Infinite Population Utilitarian Criteria

We examine utilitarian criteria for ranking well-being distributions for infinitely many individuals. One possible interpretation of such distributions is that they represent intergenerational well-being distributions where the possibly different number of individuals are alive in each generation. Since there is no natural order for counting individuals and no natural isomorphism between individuals alive in different distributions, we examine strongly anonymous utilitarian criteria. We introduce four strongly anonymous utilitarian criteria, including the limit of rankdiscounting criterion, the strongly anonymous Cesàro summation criterion, and the strongly anonymous catching-up criterion. We clarify the relationship between them and present an axiomatic characterization of a class of evaluation criteria that includes two of them using sensitivity, independence, and continuity axioms.