Algebraic properties of satisficing decision criterion

Abstract The satisficing decision criterion is one of the decision criteria under uncertainty which has been studied especially in management theory and organization theory, and recently in systems theory. This criterion has many applications in theory and practice, as shown by H. A. Simon and M.D. Mesarovic. However, there is some gap between theoretical results on and potential applications of the satisficing criterion, because many of its fundamental properties have not yet been studied satisfactorily. In order to narrow the gap, it is necessary to study it algebraically, because this makes it possible to grasp its most fundamental properties without excessive mathematical structure. Hence, the main object of this paper is to show algebraic properties of the satisficing decision criterion under a given lattice structure, by the following steps: 1. (1) to embed a partial order, constructed from a vector comparison of payoffs, into some lattice; 2. (2) conversely, from any two-class partition of an alternative space and an order-homomorphic embedding, to deduce some aspiration level (tolerance) function which realizes the partition meaningfully, so that all elements of one set of this partition are satisfactory and those of the other are not; 3. (3) to prove some existence theorems for satisficing alternatives.