Fair Division and Collective Welfare

The concept of fair division is as old as civil society itself. Aristotle's "equaltreatment of equals" was the first step toward a formal definition of distributive fairness. Theconcept 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 microeconomicthinking to distributive justice. Taking the modern axiomatic approach, it compares normativearguments of distributive justice and their relation to efficiency and collective welfare.The bookbegins with the epistemological status of the axiomatic approach and the four classic principles ofdistributive justice: compensation, reward, exogenous rights, and fitness. It then presents thesimple ideas of equal gains, equal losses, and proportional gains and losses. The book discussesthree cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximizethe sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It alsodiscusses the two main ordinal definitions of collective welfare: the majority relation and theBorda scoring method.The Shapley value is the single most important contribution of game theory todistributive justice. A formula to divide jointly produced costs or benefits fairly, it isespecially useful when the pattern of externalities renders useless the simple ideas of equality andproportionality. The book ends with two versatile methods for dividing commodities efficiently andfairly when only ordinal preferences matter: competitive equilibrium with equal incomes andegalitarian equivalence. The book contains a wealth of empirical examples and exercises.