HOW CAN AN EXPERT SYSTEM HELP IN CHOOSING THE OPTIMAL DECISION

We introduce a rationality principle for a preference relation curly less than or equal to on an arbitrary set of lotteries. Such a principle is a necessary and sufficient condition for the existence of an expected utility agreeing with curly less than or equal to. The same principle also guarantees a rational extension of the preference relation to any larger set of lotteries. When the extended relation is unique with respect to the alternatives under consideration, the decision maker does not need a numerical evaluation in order to make a choice. Such a rationality condition needs little information in order to be applied, and its verification amounts to solving a linear system.