Memory & Cognition

, Volume 30, Issue 2, pp 171–178 | Cite as

The inverse fallacy: An account of deviations from Bayes’s theorem and the additivity principle

  • Gaëlle VillejoubertEmail author
  • David R. Mandel


In judging posterior probabilities, people often answer with the inverse conditional probability—a tendency named theinverse fallacy. Participants (N=45) were given a series of probability problems that entailed estimating bothp(H\vbD) andp(≈,H\vbD). The findings revealed that deviations of participants’ estimates from Bayesian calculations and from the additivity principle could be predicted by the corresponding deviations of the inverse probabilities from these relevant normative benchmarks. Methodological and theoretical implications of the distinction between inverse fallacy and base-rate neglect and the generalization of the study of additivity to conditional probabilities are discussed.


Sample Space Inverse Probability Bayesian Probability Support Theory Additivity Principle 
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  1. Ayton, P. (1997). How to be incoherent and seductive: Bookmakers’ odds and support theory.Organizational Behavior & Human Decision Processes,72, 99–115.CrossRefGoogle Scholar
  2. Baratgin J., &Noveck, I. A. (2000). Not only base rates are neglected in the Engineer-Lawyer problem: An investigation of reasoners’ underutilization of complementarity.Memory & Cognition,28, 79–91.CrossRefGoogle Scholar
  3. Bar-Hillel, M. (1980). The base rate fallacy in probability judgments.Acta Psychologica,44, 211–233.CrossRefGoogle Scholar
  4. Cosmides, L., &Tooby, J. (1996). Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty.Cognition,58, 1–73.CrossRefGoogle Scholar
  5. Dawes, R. M., Mirels, H. L., Gold, E., &Donahue, E. (1993). Equating inverse probabilities in implicit personality judgments.Psychological Science,4, 396–400.CrossRefGoogle Scholar
  6. Doherty, M. E., Mynatt, C. R., Tweney, R. D., &Schiavo, M. D. (1979). Pseudodiagnosticity.Acta Psychologica,43, 11–21.CrossRefGoogle Scholar
  7. Eddy, D. M. (1982). Probabilistic reasoning in clinical medicine: Problems and opportunities. In D. Kahneman, P. Slovic, & A. Tversky (Eds.),Judgment under uncertainty: Heuristics and biases (pp. 249–267). Cambridge: Cambridge University Press.Google Scholar
  8. Evans, J. St. B. T. (1998). Matching bias in conditional reasoning: Do we understand it after 25 years?Thinking & Reasoning,4, 45–82.CrossRefGoogle Scholar
  9. Gavanski, I., &Hui, C. (1992). Natural sample spaces and uncertain belief.Journal of Personality & Social Psychology,63, 766–780.CrossRefGoogle Scholar
  10. Gigerenzer, G., &Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats.Psychological Review,102, 684–704.CrossRefGoogle Scholar
  11. Girotto, V., &Gonzalez, M. (2001). Solving probabilistic and statistical problems: A matter of information structure and question form.Cognition,78, 247–276.CrossRefPubMedGoogle Scholar
  12. Hamm, R. M. (1993). Explanation for common responses to the blue/ green cab probabilistic inference word problem.Psychological Reports,72, 219–242.Google Scholar
  13. Hammerton, M. (1973). A case of radical probability estimation.Journal of Experimental Psychology,101, 252–254.CrossRefGoogle Scholar
  14. Hanita, M., Gavanski, I., &Fazio, R. H. (1997). Influencing probability judgments by manipulating the accessibility of sample spaces.Personality & Social Psychology Bulletin,23, 801–813.CrossRefGoogle Scholar
  15. Kahneman, D., & Tversky, A. (1972). On prediction and judgment.ORI Research Monographs,12.Google Scholar
  16. Kahneman, D., &Tversky, A. (1973). On the psychology of prediction.Psychological Review,80, 237–251.CrossRefGoogle Scholar
