Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Individual and Social Orderings
- 3 May’s Theorem
- 4 Arrow’s Theorem with Individual Preferences
- 5 Relaxing Arrow’s Axioms
- 6 Arrow’s Theorem with Utilities
- 7 Harsanyi’s Social Aggregation Theorem
- 8 Distributional Ethics: Single Dimensional Approaches
- 9 Distributional Ethics: Multidimensional Approaches
- 10 Social Choice Functions
- 11 Strategyproofness on Quasi-linear Domains
- Index
Preface
Published online by Cambridge University Press: 11 January 2023
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Individual and Social Orderings
- 3 May’s Theorem
- 4 Arrow’s Theorem with Individual Preferences
- 5 Relaxing Arrow’s Axioms
- 6 Arrow’s Theorem with Utilities
- 7 Harsanyi’s Social Aggregation Theorem
- 8 Distributional Ethics: Single Dimensional Approaches
- 9 Distributional Ethics: Multidimensional Approaches
- 10 Social Choice Functions
- 11 Strategyproofness on Quasi-linear Domains
- Index
Summary
Social aggregation theory deals with the problem of amalgamation of the values assigned by different individuals to alternative social or economic states in a society into values for the entire society. A social state provides a description ofmaterials that are related to thewell-being of a population in different ways. One fundamental question that arises at the outset is how an individual can rank two alternative states in a well-defined manner. The problem of social aggregation theory can then be regarded as one of clubbing individual rankings into a social ranking in a meaningful way.
Chapter 1 presents an introductory outline of the materials analyzed in the remaining chapters. Chapter 2 of the monograph formally defines individual and social rankings of alternative states of affairs. Chapter 3 provides a rigorous discussion on May’s remarkable theorem on “social choice functions,” which represents group or collective decision rules, limited to two alternatives. In Chapter 4 we analyze Arrow’s social welfare function, a mapping from the set of all possible profiles of individual orderings of social states to the set of all possible orderings. We discuss this with some elaboration in view of the fact that Arrow’s model forms the basis of almost the entire social choice theory. Chapter 5 investigates to what extent the “dictatorship” result can be avoided when some of Arrow’s axioms are relaxed. In Arrow’s framework, when individual preferences are represented by utility functions, utilities are of the ordinal and non-comparable types. Arrow’s theorem with utility functions constitutes a part of Chapter 6 of the book. We use geometric technique to prove this fundamental result. In the recent past, the non-comparability assumption has been relaxed to partial and full comparability assumptions. A discussion on alternative notions of measurability and comparability of utility functions is also presented in Chapter 6. Simple numerical examples have been provided to illustrate the ideas. Possibilities of social welfare functions are expanded as a consequence of interpersonal comparability. Proofs of most theorems in the literature are sophisticated mathematically, which may not be easygoing for non-specialist readers. In view of this, we use simple graphical proofs for many such results.
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- Information
- Social Aggregations and Distributional Ethics , pp. ix - xiiPublisher: Cambridge University PressPrint publication year: 2023