Fairness and Envy

Abstract

Standard neoclassical economic analysis is typically concerned with individual utility maximization. In this paper we shall consider a problem of constrained social welfare maximization. Our criterion of social welfare is and we shall discuss how this may be maximized by a move from an initial allocation to a final fairer allocation, subject to the constraint that no one be made worse off by the move. We think the goal of fairness maximization characterizes, albeit in a simplistic way, the goals pursued by enlightened governments in their redistributional policies. We shall also discuss a concept of complete fairness and illustrate some of its weaknesses. The fairness problem is ancient and dates back at least to classical Greece. It has been treated recently by mathematicians who typically are concerned with the existence of a of a nonuniform object among n persons; that is, a division with the property that each party thinks he is getting at least t/nth of the value of the object. (See, for example, Lester Dubins and Edwin Spanier, Harold Kuhn, and Hugo Steinhaus.) This is not the approach we will take, since we will assume a world of homogeneous infinitely divisible goods in which the mathematical fair division problem becomes trivial. The concept of fairness has also been treated extensively by philosophers. The most recent philosophical approach is that of John Rawls, who argues at length for a social contract theory of justice: a society which maximizes the welfare of its worst off members is most just and that is the sort of society people will, from an initial position of ignorance about their endowments and interests, contract to enter. Rawls' approach has been extended to a theory of taxation by Edmund Phelps. Again, Rawlsian fairness, or justice, is not the fairness we are interested in; we do not assume a precontractual state of ignorance, we do assume that knowledge of wealth and tastes is given. In fact, knowledge about one's own and others' bundles of goods is crucial in our discussion. What then is our notion of fairness? It is fairness in the sense of non-envy. A completely fair social state is one in which no citizen would prefer what another has to what he himself has; a relatively fair social state is one in which few citizens would prefer what others have to what they themselves have; a totally unfair state is one in which every citizen finds his position to be inferior to that of everyone else. This concept of fairness is appealing because it only depends, like other economic concepts, on individual tastes and endowments. Fairness in the non-envy sense has been discussed in several recent papers by economists. Serge Christophe Kolm considers allocative fairness, and shows that there exist allocations which are both completely fair and efficient.' David Schmeidler and Karl Vind define fair trades as