Some remarks on the ranking of infinite utility streams

A long tradition in welfare economics and moral philosophy, dating back at least to Sidgwick(1907) is the idea that all generations must be treated alike. Perhaps, the most forceful assertion of this idea comes from Ramsey (1928) who declared that any argument for preferring one generation over another must come “merely from the weakness of the imagination”. The “equal treatment of all generations” or the intergenerational equity principle has been formalised in the subsequent literature as the axiom of Anonymity, which requires that two infinite utility streams be judged indifferent to one another if one can be obtained from the other through a permutation of utilities of a finite number of generations. Since it also seems “natural” to require that any social evaluation of infinite utility streams respond positively to an increase in the utility of any generation, the Pareto Axiom is also desirable. Unfortunately, Diamond(1965) showed that there is no social welfare function satisfying these axioms along with a continuity axiom. In a more recent paper, Basu and Mitra( 2003) prove a more general result by showing that the continuity axiom is superfluous