  17. Koehler, J. J. (1996a). The base rate fallacy reconsidered: Descriptive, normative and methodological challenges.Behavioral & Brain Sciences,19, 1–53.CrossRefGoogle Scholar
  18. Koehler, J. J. (1996b). On conveying the probative value of DNA evidence: Frequencies, likelihood ratios and error rates.University of Colorado Law Review,67, 859–886.Google Scholar
  19. Liu, A. Y. (1975). Specific information effect in probability estimation.Perceptual & Motor Skills,41, 475–478.Google Scholar
  20. Lyon, D., &Slovic, P. (1976). Dominance of accuracy information and neglect of base rates in probability estimation.Acta Psychologica,40, 287–298.CrossRefGoogle Scholar
  21. Macchi, L. (1995). Pragmatic aspects of the base rate fallacy.Quarterly Journal of Experimental Psychology,48A, 188–207.Google Scholar
  22. Macchi, L. (2000). Partitive formulation of information in probabilistic problems: Beyond heuristics and frequency format explanations.Organizational Behavior & Human Decision Processes,82, 217–236.CrossRefGoogle Scholar
  23. Macchi, L., Osherson, D., &Krantz, D. H. (1999). A note on superadditive probability judgment.Psychological Review,106, 210–214.CrossRefGoogle Scholar
  24. Meehl, P., &Rosen, A. (1955). Antecedent probability and the efficiency of psychometric signs of patterns, or cutting scores.Psychological Bulletin,52, 194–215.CrossRefPubMedGoogle Scholar
  25. Pollard, P., &Evans, J. St. B. T. (1983). The role of representativeness in statistical inference. In J. St. B. T. Evans (Ed.),Thinking and reasoning (pp. 309–330). London: Routledge & Kegan Paul.Google Scholar
  26. Rottenstreich, Y., &Tversky, A. (1997). Unpacking, repacking, and anchoring: Advances in support theory.Psychological Review,104, 406–415.CrossRefPubMedGoogle Scholar
  27. Sherman, S. J., &Corty, E. (1984). Cognitive heuristics. In R. S. Wyer & T. K. Srull (Eds.),Handbook of social cognition (Vol. 1, pp. 189–286). Hillsdale, NJ: Erlbaum.Google Scholar
  28. Sherman, S. J., McMullen, M. N., &Gavanski, I. (1992). Natural sample spaces and the inversion of conditional judgments.Journal of Experimental Social Psychology,28, 401–421.CrossRefGoogle Scholar
  29. Skov, R. B., &Sherman, S. J. (1986). Information-gathering processes: Diagnosticity, hypothesis-confirmatory strategies, and perceived hypothesis confirmation.Journal of Experimental Social Psychology,22, 93–121.CrossRefGoogle Scholar
  30. Slowiaczek, L. M., Klayman, J., Sherman, S. J., &Skov, R. B. (1992). Information selection and use in hypothesis testing: What is a good question, and what is a good answer?Memory & Cognition,20, 392–405.CrossRefGoogle Scholar
  31. Thompson, W. C., &Schumann, E. L. (1987). Interpretation of statistical evidence in criminal trials: The prosecutor’s fallacy and the defense attorney’s fallacy.Law & Human Behavior,11, 167–187.CrossRefGoogle Scholar
  32. Tversky, A., &Kahneman, D. (1980). Causal schemata in judgments under uncertainty. In M. Fishbein (Ed.),Progress in social psychology (Vol. 1, pp. 49–72). Hillsdale, NJ: Erlbaum.Google Scholar
  33. Tversky, A., &Koehler, D. J. (1994). Support theory: A nonextensional representation of subjective probability.Psychological Review,101, 547–567.CrossRefGoogle Scholar
  34. Wolfe, C. R. (1995). Information seeking on Bayesian conditional probability problems: A fuzzy-trace theory account.Journal of Behavioral Decision Making,8, 85–108.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2002

Authors and Affiliations

  1. 1.University of VictoriaVictoriaCanada
  2. 2.University Business SchoolUniversity of LeedsLeedsEngland

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