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Communication on the paper ‘‘A reference‐dependent regret model for deterministic tradeoff studies’’

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  • Xiaoting Wang
  • Evangelos Triantaphyllou
  • Edouard Kujawski

Abstract

This communication focuses on a fundamental problem related to the recently introduced Reference‐Dependent Regret Model (RDRM) [E. Kujawski, Syst Eng 8(2) (2005), 119– 137] for deterministic multi‐criteria decision‐making. Kujawski asserted that the RDRM model satisfies three properties. The first of these properties, referred to as the ‘‘independence of dominated alternatives,’’ seems to be an intuitive one. According to this property, the RDRM model preserves the ranking of two alternatives Ai and Aj with ranking Ai>Aj when a new alternative dominated by Ai is introduced or an old alternative dominated by Aj is dropped. In this communication it is demonstrated algebraically and also by means of a numerical example that the RDRM model may fail to satisfy this property. The implication is that when the concepts of regret and/or rejoicing are considered and defined in terms of all the available alternatives in accordance with the RDRM, adding or dropping a dominated alternative can change the ranking of the alternatives and violate the independence of dominated alternatives property. © 2008 Wiley Periodicals, Inc. Syst Eng.

Suggested Citation

  • Xiaoting Wang & Evangelos Triantaphyllou & Edouard Kujawski, 2008. "Communication on the paper ‘‘A reference‐dependent regret model for deterministic tradeoff studies’’," Systems Engineering, John Wiley & Sons, vol. 11(4), pages 360-364, December.
    • Handle: RePEc:wly:syseng:v:11:y:2008:i:4:p:360-364
    DOI: 10.1002/sys.20115
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    References listed on IDEAS

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    1. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    2. Edouard Kujawski, 2005. "A reference‐dependent regret model for deterministic tradeoff studies," Systems Engineering, John Wiley & Sons, vol. 8(2), pages 119-137.
    3. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    4. Quiggin, John, 1994. "Regret Theory with General Choice Sets," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 153-165, March.
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