On Interpersonal Comparability and Social Welfare Orderings

Abstract

THE PRESENT PAPER adds some new results to the rapidly growing literature on social welfare judgements based on interpersonal utility comparisons.2 A. K. Sen [9] and J. Rawls [7] must be credited for stimulating interest in this essentially normative perspective on collective choice. Attention is centered on orderings which a planner wishes to define on the n-dimensional Euclidean space, interpreted as the utility space. These orderings are required to satisfy the strong Pareto principle and a symmetry or anonymity axiom. Two cases are studied. In the first case, the planner is allowed to compare utility levels interpersonally and prevented from comparing utility gains. Under this asumption, there must be what we call rank dictatorship. This term refers to a two-step comparison between utility vectors: first, the planner must rank utility levels from the lowest to the largest within each utility vector and secondly, in order to compare vectors, he must always endorse the strict preference of one particular rank. This rank which wins in every comparison is chosen exogeneously. Turning to the second case, we allow the planner to attach significance to statements of the form: for a given utility vector, individual i is better off than individual j; while no meaning can be given to statements of the form: for a given utility vector, i's utility gain over j is larger than h's utility gain over k, assuming the gains have the same sign and the two pairs of individuals do not overlap. So far there is no difference at all with case one. In the second case, however, we endow the planner with a finer discriminating power. He is now allowed to consider as meaningful interpersonal comparisons of utility gains of the following form: going from one particular utility vector to another, individual i gains more (or less) than individual j. In this case, there exists a set of nonnegative numbers, each of which is associated with a particular rank and which is such that any given utility vector is strictly preferred to any other by the planner whenever its weighted sum is strictly larger than the corresponding sum associated with the other vector. It should be clear that rank dictatorial orderings make up a subset of the set I just described. They can be obtained by assigning zero weight to all ranks but one.

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