On Matrix Probabilities in Nonarchimedean Decision Theory.

In an earlier paper, we axiomatized a lexicographic expected utility model for preference in decision under uncertainty that is patterned on the models of Ramsey and Savage but omits their Archimedean axioms. Our model has the unusual feature that subjective probabilities are matrices that premultiply utility vectors in the lexicographic representation of preference between acts. Our purpose here is to analyze the model in relation to the Ramsey-Savage theory along with other models that have a lexicographic feature. A point of departure in Savage's postulate P4, whose purpose is to weakly order his, is more probable than relation on events. This postulate does not hold in our model and we therefore encounter incomparability between events. The paper explores the nature of incomparability, which can be widespread in high-dimensional situations. We include special cases of our model that retain a lexicographic component but also satisfy P4. Copyright 1993 by Kluwer Academic Publishers