Economic Theory

, Volume 36, Issue 2, pp 165–187 | Cite as

Utility of gambling II: risk, paradoxes, and data

  • R. Duncan Luce
  • C. T. Ng
  • A. A. J. Marley
  • János Aczél
Research Article


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.


Duplex decomposition Entropy Functional equations Linear weighted utility Segregation Expected utility Utility of gambling Utility paradoxes Independence properties 

JEL Classification Numbers

C91 D46 D81 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • R. Duncan Luce
    • 1
  • C. T. Ng
    • 2
  • A. A. J. Marley
    • 3
  • János Aczél
    • 2
  1. 1.Institute for Mathematical Behavioral Sciences, Social Science PlazaUniversity of CaliforniaIrvineUSA
  2. 2.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  3. 3.Department of PsychologyUniversity of VictoriaVictoriaCanada

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