Probability Dominance in Random Outcomes

Abstract

In making decisions under uncertainty the following rationale or justification is often heard: “A is chosen because A is likely to outperform B” or “A is chosen because A’s prospect is likely to be better than B’s.” The argument based on this rationale or justification is simple and can be effective. The rationale may be a habitual one in many people’s information processing when making a decision. Unfortunately, the rationale may be too simple to be directly analyzed by more elaborate concepts such as utility functions (for instance see Fishburn (Ref. 1), stochastic dominance (for instance see Brumelle and Vickson (Ref. 2), Fishburn (Refs. 3,4), Hanoch and Levy (Ref. 5)), mean-variance (and the third moment) dominance (Markowitz (Refo. 6)), chance constrained programming (for instance, Charnes and Cooper (Ref. 7)), maximizing the probability of achieving an aspiration level or minimizing the probability of insolvency etc.

The entire article will appear in the Journal of Optimization Theory and Applications. Interested readers please contact P. L. Yu for a copy of the article.