Walter the banker: the conjunction fallacy reconsidered


In a famous experiment by Tversky and Kahneman (Psychol Rev 90:293–315, 1983), featuring Linda the bank teller, the participants assign a higher probability to a conjunction of propositions than to one of the conjuncts, thereby seemingly committing a probabilistic fallacy. In this paper, we discuss a slightly different example featuring someone named Walter, who also happens to work at a bank, and argue that, in this example, it is rational to assign a higher probability to the conjunction of suitably chosen propositions than to one of the conjuncts. By pointing out the similarities between Tversky and Kahneman’s experiment and our example, we argue that the participants in the experiment may assign probabilities to the propositions in question in such a way that it is also rational for them to give the conjunction a higher probability than one of the conjuncts.


  1. Atkinson D., Peijnenburg J., Kuipers T. (2009) How to confirm the disconfirmed. On conjunction fallacies and robust confirmation. Philosophy of Science 76: 1–21

    Article  Google Scholar 

  2. Bovens L., Hartmann S. (2003) Bayesian epistemology. Oxford University Press, Oxford

    Google Scholar 

  3. Bovens L., Olsson E. J. (2000) Coherentism, reliability and Bayesian networks. Mind 109: 685–719

    Article  Google Scholar 

  4. Crupi V., Fitelson B., Tentori K. (2008) Probability, confirmation, and the conjunction fallacy. Thinking and Reasoning 14(2): 182–199

    Article  Google Scholar 

  5. Fitelson B. (2003) A probabilistic theory of coherence. Analysis 63: 195–199

    Article  Google Scholar 

  6. Hájek A., Hartmann S. (2009) Bayesian epistemology. In: Steup M. (eds) Blackwell companion to epistemology. Blackwell, Oxford

    Google Scholar 

  7. Hansson B. (1983) Epistemology and evidence. In: Gärdenfors P., Hansson B., Sahlin N. (eds) Evidentiary value: Philosophical, judicial and psychological aspects of a theory—Essays dedicated to Sören Halldén on his sixtieth birthday (Library of Theoria 15). Gleerup, Lund, pp 75–97

    Google Scholar 

  8. Hertwig, R., Benz, B., & Krauss, S. (2008). The conjunction fallacy and the many meanings of and. Cognition, 108, 740–753.

    Google Scholar 

  9. Klein P., Warfield T. (1994) What price coherence?. Analysis 54: 129–132

    Article  Google Scholar 

  10. Meijs W. (2006) A corrective to Bovens and Hartmann’s measure of coherence. Philosophical Studies 133: 151–180

    Article  Google Scholar 

  11. Meijs, W. (2009). Coherentism and justification. Unpublished manuscript.

  12. Meijs W., Douven I. (2007) On the alleged impossibility of coherence. Synthese 157: 347–360

    Article  Google Scholar 

  13. Neapolitan R. (1990) Probabilistic reasoning in expert systems. Wiley, New York

    Google Scholar 

  14. Olsson E. J. (2005) Against coherence. Oxford University Press, Oxford

    Google Scholar 

  15. Schupbach, J. N. (2009a). Is the conjunction fallacy tied to probabilistic confirmation? Synthese, this special issue.

  16. Schupbach, J. N. (2009b). New hope for Shogenji’s coherence measure. Unpublished manuscript.

  17. Shogenji T. (1999) Is coherence truth-conducive?. Analysis 59: 338–345

    Article  Google Scholar 

  18. Shogenji, T. (2009). The degree of epistemic justification and the conjunction fallacy. Synthese, this special issue.

  19. Tentori, K., & Crupi, V. (2009). How the conjunction fallacy is tied to probabilistic confirmation: A reply to Schupbach (2009). Synthese, this special issue.

  20. Tversky A., Kahneman D. (1983) Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review 90: 293–315

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Stephan Hartmann.

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Cite this article

Hartmann, S., Meijs, W. Walter the banker: the conjunction fallacy reconsidered. Synthese 184, 73–87 (2012).

Download citation


  • Conjunction fallacy
  • Linda problem
  • Psychology of reasoning
  • Bayesian epistemology