  Coherent sets of almost desirable gambles and credal sets are known to be
equivalent models. That is, there exists a bijection between the two
collections of sets preserving the usual operations, e.g. conditioning. Such a
correspondence is based on the polarity theory for closed convex cones.
Learning from this simple observation, in this paper we introduce a new
(lexicographic) polarity theory for general convex cones and then we apply it
in order to establish an analogous correspondence between coherent sets of
desirable gambles and convex sets of lexicographic probabilities.
