Probabilistic dominance criteria for comparing uncertain alternatives: A tutorial

This paper is a tutorial which demonstrates the current state‐of‐the‐art methods for incorporating risk into project selection decision making. The projects under consideration might be R&D, IT, or other capital expenditure programs. We will show six decision making methods: 1. mean‐variance (MV), 2. mean‐semivariance, 3. mean‐critical probability, 4. stochastic dominance, 5. almost stochastic dominance (ASD), and 6. mean‐Gini. We will also describe the assumptions about the risk attitudes of the decision maker which are associated with each of the techniques. While all these methods have been previously applied elsewhere, this is the first paper which shows all of their applications in the project selection context, together with their interrelationships, strengths and weaknesses. We have applied all six techniques to the same group of five hypothetical projects and evaluated the resulting nondominated sets. Among the methods reviewed here, stochastic dominance is recommended because it requires the least restrictive assumptions. ASD and mean‐Gini are recommended when stochastic dominance is not practical or when it does not yield definitive choices. MV, mean‐semivariance, and mean‐critical probability are shown to be flawed.