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Dutch book rationality conditions for conditional preferences under ambiguity

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Abstract

We study preference relations on conditional gambles of a decision maker acting under ambiguity. Dutch book rationality conditions are provided under a linear utility scale, encoding either an optimistic or a pessimistic attitude towards uncertainty. These conditions characterize possibly incomplete preferences representable by totally alternating or monotone conditional functionals. In general, the uniqueness of the representation is not guaranteed, but it can be obtained by adding the hypothesis of existence of a conditional fair price for every conditional gamble. The given rationality conditions have a betting scheme interpretation relying on “penalty fees” for betting on strict preference comparisons.

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Acknowledgements

We thank the anonymous reviewers for their very detailed and constructive suggestions. The authors are members of the INdAM-GNAMPA research group. This work was partially supported by the University of Perugia, funding of 2015 Research Projects under grant “Decisions under risk, uncertainty and imprecision”, La Sapienza University of Rome funding of 2015 under Grant C26A15Y4EZ “Numerical and probabilistic models for the management of information”, the Italian Ministry of Health under Grant J521I14001640001 “Intelligent systems helping in decisions for the early alert and the dissuasion to the use of doping”.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Giulianella Coletti

  2. Department of Economics, University of Perugia, Perugia, Italy

    Davide Petturiti

  3. Department of S.B.A.I., “La Sapienza” University of Rome, Rome, Italy

    Barbara Vantaggi

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  1. Giulianella Coletti
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  2. Davide Petturiti
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Correspondence to Barbara Vantaggi.

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Coletti, G., Petturiti, D. & Vantaggi, B. Dutch book rationality conditions for conditional preferences under ambiguity. Ann Oper Res 279, 115–150 (2019). https://doi.org/10.1007/s10479-019-03299-8

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