A Symmetric View of Utilities and Probabilities
نویسنده
چکیده
Motivated by the need to reason about u t i l ities, and inspired by the success of bayesian networks in representing and reasoning about probabilities, we introduce the notion of ut i l i ty distr ibutions, in which uti l i t ies have the structure of probabilit ies. We furthermore define the notion of a bi-d istr ibut ion, a structure that includes in a symmetric fashion both a probabil i ty distr ibut ion and a u t i l i ty distr ibut ion. We give several examples of bi-distr ibutions. We also show that every state space wi th standard probabil i ty distr ibut ion and ut i l i ty function can be embedded in a bi-distr ibut ion, and provide bounds on the size requirements of this bi-distr ibut ion. Final ly, we suggest a reinterpretation of the von-Neumann and Morgenstern theorem in l ight of this new model.
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