Fair Division and Collective Welfare

Fair Division and Collective Welfare

By Hervé Moulin





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.


Out of Print ISBN: 9780262134231 296 pp. | 7 in x 9 in 54 illus.


$35.00 X ISBN: 9780262633116 296 pp. | 7 in x 9 in 54 illus.


  • How to promote thinking on distributive justice? Education at the Kindergarten level is still the most effective way. However, for economists, philosophers, and thinkers who are familiar with the formal arguments, I strongly recommend a course or seminar based on Moulin's superb book.

    Ariel Rubinstein

    Department of Economics, Princeton University

  • Herve Moulin is one of the deepest thinkers in welfare economics. His book on fair division is an elegant overview of modern contributions to an ancient problem.

    Eric S. Maskin

    A.O. Hirschman Professor of Social Science, Institute for Advanced Study

  • Fair Division and Collective Welfare is a distinguished book which furnishes a rigorous exposition of distributive justice with many well-crafted examples. It fills a signifigant gap in the literature of modern microeconomics, and enables students and researchers to unfold the complete picture of the discipline.

    Stephen Ching

    School of Economics & Finance, University of Hong Kong

  • Moulin identifies common principles in discussions of social dilemmas across a wide range of problems—taxation, bargaining, voting—and shows how these principles lead to specific solutions. It is historically integrated as well, identifying common themes that range from Aristotle and the Talmud on one hand, to modern thinkers such as Arrow, Aumann, Harsanyi, Nash and Shapley on the other. This is an excellent introduction to distributive justice, social choice, bargaining, fair division and related subjects, but those already working in these fields can also find the broad overview here, wonderfully unfolded.

    Ehud Kalai

    James J. O'Connor Distinguished Professor of Decision and Game Sciences, Northwestern University