Stochastic Utility Evaluation

1. Preferences Relations, Axioms, Utility Existence, Interval Scale, Gambling Approach

The advances in science and technology require broader use of contemporary engineering, mathematical and computer methods and tools. On the other hand, the adequate reactions of the expert or the Decision Maker (DM) are of crucial significance in goal-oriented systems. An important limitation is the qualitative, verbal-conceptual manner of human reasoning and judgments. This imposes the use of specific approaches and evaluation methods for the conceptual empirical information (verbal expression or second order knowledge) (Larichev, 2001). Human values (utilities) are integral part of the decision-making process of the individual. They are the internal motivation for determining the main objective in the goal-oriented systems. Unfortunately, in most scientific investigations and developments, the subjective values and probabilistic expectations are not explicitly related and directly oriented towards the considered problem (Raiffa, 1968; Keeney, 1993). In this aspect, especially important is the task of connecting the two contradicting tendencies—the requirement of ordinal information from mathematical and computational point of view and the cardinal nature of the empirical (second order) knowledge, empirical ability, intuition, etc. representative for the particular subject (Pavlov, 2004; Mengov, 2010).

In scientific investigation, two main approaches are utilized, analytic, and synthetic. The analytic method is intrinsic to the human thinking, but in explicit form as main technical practice, representing the rationality of the human behavior was not introduced until 17 century. The success of this analytic approach lies not only in dividing the whole into smaller simpler parts, but also in the fact that by combining them in an appropriate goal-orientated way we obtain again another whole related to the investigated phenomena. The point of view is now bringing into line with our utility oriented position. Only in this stage can we explain the occurrence of the whole as a synchronous occurrence of its composing parts through the structure of synthesis. The above may be rephrased as “we perceive the real world through our goal-driven thinking and experience” and also as “no reality and rationality exist to us unless pierced by our intellect.” We can generally accept that the analytic approach is realization of our intellect, as rationality and goal focus. In analysis, the main essential aspects of the systems are expressed as sub-objectives to the point of view of our interest towards the event, to our utility from the occurrence of the investigated event. On a following stage, inseparable from analysis, is the synthesis of the individual elements or sub-objectives in a unified structure, in which the interrelations reveal the mechanism of occurrence of the synthesized whole, but now in the direction of our main objective.

One of the possible scientific approaches to these problems is that of multiattribute utility. In this aspect, the program for action from the subject to the computer is structurization of the considered goal in the given system, fixation of scales by individual criteria, evaluating the structural sub-objectives (Raiffa, 1968; Keeney, 1993). Then comes the expression of the preferences of the decision maker and construction of the value or utility function, evaluation of the subjective probabilities and further standard mathematical processing.