Social Welfare Functions which preserve distances

The notion of keeping distances, introduced by N. Baigent in [2], avoids th e need to introduce topological concepts when defining Social Welfare Funct ions with requirements analogous to those established by Chichilnsky in [3] . In the following study we propose an extension of the results of Baigent, in a non topological framework, to a much broader class of metrics which e nables the case of infinite agents to be considered in a natural fashion.