Utility of Gambling II: Risk, Paradoxes, and Data

• Published in: Economic theory Vol. 36; no. 2; pp. 165 - 187
• Main Authors: Luce, R. Duncan, Ng, C. T., Marley, A. A. J., Aczél, János
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer 01.08.2008; Springer-Verlag; Springer Nature B.V
• Subjects: Algebra; Data visualization; Decision making; Decomposition; Economic theory; Economic Theory/Quantitative Economics/Mathematical Methods; Economic utility; Economics; Economics and Finance; Entropy; Expected utility; Gambling; Game Theory; Logical givens; Mathematical theorems; Microeconomics; Paradoxes; Probability; Probability distribution; Probability distributions; Public Finance; Research Article; Shannon entropy; Social and Behav. Sciences; Studies; Utility of gambling; Utility paradoxes; Duplex decomposition; Functional equations; Segregation; D46; Entropy; C91; Linear weighted utility; Expected utility; D81; Independence properties
• ISSN: 0938-2259; 1432-0479
• DOI: 10.1007/s00199-007-0259-y

We specialize our results on entropy-modified representations of event-based gambles to representations of probability-based gambles by assuming an implicit event structure underlying the probabilities, and adding assumptions linking the qualitative properties of the former and the latter. Under segregation and under duplex decomposition, we obtain numerical representations consisting of a linear weighted utility term plus a term corresponding to information-theoretical entropies. These representations accommodate the Allais paradox and most of the data due to Birnbaum and associates. A representation of mixed event-and probability-based gambles accommodates the Ellsberg paradox. We suggest possible extensions to handle the data not accommodated.