An Alternative Characterization of Paretian Generalized Median Social Welfare Functions

Abstract

This article considers social welfare functions for which the set of alternatives is the two-dimensional nonnegative orthant and for which individuals can have any strictly monotonic, linear preference ordering. A Paretian generalized median social welfare function is defined by augmenting the n individuals in society with n — 1 phantom individuals each of whom has a fixed weakly monotonic, linear ordering and, for each profile of preferences, choosing the social preference to be the linear preference with slope equal to the median of all 2n — 1 individual slopes. Bossert and Weymark (1992) showed that the class of Paretian generalized median social welfare functions is characterized by anonymity, weak Pareto, and binary independence of irrelevant alternatives if the social preferences are restricted to be strictly monotonic, linear orderings. In this article we show that the monotonicity and linearity assumptions on social preferences can be weakened to continuity if we add an intra-profile neutrality condition.