Multi-Attribute Decision Making by Stochastic Dominance

Abstract

In practical problems of decision making by the maximum expected utility criterion, there are not a few cases where it is difficult to identify utility functions. For such cases, however, it is relatively easy to find what the decision maker's attitude toward risk is, i.e., whether it is risk aversion or decreasing risk aversion. With such a partial knowledge of utility functions, stochastic dominance (SD) can be used as an approach in ranking alternatives by comparing their structure of probability distributions. In this paper, single-attribute SD rules are first surveyed. Then, by introducing multi-attribute value functions, multi-attribute SD rules are derived with the aid of single-attribute SD rules. Finally, the relations between the multi-attribute SD rules and statistical parameters are examined. It is found that the relations of statistical parameters obtained represent the decision maker's preference by statistical parameters. Therefore, he could readily understand the content of stochastic dominance by those relations and accept stochastic dominance as a decision supporting method.