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Theory and Decision

, Volume 67, Issue 1, pp 23–63 | Cite as

Utility of Gambling when Events are Valued: an Application of Inset Entropy

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

Abstract

The present theory leads to a set of subjective weights such that the utility of an uncertain alternative (gamble) is partitioned into three terms involving those weights—a conventional subjectively weighted utility function over pure consequences, a subjectively weighted value function over events, and a subjectively weighted function of the subjective weights. Under several assumptions, this becomes one of several standard utility representations, plus a weighted value function over events, plus an entropy term of the weights. In the finitely additive case, the latter is the Shannon entropy; in all other cases it is entropy of degree not 1. The primary mathematical tool is the theory of inset entropy.

Keywords

duplex decomposition functional equation Shannon entropy gamble decomposition inset entropy segregation utility of gambling valued events 

JEL Classification

C91 D46 D81 

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Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

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

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