Some New Results on Compromise Solutions for Group Decision Problems

We report some new results on compromise solutions studied by Yu Yu, P. L. 1973. A class of decisions for group decision problems. Management Sci. 19 (8, April) 936–946. The following article focuses on the relation between the compromise solution and its parameter. In particular, we show that, under some nice conditions, the compromise solution is a continuous function of its parameter. A fundamental monotonicity result (Theorem 3.1) concerning compromise solutions is derived. The result enables us to generate the bounds of all compromise solutions. When n = 2, two monotonicity results are derived. These yield a good interpretation of the parameter p. When p is small the “group utility” is emphasized; and when p increases the individual regrets receive more weight. Finally we construct an example to illustrate that the monotonicity results for n = 2 are almost impossible to be generated for n > 2.