pp 1–42 | Cite as

Desirability foundations of robust rational decision making

  • Marco ZaffalonEmail author
  • Enrique Miranda
S.I.: DecTheory&FutOfAI


Recent work has formally linked the traditional axiomatisation of incomplete preferences à la Anscombe-Aumann with the theory of desirability developed in the context of imprecise probability, by showing in particular that they are the very same theory. The equivalence has been established under the constraint that the set of possible prizes is finite. In this paper, we relax such a constraint, thus de facto creating one of the most general theories of rationality and decision making available today. We provide the theory with a sound interpretation and with basic notions, and results, for the separation of beliefs and values, and for the case of complete preferences. Moreover, we discuss the role of conglomerability for the presented theory, arguing that it should be a rationality requirement under very broad conditions.


Decision theory Incomplete preferences Desirability Imprecise probability Foundations 



The authors are grateful to the anonymous referees for a careful reading of the paper and in particular to Referee 1 for having spotted some technical problems that are now fixed.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)LuganoSwitzerland
  2. 2.Department of Statistics and Operations ResearchUniversity of OviedoOviedoSpain

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