Utility of gambling II: risk,paradoxes, and data |
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Authors: | R. Duncan Luce C. T. Ng A. A. J. Marley János Aczél |
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Affiliation: | (1) Institute for Mathematical Behavioral Sciences, Social Science Plaza, University of California, Irvine, CA 92697-5100, USA;(2) Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;(3) Department of Psychology, University of Victoria, Victoria, Canada |
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Abstract: | 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. |
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Keywords: | Duplex decomposition Entropy Functional equations Linear weighted utility Segregation Expected utility Utility of gambling Utility paradoxes Independence properties |
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