Continuity and egalitarianism in the evaluation of infinite utility streams

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• There exists a utilitarian tradition à la Sidgwick of treating equal generations equally. Diamond showed that there exists no social evaluation ordering over infinite utility streams in the presence of the Pareto principle, the Sidgwick principle, and continuity. Instead of requiring the Sidgwick principle of procedural fairness, we focus on two principles of distributional egalitarianism along the line of the Pigou–Dalton transfer principle and the Lorenz domination principle, and show that there exists no social evaluation relation satisfying one of these egalitarian principles and the weakened continuity and rationality axioms even in the absence of the Pareto principle.This paper is a substantially revised version of our foregoing paper, “On the Possibility of Continuous, Paretian and Egalitarian Evaluation of Infinite Utility Streams,” which was based on our joint research conducted as a part of the Project on Intergenerational Equity under the auspices of the Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Thanks are due to Geir Asheim, Kaushik Basu, Walter Bossert, Hajime Hori, Tomoki Inoue, Mitsunori Noguchi and Koichi Tadenuma with whom we had several discussions on this and related issues. We are also grateful to the anonymous referees and the Associate Editor in charge of our earlier paper for their helpful comments and suggestions. Needless to say, no one other than ourselves should be held responsible for any remaining defect of this paper.

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