On Ordered Weighted Averaging Social Optima

Abstract

In this paper, we look at the classical problem of aggregating individual utilities and study social orderings which are based on the concept of Ordered Weighted Averaging Aggregation Operator. In these social orderings, called Ordered Weighted Averaging Social Welfare Functions, weights are assigned a priori to the positions in the social ranking and, for every possible alternative, the total welfare is calculated as a weighted sum in which the weight corresponding to the kth position multiplies the utility in the kth position. In the α-Ordered Weighted Averaging Social Welfare Function, the utility in the kth position is the kth smallest value assumed by the utility functions, whereas in the β-Ordered Weighted Averaging Social Welfare Function it is the utility of the kth poorest individual. We emphasize the differences between the two concepts, analyze the continuity issue, and provide results on the existence of maximum points.