The theory of social choice deals with both the processes and results of col­ lective decision making. In this book, we explore some issues in the theory of social choice and mechanism design. We examine the premises of this theory, the axiomatic approach, and the mechanism design approach. The main questions are what is collective interest, how is it related to individuals' interests, how should one design social interactions, laws, and in­ stitutions? These questions are not new. Philosophers, social scientists have indeed pondered upon them for years. And, in fact, the organizational struc­ tures of many social institutions -courts, parliaments, committees and reg­ ulatory boards -often lack a sound theoretical base. This is not surprising, as it is, indeed, difficult to provide for a comprehensive formalization of the activities of such organizations. Nevertheless, there has been a definite trend towards providing clear and unambiguous rules for collective decision mak­ ing. These very rules constitute the body of social choice theory and its main object. The basic problem of social choice We explain here more precisely what a problem of social choice is, what approaches might be used to tackle it, and what kind of solutions it leads to. We introduce a few basic notions in preliminarily fashion and, in doing so, we stress both motivations and explanations.

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1. Basic Concepts.- 1.1 Preferences.- 1.2 Social Choice Correspondences.- 1.3 Monotone Social Choice Correspondences.- 1.4 Social Choice Mechanisms.- 1.5 Effectivity Functions and Blockings.- 1.A1 Arrow's Impossibility Theorem.- 1.A2 Non-manipulable SCFs.- 1.A3 Minimal Monotone SCCs.- Bibliographic Comments.- 2. Nash-consistent Mechanisms.- 2.1 Definitions and Examples.- 2.2 Blockings Generated by Consistent Mechanisms.- 2.3 Strongly Monotone Social Choice Correspondences.- 2.4 Nash-implementable Correspondences.- 2.5 Implementation: the Case of Two Participants.- 2.6 Acceptable Mechanisms.- 2.A A Simple Mechanism for the Implementation of Walrasian Equilibria.- Bibliographic Comments.- 3. Strategy-proof Mechanisms.- 3.1 Dominant Strategies. The Revelation Principle.- 3.2 Single-Peaked Environment.- 3.3 Linear Environment.- 3.4 The Transferable Environment. Groves Mechanisms.- 3.5 Further Properties of Groves Mechanisms.- 3.A1 The Simple Transferable Environment Case.- 3.A2 Acceptable Mechanisms in Transferable Environment.- Bibliographic Comments.- 4. Cores and Stable Blockings.- 4.1 Stable Outcomes.- 4.2 Additive Blockings.- 4.3 Convex Blockings.- 4.4 Almost Additive Blockings.- 4.5 Necessary Stability Conditions.- 4.6 Veto as a Decision-making Procedure.- 4.A1 Balanced Blockings.- 4.A2 Blockings with Infinite Number of Alternatives.- 4.A3 The Harems Lemma.- Bibliographic Comments.- 5. Strongly Consistent Mechanisms.- 5.1 Definitions and Examples.- 5.2 A Tokens Mechanism (or Veto-mechanism).- 5.3 Blockings Generated by SC-mechanisms.- 5.4 Direct Core Mechanisms.- 5.5 Laminable Blockings.- 5.6 A Necessary and Sufficient Condition of Laminability.- 5.7 Neutral Laminable Blockings.- 5.A Implementation via Strong Equilibria.- Bibliographic Comments.- References.