Fair Division and Collective Welfare / Edition 1

Fair Division and Collective Welfare / Edition 1

by Herv? Moulin
     
 

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ISBN-10: 0262633116

ISBN-13: 9780262633116

Pub. Date: 09/01/2004

Publisher: MIT Press

The concept of fair division is as old as civil society itself.

Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern

Overview

The concept of fair division is as old as civil society itself.

Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare.

The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method.

The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.

Product Details

ISBN-13:
9780262633116
Publisher:
MIT Press
Publication date:
09/01/2004
Edition description:
New Edition
Pages:
295
Product dimensions:
7.00(w) x 9.00(h) x 0.60(d)
Age Range:
18 Years

Table of Contents

1Microeconomic Foundations1
1.1Fairness: Equal and Unequal Treatment1
1.2Collective Welfare: Cardinal3
1.3Collective Welfare: Ordinal6
1.4Externalities and Fair Division9
1.5Private versus Public Contracts13
1.6Organization and Overview of the Book15
1.7Introduction to the Literature18
2Fair Distribution21
2.1Four Principles of Distributive Justice21
2.2A Simple Model of Fair Distribution27
2.3Contested Garment Method37
2.4Equal Sacrifice in Taxation41
2.5Sum-Fitness and Equality44
2.6Introduction to the Literature51
Exercises to Chapter 252
3Cardinal Welfarism63
3.1Welfarism63
3.2Additive Collective Utility Functions66
3.3Egalitarianism and the Leximin Social Welfare Ordering70
3.4Comparing Classical Utilitarianism, Nash, and Leximin76
3.5Failures of Monotonicity81
3.6Bargaining Compromise86
3.7Introduction to the Literature95
Exercises to Chapter 396
4Voting and Social Choice107
4.1Ordinal Welfarism107
4.2Condorcet versus Borda110
4.3Voting over Resource Allocation116
4.4Single-Peaked Preferences118
4.5Intermediate Preferences122
4.6Preference Aggregation and Arrow's Theorem126
4.7Introduction to the Literature130
Exercises to Chapter 4131
5The Shapley Value139
5.1The Problem of the Commons and Two Examples139
5.2The Shapley Value: Definition143
5.3The Stand-alone Test and Stand-alone Core147
5.4Stand-alone Surplus156
5.5Axiomatizations of the Shapley Value159
5.6Introduction to the Literature162
Exercises to Chapter 5163
6Managing the Commons169
6.1The Tragedy of the Commons169
6.2Constant Returns to Scale173
6.3Fair Compensation: Three Interpretations175
6.4Free Access versus Random Priority: Decreasing Returns184
6.5Increasing Returns190
6.6Axiomatic Comparison of the Three Solutions199
6.7Introduction to the Literature208
Exercises to Chapter 6209
7Fair Trade and Fair Division221
7.1Private Ownership and Competitive Trade221
7.2Imperfect Competition228
7.3Destructive Competition232
7.4No Envy and the Assignment Problem235
7.5The CEEI and Egalitarian Equivalent Solutions240
7.6Axiomatics of Fair Division248
7.7Introduction to the Literature251
Exercises to Chapter 7252
8A Glossary of Definitions and Results261
References277
Index281

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