Abstract
In response to the increasing use of discrete cardinal data with limited numbers of outcomes, Stochastic Dominance Theory is here extended to facilitate its application. Framed in terms of Successive Sums of Cumulative Distribution Functions and Lower Partial Moments, convenient formulae, along with necessary and sufficient conditions for different orders of dominance are derived, which reveal some key facts that have eluded general attention. Engendered by restrictions on the finite differences between utility functions and the limited number of outcomes, degrees of freedom are lost as the dominance order increases, imposing an upper bound on the order that can be considered. Simple formulae for computing successive sums of cumulative distributions are developed, and the relationship between lower and higher order dominance is proven in this discrete cardinal case.
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