Abstract
Stochastic dominance is a form of stochastic ordering, which stems from decision theory when one gamble can be ranked as superior to another one for a broad class of decision makers whose utility functions, representing preferences, have very general form. There exists extensive theory concerning one dimensional stochastic dominance of different orders.
However it is not obvious how to extend the concept to multiple dimension which is especially crucial when utilizing multidimensional non separable utility functions. One possible approach is to transform multidimensional random vector to one dimensional random variable and put equivalent stochastic dominance in multiple dimension to stochastic dominance of transformed vectors in one dimension.
We suggest more general framework which does not require reduction of dimensions of random vectors. We introduce two types of stochastic dominance and seek for their generators in terms of von Neumann -Morgenstern utility functions.
Moreover, we develop necessary and sufficient conditions for stochastic dominance between two discrete random vectors with uniform distribution.