Stochastic dominance for ranking ventures

Tests for stochastic dominance help to rank ventures in order of preference. An example is given to show how Second Degree Stochastic Dominance can improve on the results of First Degree Stochastic Dominance but in another example, they do not yield a complete ordering of ventures. A reduction of the size of the efficient set of ventures is possible for the case where the utility function consists of two linear sections, and results for this case are given.