Lexicographic order preservation and stochastic dominance

Stochastic dominance concerns conditions on outcome probabilities that are necessary and sufficient for one act to be (strictly) preferred to another according to all preference relations that share certain properties, one of which customarily is an Archimedean property sufficient to entail existence of real-valued representations. This paper relaxes this assumption to permit linear lexicographic utility of finite and known dimensionality. In some situations, levels of the lexicographic hierarchy could correspond to explicit criteria or attributes. In this model, subjective probabilities emerge as matrix premultipliers of the outcome utility vectors. It thus obtains matrix probability generalizations of the familiar cumulative probability conditions for stochastic dominance.