Composition rules in original and cumulative prospect theory

• Published in: Theory and decision Vol. 92; no. 3-4; pp. 647 - 675
• Main Authors: Gonzalez, Richard, Wu, George
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2022; Springer Nature B.V
• Subjects: Behavioral/Experimental Economics; Composition; Decision making; Domains; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; Equivalence; Expected utility; Expected values; Finance; Game Theory; Heterogeneity; Insurance; Management; Operations Research/Decision Theory; Predictions; Probability; Prospect theory; Social and Behav. Sciences; Statistics for Business; Violations; Weighting; Weighting functions; Prospect theory; Probability weighting function; Rank-dependent expected utility; Composition rules
• ISSN: 0040-5833; 1573-7187
• DOI: 10.1007/s11238-022-09873-0

Original and cumulative prospect theory differ in the composition rule used to combine the probability weighting function and the value function. We test the predictive power of these composition rules by performing a novel out-of-sample prediction test. We apply estimates of prospect theory’s weighting and value function obtained from two-outcome cash equivalents, a domain where original and cumulative prospect theory coincide, to three-outcome cash equivalents, a domain where the composition rules of the two theories differ. Although both forms of prospect theory predict three-outcome cash equivalents very well, at the aggregate level, we find small but systematic under-prediction of cash equivalents for cumulative prospect theory and small but systematic over-prediction of cash equivalents for original prospect theory. We also observe substantial heterogeneity across subjects and types of gambles, some of which is accounted for by differences in the curvature and elevation of the weighting function across individuals. We also find differences in prediction related to whether the worst outcome is zero or non-zero.