Psychology, 70, 174–185.PubMedCrossRefGoogle Scholar
  7. Gilovich, T., Medvec, V. H., & Chen, S. (1995). Commission, omission, and dissonance reduction: Coping with regret in the “Monty Hall” problem. Personality and Social Psychology Bulletin, 21, 182–190.CrossRefGoogle Scholar
  8. Granberg, D. (1999). A new version of the Monty Hall dilemma with unequal probabilities. Behavioural Processes, 48, 25–34.CrossRefGoogle Scholar
  9. Granberg, D., & Brown, T. A. (1995). The Monty Hall dilemma. Personality and Social Psychology Bulletin, 21, 711–723.CrossRefGoogle Scholar
  10. Granberg, D., & Dorr, N. (1998). Further exploration of two-stage decision making in the Monty Hall dilemma. American Journal of Psychology, 111, 561–579.CrossRefGoogle Scholar
  11. Herbranson, W. T. (2012). Pigeons, humans and the Monty Hall dilemma. Current Directions in Psychological Science, 21, 297–301.CrossRefGoogle Scholar
  12. Herbranson, W. T., & Schroeder, J. (2010). Are birds smarter than mathematicians? Pigeons (Columba livia) perform optimally on a version of the Monty Hall Dilemma. Journal of Comparative Psychology, 124, 1–13.PubMedCentralPubMedCrossRefGoogle Scholar
  13. Herbranson, W. T., & Stanton, G. L. (2011). Flexible serial response learning by pigeons (Columba livia) and humans (Homo sapiens). Journal of Comparative Psychology, 125, 328–340.PubMedCrossRefGoogle Scholar
  14. Herrnstein, R. J. (1997). The matching law. Cambridge, MA: Harvard University Press.Google Scholar
  15. Howard, J. H., Jr., & Howard, D. V. (1997). Age differences in implicit learning of higher-order dependencies in serial patterns. Psychology and Aging, 12, 634–656.PubMedCrossRefGoogle Scholar
  16. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263–291.CrossRefGoogle Scholar
  17. Miller, G. A., & Frick, F. C. (1949). Statistical behavioristics and sequences of responses. Psychological Review, 56, 311–324.PubMedCrossRefGoogle Scholar
  18. Nissen, M. J., & Bullemer, P. (1987). Attentional requirements of learning: Evidence from performance measures. Cognitive Psychology, 19, 1–32. doi: 10.1016/0010-0285(87)90002-8 CrossRefGoogle Scholar
  19. Poling, A., Nickel, M., & Alling, K. (1990). Free birds aren’t fat: Weight gain in captured wild pigeons maintained under laboratory conditions. Journal of the Experimental Analysis of Behavior, 53, 423–424.PubMedCentralPubMedCrossRefGoogle Scholar
  20. Stevens, D. W., & Krebs, J. R. (1986). Foraging theory. Princeton, NJ: Princeon University Press.Google Scholar
  21. Tubau, E., & Alonso, D. (2003). Overcoming illusory differences in a probabilistic counterintuitive problem: The role of explicit representations. Memory & Cognition, 31, 596–607.CrossRefGoogle Scholar
  22. von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton, NJ: Princeton University Press.Google Scholar
  23. Zentall, T. R. (2011). Maladaptive “gambling” by pigeons. Behavioural Processes, 87, 50–56.PubMedCentralPubMedCrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2013

Authors and Affiliations

  1. 1.Whitman CollegeWalla WallaUSA
  2. 2.Department of PsychologyWhitman CollegeWalla WallaUSA

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