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Theory of social choice mechanisms is a comparatively new theory. The first results were obtained as early as the beginning of the seventies. The book contains the most important results of the theory. In two main topics the book describes what mechanisms allow equilibrium solutions at any agents` preference profiles, and what outcomes can be implemented. The answer depends on the equilibrium concept. Furthermore the four equilibrium concepts Nash equilibrium, strong Nash equilibrium, equilibrium in dominant strategies, and the core were described in detail

Intro -- Social Choice Theory -- Copyright -- Table of Contents -- Guide to Chapter Dependencies -- To the Student -- Acknowledgements -- Chapter 0. What is Social Choice Theory? -- Chapter 1. Simple Majority Voting -- Chapter 2. The Voting Paradox -- Chapter 3. Single-Peakedness -- Chapter 4. Chaos -- Chapter 5. Other Voting Extensions -- Chapter 6. Social Choice Rules -- Chapter 7. Arrow's Impossibility Theorem -- Chapter 8. Power -- Chapter 9. Rights -- Chapter 10. Strategy-Proofness -- Chapter 11. Counterthreats -- Chapter 12. Approval Voting -- Chapter 13. Mistakes -- Mathematical Appendix -- Answers and Hints to Selected Exercises -- Subject Index.

1: Introduction -- 1.1. Rational Choice -- 1.2. The Theory of Social Choice -- 1.3. Restrictions on the Set of Alternatives -- 1.4. Structural Stability of the Core -- 2: Social Choice -- 2.1. Preference Relations -- 2.2. Social Preference Functions -- 2.3. Arrowian Impossibility Theorems -- 2.4. Power and Rationality -- 2.5. Choice and Functions -- 3: Voting Rules -- 3.1. Simple Binary Preference Functions -- 3.2. Acyclic Voting Rules on Restricted Sets of Alternatives -- 3.3. Manipulation of Choice Functions on Finite Sets of Alternatives -- 3.4. Restrictions on the Preferences of Society -- 4: The Core -- 4.1. Existence of a Choice -- 4.2. Existence of a Core in Low Dimensions -- 4.3. Convex Preferences -- 4.4. Non-Convex Preference -- 4.5. The Necessity of the Dimension Constraint -- 5: Local Cycles -- 5.1. Voting Cycles in Dimension v(?)—1 -- 5.2. Implementation of Choice Functions in Dimension v(?) — 1 -- 5.3. Cycles and the Stability Dimension -- 5.4. The Stability Dimension v*( ?) -- 6: Structural Stability -- 6.1. Plott Symmetry Conditions -- 6.2. Structural Stability of the Optima Set -- 6.3. Structural Instability of the Optima Set -- 6.4. Stability of the Core and of Cycles -- 7: Classification of Voting Rules -- 7.1. The Stability and Instability Dimensions -- 7.2. Voting Rules in Low Dimensions -- 7.3. Majority Rule with an Infinite Electorate -- 8: Democratic Theory -- 8.1. Liberalism and Populism -- 8.2. Populist Democracy and Institutionalism -- 8.3. Liberal Theory and Electoral Politics -- 8.4. Preferences and Beliefs -- Glossary of Concepts -- Index of Authors -- Index of Terms and Definitions.

Since World War II the subject of social choice has grown in many and surprising ways. The impossibility theorems have suggested many directions: mathematical characterisations of voting structures satisfying various sets of conditions, the consequences of restricting choice to certain domaines, the relation to competitive equilibrium and the core, and trade-offs among the partial satisfactions of some conditions. The links with classical and modern theories of justice and, in particular, the competing ideas of rights and utilitarianism have shown the power of formal social choice analysis in illuminating the most basic philosophical arguments about the good social life. Finally, the ideals of the just society meet with the play of self interest; social choice mechanisms can lend themselves to manipulation, and the analysis of conditions under which given ideals can be realised under self interest is a political parallel to the welfare economics of the market. The contributors to these volumes focus on these issues at the forefront of current research.

Front Cover; Social Choice and Welfare; Copyright Page; Introduction to the series; Preface; Table of Contents; List of participants; Introduction; References; PART IA: THE ETHICAL ASPECTS OF SOCIAL CHOICE: THE AGGREGATION PROBLEM; CHAPTER 1. Arrow's theorem: Unusual domains and extended co-domains; 1. Introduction; 2. Notation; 3. From individual preferences to social preferences; 4. Dictators and oligarchies; 5. Hypothesis on individual preferences; 6. Arrow's theorem; 7. Proof of the theorem; 8. Remarks about weak orders; References.

First published in 1971, Social Choice is both a text and reference containing the proceedings of a conference dealing with contemporary work on the normative and descriptive aspects of the social choice problem. This reissue will be of interest to advanced undergraduate and graduate courses on group decision making and social choice. Economists, social psychologists, political scientists and sociologists will welcome this valuable work