There exists a utilitarian traditionà 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.

No abstract

There exists a utilitarian traditionà la Sidgwick of treating equal generations equally in the form of anonymity. Diamond showed that no social evaluation ordering over infinite utility streams satisfying the Pareto principle, Sidgwick's equity principle, and the axiom of continuity exists. We introduce two versions of egalitarianism in the spirit of the Pigou-Dalton transfer principle and the Lorenz domination principle, and examine their compatibility with the weak Pareto principle in the presence of a semi-continuity axiom. The social evaluation relation is not assumed to be either complete or transitive, yet Diamond's impossibility strenuously resurfaces.

We introduce several distinct notions of equity as no-envy into the overlapping generations economy formulated by Samuelson (1958). No-Envy in Overlapping Consumptions requires that for each time period, no person should prefer the bundle of any other person who lives in the same period to his/her own. No-Envy in Lifetime Consumptions states that no person should prefer the lifetime consumption plan of any other person to his/her own. Equity in Lifetime Rate of Return requires that the lifetime rate of return (Cass and Yaari,1966) be equal for all persons. For each of the three notions, we characterize allocations satisfying it, and clarify logical relations among these conditions. We also examine existence of a stationary allocation that attains maximal utility under No-Envy in Lifetime Consumptions.