ABSTRACT
Equity theories, like interpersonal control theories, are founded on measures of the worth or relative strength of players, and build from these measures to the formation of minimum winning coalitions. However, whereas interpersonal control theories are largely concerned with players’ preferences among competing coalitions as a function of their ability to control other players, equity theories are solutions based on players’ expectations of their shares of the values of coalitions they can join. The fundamental principle of equity theories by which such expectations arise is the proportional allocation of rewards. That is, for each winning coalition each player expects an outcome that is proportional to the ratio of his strength measure to the sum of strength measures of all players in that winning coalition. In this way, each player has an expected outcome for each winning coalition of which he is a member. Then, typically, players construct a rank order for coalition preferences based on the expected outcomes, and if one winning coalition is the first-ranked choice of all of its members, that coalition is predicted by the theory.
