Annals of Operations Research

, Volume 279, Issue 1–2, pp 115–150 | Cite as

Dutch book rationality conditions for conditional preferences under ambiguity

  • Giulianella Coletti
  • Davide Petturiti
  • Barbara VantaggiEmail author
Original Research


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.


Conditional gambles Preferences Choquet expected value Ambiguity Conditional totally alternating capacity Conditional totally monotone capacity Dutch book 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Giulianella Coletti
    • 1
  • Davide Petturiti
    • 2
  • Barbara Vantaggi
    • 3
    Email author
  1. 1.Department of Mathematics and Computer ScienceUniversity of PerugiaPerugiaItaly
  2. 2.Department of EconomicsUniversity of PerugiaPerugiaItaly
  3. 3.Department of S.B.A.I.“La Sapienza” University of RomeRomeItaly

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