Characterization of satisficing decision criterion

Abstract

There are several decision criteria (or principles) under uncertainty. Individual decision problems can be solved, provided that one of the decision criteria is given, where a decision problem means a triplet which is composed of sets of decision alternatives and of uncertainties and a payoff function (from the above sets into a set of real numbers). In decision theory, only optimizing (decision) criteria are studied in any detail. However, in some realistic decision situations, as shown by H. A. Simon and M. D. Mesarovic, satisficing (decision) criteria are very fruitful and practically important. Of formulations of the satisficing criteria, one that was formulated by M. D. Mesarovic is very suitable to studies of satisficing decision problems under uncertainties because of its formal simplicity and broad applicability. A satisficing decision problem, as specified by him, is one that seeks a set of solutions that yield decision consequences (payoffs) greater than or equal to some given aspiration level (tolerance) function (from a set of uncertainties into real numbers) for each uncertainty. The main objective of this paper are 1. (1) to formulate axioms both for optimizing criteria and the satisficing criterion of this type, and then 2. (2) to characterize the latter, without using the aspiration level function and 3. (3) to compare its characterization with those for optimizing criteria.