Arithmetic computation with probability words and numbers

• Published in: Journal of behavioral decision making Vol. 34; no. 4; pp. 593 - 608
• Main Authors: Mandel, David R., Dhami, Mandeep K., Tran, Serena, Irwin, Daniel
• Format: Journal Article
• Language: English
• Published: Chichester Wiley Periodicals Inc 01.10.2021
• Subjects: Accuracy; Arithmetic; Between-subjects design; Coherence; Communication; Computation; Computer applications; Decision making; End users; Intelligence; Mathematics; numeric probability; Probability; uncertainty communication; verbal probability
• ISSN: 0894-3257; 1099-0771
• DOI: 10.1002/bdm.2232

Probability information is regularly communicated to experts who must fuse multiple estimates to support decision making. Such information is often communicated verbally (e.g., “likely”) rather than with precise numeric (point) values (e.g., “.75”), yet people are not taught to perform arithmetic on verbal probabilities. We hypothesized that the accuracy and logical coherence of averaging and multiplying probabilities will be poorer when individuals receive probability information in verbal rather than numerical point format. In four experiments (N = 213, 201, 26, and 343, respectively), we manipulated probability communication format between subjects. Participants averaged and multiplied sets of four probabilities. Across experiments, arithmetic accuracy and coherence was significantly better with point than with verbal probabilities. These findings generalized between expert (intelligence analysts) and non‐expert samples and when controlling for calculator use. Experiment 4 revealed an important qualification: Whereas accuracy and coherence were better among participants presented with point probabilities than with verbal probabilities, imprecise numeric‐probability ranges (e.g., “.70 to .80”) afforded no computational advantage over verbal probabilities. Experiment 4 also revealed that the advantage of the point over the verbal format is partially mediated by strategy use. Participants presented with point estimates are more likely to use mental computation than guesswork, and mental computation was found to be associated with better accuracy. Our findings suggest that where computation is important, probability information should be communicated to end users with precise numeric probabilities.