CHARACTERIZATION OF THE SATISFACTORY DECISION PRINCIPLE
Yasuhiko Takahara, Bunpei Nakano, Kyoichi Jim Kijima · Journal of the Operations Research Society of Japan · 1978
This paper discusses essential significances of the satisfactory decision criterion in an axiomatical way. For decision problems under undertainty the traditional decision criteria, for instance, the max-min, the regret and the Laplace criterion are well known. The satisfactory decision criterion is another type of principle towards decision problems under uncertainty. The traditional decision criteria requires first to arrange all alternatives in a linear order and then to subset the first elements as its solution. On the other hand, the satisfactory decision criterion is one that first arranges alternative in a linear order and second devides the linear order into two parts and third selects the "good" part as its solution, which is caned a satisfactory subset. In this sense the satisfactory decision criterion is much simpler than the traditional ones. It is introduced by Simon to explain a realistic decision behaviour of human being and is formulated by Mesarovic as one of the most important decision criteria for control theory. First we investigate properties of a satisfactory subset and find that a subset of the set of alternatives is a satisfactory subset if and only if it is an algebriac closed set. Second we axiomatize the satisfactory decision criterion by decomposing the resultant properties and make its "degree of simpleness" clear. Finally by comparing our axiom system with the axion systems of the traditional decision criteria obtained by Milnor, we find that the max-min and the regret criterion can be seen as special cases of the satisfactory decision criterion, that is, as the satisfactory decision criteria with special types of aspiration levels. The Laplace and the Hurwitz, however, can not be seen as the same as the other decision criteria including the satisfactory decision criterion. In this paper we do not assume any structure in the sets of alternatives nor of uncertainties. Strong results under such more specified conditions will be presented later.