On Ordered Weighted Averaging Social Optima

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 (OWA) Aggregating Operator. In these social orderings, called OWA social welfare functions (swf), 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 k-th position multiplies the utility in the k-th position. In the –OWA swf, the utility in the k-th position is the k-th smallest value assumed by the utility functions, whereas, in the –OWA swf, it is the utility of the k-th poorest individual. We emphasize the differences between the two concepts, analyze the continuity issue and provide maximum points existence results.