Danilov and Sotskov only consider models for which there is a fixed, abstract set of alternatives that is exogenously given and which is linearly ordered by each individual (i.e., individual preferences are transitive and no one is ever indifferent between distinct alternatives). Individual uncertainty about outcomes or preferences is never considered. For the most part, the book considers social choice correspondences that are defined for the full range of individual preferences, except as restricted by the linearity assumption. The authors explore the possibilities for implementation with respect to several equilibrium concepts - primarily Nash equilibrium, strong Nash equilibrium, equilibrium in dominant strategies, and the core. Social Choice Mechanisms has five chapters: 1. The introductory chapter presents the basic concepts and definitions for studying social choice correspondences and mechanisms, particularly from the standpoint of strategic maneuvering by individuals and coalitions. Considerable space is devoted to monotonicity, non-manipulability, effectivity functions, and blocking. There are also a few basic results on monotone social choice correspondences and non-manipulable social choice functions in this chapter, and a sketch of a proof of Arrow's impossibility theorem. Chapter 2 deals with Nash-imple- mentation - i.e., social choice correspondences for which one can find a mechanism whose Nash equilibrium outcomes at each configuration of individual preferences coincide with the image of the correspondence. Chapter 3 deals with strategy-proof mechanisms, and includes a thorough discussion of single-peaked preferences and generalizations of single- peakedness. It also includes a discussion of Groves mechanisms. There is a thorough analysis of subsets of the entire family of profiles of quasi-linear preferences that admit the existence of a Groves mechanism that always yields a balanced budget - and hence, always generates an efficient outcome. The theme of Chapt. 4 is "Cores and Stable Blockings" and the last chapter deals with strong Nash-implementation - i.e., social choice correspondences for which one can find a mechanism such that, at each configuration of individual preferences, an outcome x is in the image of the correspondence if and only if there is some configuration S of individual strategies yielding outcome x and such that such no coalition can improve on x by deviating from S. (Unfortunately, there is an inordinate number of printing errors. some of them serious.)