The present book treats a highly specialized topic, namely effec­ tivity functions, which are a tool for describing the power structure implicit in social choice situations of various kind. One of the ad­ vantages of effectivity functions is that they seem to contain exactly the information which is needed in several problems of implementa­ tion, that is in designing the rules for individual behaviour given that this behaviour at equilibrium should result in a prescribed functional connection between preferences and outcome. We shall be interested in both formal properties of effectiv­ ity functions and applications of them in social choice theory, and among such applications in