Abstract
A constellation of joint probability estimates is semantically coherent when the quantitative relationship among estimates of P(A), P(B), P(A and B), and P(A or B) is consistent with the relationship among the sets described in the problem statement. The possible probability estimates can form an extremely large number of permutations. However, this entire problem space can be reduced to six theoretically meaningful patterns: logically fallacious (conjunction or disjunction fallacies), identical sets (e.g., water and H2O), mutually exclusive sets (e.g., horses and zebras), subsets (e.g., robins and birds), overlapping sets (e.g., accountants and musicians), and inconsistent overlapping sets. Determining which of these patterns describes any set of probability estimates has been automated using Excel spreadsheet formulae. Researchers may use the semantic coherence technique to examine the consequences of differently worded problems, individual differences, or experimental manipulations. The spreadsheet described above can be downloaded as a supplement from http://brm.psychonomic-journals.org/content/supplemental.
Similar content being viewed by others
References
Adam, M. B., & Reyna, V. F. (2005). Coherence and correspondence criteria for rationality: Experts’ estimation of risks of sexually transmitted infections. Journal of Behavioral Decision Making, 18, 169–186.
Bar-Hillel, M., & Neter, E. (1993). How alike is it versus how likely is it? A disjunction fallacy in probability judgments. Journal of Personality & Social Psychology, 65, 1119–1131.
Evans, J. St. B. T. (2007). Hypothetical thinking: Dual processes in reasoning and judgement. Hove, U.K.: Psychology Press.
Gilovich, T., Griffin, D. [W.], & Kahneman, D. (Eds.) (2002). Heuristics and biases: The psychology of intuitive judgment. Cambridge: Cambridge University Press.
Hammond, K. R. (2000). Coherence and correspondence theories in judgment and decision making. In T. Connolly, H. R. Arkes, & K. R. Hammond (Eds.), Judgment and decision making: An interdisciplinary reader (2nd ed., pp. 53–65). Cambridge: Cambridge University Press.
Keren, G. (1991). Calibration and probability judgments: Conceptual and methodological issues. Acta Psychologica, 77, 217–273.
Lagnado, D. A., & Shanks, D. R. (2003). The influence of hierarchy on probability judgment. Cognition, 89, 157–178.
Lien, Y., & Cheng, P. W. (2000). Distinguishing genuine from spurious causes: A coherence hypothesis. Cognitive Psychology, 40, 87–137.
Oaksford, M., & Chater, N. (2007). Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.
Over, D. E. (2009). New paradigm psychology of reasoning. Thinking & Reasoning, 15, 431–438.
Reyna, V. F. (2004). How people make decisions that involve risk. A dual-processes approach. Current Directions in Psychological Science, 13, 60–66.
Reyna, V. F., & Adam, M. B. (2003). Fuzzy-trace theory, risk communication, and product labeling in sexually transmitted diseases. Risk Analysis, 23, 325–342.
Reyna, V. F., & Brainerd, C. J. (1995). Fuzzy-trace theory: An interim synthesis. Learning & Individual Differences, 7, 1–75.
Reyna, V. F., & Mills, B. [A.] (2007). Converging evidence supports fuzzy-trace theory’s nested sets hypothesis, but not the frequency hypothesis. Behavioral & Brain Sciences, 30, 278–280.
Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.
Wolfe, C. R. (1995). Information seeking on Bayesian conditional probability problems: A fuzzy-trace theory account. Journal of Behavioral Decision Making, 8, 85–108.
Wolfe, C. R., & Reyna, V. F. (2010). Semantic coherence and fallacies in estimating joint probabilities. Journal of Behavioral Decision Making, 23, 203–223. doi:10.1002/bdm.650
Wright, G., Bolger, F., & Rowe, G. (2002). An empirical test of the relative validity of expert and lay judgments of risk. Risk Analysis, 22, 1107–1122.
Yates, J. F., Lee, J.-W., Shinotsuka, H., Patalano, A. L., & Sieck, W. R. (1998). Cross-cultural variations in probability judgment accuracy: Beyond general knowledge overconfidence? Organizational Behavior & Human Decision Processes, 74, 89–117.
Young, S. D., Nussbaum, A. D., & Monin, B. (2007). Potential moral stigma and reactions to sexually transmitted diseases: Evidence for a disjunction fallacy. Personality & Social Psychology Bulletin, 33, 789–799.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Wolfe, C.R., Reyna, V.F. Assessing semantic coherence and logical fallacies in joint probability estimates. Behavior Research Methods 42, 373–380 (2010). https://doi.org/10.3758/BRM.42.2.373
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3758/BRM.42.2.373