Handbook of Social Choice and Welfare

Edited by

  • Kenneth Arrow, Kenneth Arrow, Joan Kenney Professor of Economics and Professor of Operations Research, Emeritus, Stanford University, Stanford, CA, USA
  • A.K. Sen, Harvard University, Cambridge, MA, USA
  • Kotaro Suzumura, Waseda University, Tokyo, Japan

The Handbook of Social Choice and Welfare presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. The first volume consists of four parts. In Part 1 (Arrovian Impossibility Theorems), various aspects of Arrovian general impossibility theorems, illustrated by the simple majority cycle first identified by Condorcet, are expounded and evaluated. It also provides a critical survey of the work on different escape routes from impossibility results of this kind. In Part 2 (Voting Schemes and Mechanisms), the operation and performance of voting schemes and cost-sharing mechanisms are examined axiomatically, and some aspects of the modern theory of incentives and mechanism design are expounded and surveyed. In Part 3 (structure of social choice rules), the positional rules of collective decision-making (the origin of which can be traced back to a seminal proposal by Borda), the game-theoretic aspects of voting in committees, and the implications of making use of interpersonal comparisons of welfare (with or without cardinal measurability) are expounded, and the status of utilitarianism as a theory of justice is critically examined. It also provides an analytical survey of the foundations of measurement of inequality and poverty. In order to place these broad issues (as well as further issues to be discussed in the second volume of the Handbook) in perspective, Kotaro Suzumura has written an extensive introduction, discussing the historical background of social choice theory, the vistas opened by Arrow's Social Choice and Individual Values, the famous "socialist planning" controversy, and the theoretical and practical significance of social choice theory. The primary purpose of this Handbook is to provide an accessible introduction to the current state of the art in social choice theory and welfare economics. The expounded theory has a strong and constructive message for pursuing human well-being and facilitating collective decision-making.
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Book information

  • Published: August 2002
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-82914-6


"This book, together with the forthcoming second volume, presents careful surveys of various aspects of social choice and welfare. Each chapter is written by a well-cast expert in the area. ...Suzumura also summarizes the main lines of ongoing and future research."
Journal of Economic Literature, 2004

Table of Contents

Preface to Volume 1 (K. Arrow, A. Sen, K. Suzumura). Introduction (K. Suzumura). Part 1: Arrovian Impossibility Theorems. 1. Impossibility theorems in the Arrovian framework (D. Campbell, J. Kelly). Introduction. Definitions and framework. Fundamental Lemmas and Arrows's theorem. Relaxing the Pareto criterion. Relaxing transitivity. Relaxing the domain condition. Relaxing independence of irrelevant alternatives. Modifications of the Arrovian framework. Concluding remarks. 2. Categories of Arrovian Voting Schemes (F. Aleskerov). Introduction. Voting: A general description. Rationality of individual opinions and collective decisions. Social decision rules. Functional voting rules. Social choice correspondences. Conclusion. 3. Domain Restrictions (W. Gaertner). Introduction. Notation and definitions. The existence of collective choice rules under exclusion conditions for finite sets of discrete alternatives. The existence of Arrovian social welfare functions and the domain of the simple majority rule. Distributional restrictions over the set of individual preferences under simple majority rule. Social choice in continuous space. Concluding remarks. Part 2: Voting Schemes and Mechanisms. 4. Voting Procedures (S. Brams, P. Fishburn). Introduction. Voter preferences and social choice functions. Voting procedures for two candidates. Introduction to voting procedures for three or more candidates. Nonranked voting and dominated strategies. Strategic analysis of nonranked voting. Nonranked multistage voting: Successive elimination. Condorcet choices and ranked voting. Positional scoring procedures and Borda choices. Point distribution procedures. Proportional representation. Conclusion. 5. Implementation Theory (E. Maskin, T. Sjöström). Introduction. Nash implementation. Implementation with complete information: Further topics. Bayesian implementation. Concluding remarks. 6. Axiomatic Cost and Surplus-Sharing (H. Moulin). Introduction. Rationing. Sharing variable returns. Heterogeneous inputs or outputs. Part 3: Structure of Social Choice Rules. 7. Positional Rules of Collective Decision-Making (P. Pattanaik). Introduction. The basic notation and definitions. Some notions of positionalist social ranking rules and social decision rules. Arrow's conditions, the principle of simple majority, and positionalist SDR's. The structure of the Borda rule. Score-based rules and runoff procedures. Concluding remarks. 8. Game-Theoretic Analysis of Voting in Committees (B. Peleg). Introduction. Plurality voting, Borda count, and feasible elimination procedures: Some examples. Basic concepts. Representations of committees. Undistorted and consistent SCF's. Strong representations of committees. Continuation and generalizations. Concluding remarks. 9. Representative Democracy and Social Choice Theory (N. Schofield). Introduction: Constitutional choices. Voters as a "committee". A "committee"of politicians. Elections as methods of belief aggregation. Electoral risk-taking and economic or political quandaries. Concluding remarks. Part 4: Welfare, Justice and Poverty. 10. Social Welfare Functionals and Interpersonal Comparability (C. d'Aspremont, L. Gevers). Introduction. Social welfare functionals and related concepts. Axioms and their use. Independence and invariance-based characterizations. Disgarding neutrality or invariance. Conclusion. 11. Utilitarianism and the Theory of Justice (C. Blackorby, W. Bossert, D. Donaldson). Introduction. Social-evaluation functionals. Welfarism. Generalized utilitarianism. Utilitarianism. Variable-population extensions. Uncertainty. Conclusions. 12. Inequality, Poverty and Welfare (B. Dutta). Introduction. Preliminaries. Measurement of inequality. Measurement of poverty. Concluding remarks.