Notes on desirability and conditional lower previsions



We detail the relationship between sets of desirable gambles and conditional lower previsions. The former is one the most general models of uncertainty. The latter corresponds to Walley’s celebrated theory of imprecise probability. We consider two avenues: when a collection of conditional lower previsions is derived from a set of desirable gambles, and its converse. In either case, we relate the properties of the derived model with those of the originating one. Our results constitute basic tools to move from one formalism to the other, and thus to take advantage of work done in the two fronts.


Lower and upper previsions Sets of desirable gambles Coherence Natural extension Equal expressivity 

Mathematics Subject Classifications (2010)

28E05 03B48 28A12 60A86 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of OviedoOviedoSpain
  2. 2.IDSIAMannoSwitzerland

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