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The bipolar Choquet integral representation

Author

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  • Salvatore Greco
  • Fabio Rindone

Abstract

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Salvatore Greco & Fabio Rindone, 2014. "The bipolar Choquet integral representation," Theory and Decision, Springer, vol. 77(1), pages 1-29, June.
    • Handle: RePEc:kap:theord:v:77:y:2014:i:1:p:1-29
    DOI: 10.1007/s11238-013-9390-3
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    1. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.

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    More about this item

    Keywords

    Cumulative Prospect Theory; Gains-loss separability; bi-Weighting function; Bipolar Choquet integral; D81; C60;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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