A Polarity Theory for Sets of Desirable Gambles
نویسندگان
چکیده
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.
منابع مشابه
A POLARITY THEORY FOR SETS OF DESIRABLE GAMBLES A polarity theory for sets of desirable gambles
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...
متن کاملSets of Desirable Gambles and Credal Sets
Sets of desirable gambles were proposed by Walley [7] as a general theory of imprecise probability. The main reasons for this are: it is a very general model, including as particular cases most of the existing theories for imprecise probability; it has a deep and simple axiomatic justification; and mathematical definitions are natural and intuitive. However, there is still a lot of work to be d...
متن کاملIrrelevant and independent natural extension for sets of desirable gambles
The results in this paper add useful tools to the theory of sets of desirable gambles, a growing toolbox for reasoning with partial probability assessments. We investigate how to combine a number of marginal coherent sets of desirable gambles into a joint set using the properties of epistemic irrelevance and independence. We provide formulas for the smallest such joint, called their independent...
متن کاملSome Remarks on Sets of Lexicographic Probabilities and Sets of Desirable Gambles
Sets of lexicographic probabilities and sets of desirable gambles share several features, despite their apparent differences. In this paper we examine properties of marginalization, conditioning and independence for sets of lexicographic probabilities and sets of desirable gambles.
متن کاملExchangeability for sets of desirable gambles
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We study exchangeability assessments for such models, and prove a counterpart of de Finetti’s finite representation theorem. We show that this representation theorem has a very nice geometrical interpretation. We also lay bare the relationships between the representatio...
متن کامل