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.