### 2017

Benavoli, Alessio; Facchini, Alessandro; Vicente-Perez, Jose; Zaffalon, Marco

A polarity theory for sets of desirable gambles Conference

Proc. ISIPTA'17 Int. Symposium on Imprecise Probability: Theories and Applications, , PJMLR, 2017.

Abstract | Links | BibTeX | Tags: desirability, lexicographic

@conference{Benavoli2017c,

title = {A polarity theory for sets of desirable gambles},

author = {Benavoli, Alessio and Facchini, Alessandro and Vicente-Perez, Jose and Zaffalon, Marco},

url = {https://arxiv.org/abs/1705.09574},

year = {2017},

date = {2017-05-07},

booktitle = {Proc. ISIPTA'17 Int. Symposium on Imprecise Probability: Theories and Applications, },

pages = {1-12},

publisher = {PJMLR},

abstract = {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.},

keywords = {desirability, lexicographic},

pubstate = {published},

tppubtype = {conference}

}

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.

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.