Multi-person decision analysis in large scale systems—group decision making

This paper treats the problem of amalgamating the preference orderings of individuals into an overall preference ordering for the society comprised of those individuals. A mathematical rule for doing this is known as a “social welfare function”. The imposition of five seemingly desirable conditions on the social welfare function leads to Arrow's Impossibility Theorem, which states that there is no function which satisfies these five conditions. To circumvent this problem, several proposed restrictions on the social welfare function are discussed. The concept of decentralized group decision making, in which the members of the group are arranged in a hierarchical structure, is described. Here decision making takes place within subgroups and then the subgroups are treated as individuals in the decision making process for the group as a whole. Conditions under which decentralized decision making leads to the same results as centralized decision making are stated and proved.