Handbook of Social Choice and Welfare

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.