On the Possibility of Continuous, Paretian and Egalitarian Evaluation of Infinite Utility Streams

There exists a utilitarian tradition à 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.

Characterizing the Nash social welfare relation for infinite utility streams: a note

This note provides an axiomatic analysis of a social welfare ordering over infinite utility streams. We offer two characterizations of an infinite-horizon version of the Nash criterion.Infinite generations, intergenerational equity, the Nash criterion

The impossibility of social evaluations of infinite streams with strict inequality aversion

[EN]We are concerned with the problem of aggregating infinite utility streams and the possible adoption of consequentialist equity principles. We find a virtually universal incompatibility between the Basu–Mitra approach (that advocates for social welfare functions and renounces continuity assumptions) and postulates that capture various forms of strict preference for a reduction in inequality like the Strong Equity Principle, the Pigou–Dalton Transfer principle, or Altruistic Equity. We also prove that the Hara–Shinotsuka–Suzumura–Xu impossibility for semicontinuous social welfare relations remains under the latter distributional postulate

Impossibilities of Paretian Social Welfare Functions for Infinite Utility Streams with Distributive Equity

This paper examines the logical relationship between distributive equity and efficiency in aggregating infinite utility streams. Our main results show that there exist social welfare functions which satisfy the axioms of Pigou-Dalton Transfer Principle and a weak version of efficiency, but there exists no social welfare function which satisfies all of the distributive equity requirements and Weak Pareto Principle at the same time. Thus, we can prove that no Paretian ranking can satisfy the numerical representability and all of the distributive equity properties in the setting of intertemporal social choice.

Liberal approaches to ranking infinite utility streams: When can we avoid interference?

[EN]In this work we analyse social welfare relations on sets of finite and infinite utility streams that satisfy various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that verify non-interference axioms together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if the weak Pareto principle is imposed. We first prove that this impossibility result vanishes when we extend the horizon to infinity. Then we investigate a related problem: namely, the possibility of combining \standard" semicontinuity with eficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between relaxed forms of continuity and non- interference principles, both under ordinal and cardinal views of the problem

Evaluations of inifinite utility streams: Pareto efficient and egalitarian axiomatics

[EN]This investigation focuses on the aggregation of infinite utility streams by social welfare functions. We analyze the possibility of combining Pareto-efficiency and Hammond Equity principles when the feasible utilities for each generation are [0, 1] and the natural numbers. In the latter case, the Hammond Equity ethics can be combined with non-trivial specifications of the Pareto postulate, even through anonymous social welfare functions. As a consequence, any evaluation of infinite utility streams that verifies a mild specification of the Paretian axiom must exert some interference on the affairs of particular generations

The compromise efficiency vs. egalitarianism among generations with an infinite horizon

This paper concerns ethical aggregation of infinite utility streams. Position i is typically interpreted as the endowment of generation i. We analyze the broad question: In order for the social welfare to increase, the interest of how many generations can be respected if we intend to be "ethical"? Here "ethical" refers to verifying adequate equity axioms, and case-studies cover: extensions of restricted non-substitution; or Hammond Equity-related principles; together with the usual Anonymity axiom