Stochastic Dominance on Unidimensional Grids

Special stochastic-dominance relations for probability distributions on a finite grid of evenly-spaced points are considered. The relations depend solely on iterated partial sums of grid-point probabilities and are very computer efficient. Their corresponding classes of utility functions for expected-utility comparisons consist of functions defined on the grid that mimic in the large the traditional continuous functions whose derivatives alternate in sign. The first-degree and second-degree relations are identical to their traditional counterparts defined from iterated integrals of cumulative distribution functions. The higher-degree relations differ from the traditional relations in interesting and sometimes subtle ways. The paper explores aspects of the partial-sums relations, including effects of grid refinements and extensions, and describes their relationships to the traditional relations.