Q-anonymous social welfare relations on infinite utility streams

This paper studies a class of social welfare relations (SWRs) on the set of infinite utility streams. In particular, we examine the SWRs satisfying Q-Anonymity, an impartiality axiom stronger than Finite Anonymity, as well as Strong Pareto and a certain equity axiom. First, we characterize the extension of the generalized Lorenz SWR by combining Q-Anonymity with Strong Pareto and Pigou-Dalton Equity. Second, we replace Pigou-Dalton Equity with Hammond Equity for characterizing the extended leximin SWR. Third, we give an alternative characterization of the extended utilitarian SWR by substituting Incremental Equity for Pigou-Dalton Equity.Q-Anonymity, Intergenerational equity, Generalized Lorenz criterion, Leximin principle, Utilitarianism, Simplified criterion

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

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

Q-anonymous social welfare relations on infinite utility streams

Revised version of No.41: Concluding remarks are slightly changed

On the extensions of the infinite-horizon leximin and the overtaking criteria

Revised version of No.36: The earlier version of this manuscript was entitled "Q-Anonymity and preference continuity." Main results of the earlier draft are restated in a different form

Generalized time-invariant overtaking

We present a new version of the overtaking criterion, which we call generalized time-invariant overtaking. The generalized time-invariant overtaking criterion (on the space of infinite utility streams) is defined by extending proliferating sequences of complete and transitive binary relations defined on finite dimensional spaces. The paper presents a general approach that can be specialized to at least two, extensively researched examples, the utilitarian and the leximin orderings on a finite dimensional Euclidean spaceintergenerationa justice; utilitarianism, leximin

Generalized time-invariant overtaking

We present a new version of the overtaking criterion, which we call generalized time-invariant overtaking. The generalized time-invariant overtaking criterion (on the space of infinite utility streams) is defined by extending proliferating sequences of complete and transitive binary relations defined on finite dimensional spaces. The paper presents a general approach that can be specialized to at least two, extensively researched examples, the utilitarian and the leximin orderings on a finite dimensional Euclidean space.intergenerational justice, utilitarianism, leximin

Generalized time-invariant overtaking

We present a new version of the overtaking criterion, which we call generalized time invariant overtaking. The generalized time-invariant overtaking criterion (on the space of infinite utility streams) is defined by extending proliferating sequences of complete and transitive binary relations defined on finite dimensional spaces. The paper presents a general approach that can be specialized to at least two, extensively researched examples, the utilitarian and the leximin orderings on a finite dimensional Euclidean space.intergenerational justice, utilitarianism, leximin.

Should we discount the welfare of future generations? : Ramsey and Suppes versus Koopmans and Arrow

Ramsey famously pronounced that discounting “future enjoyments” would be ethically indefensible. Suppes enunciated an equity criterion implying that all individuals’ welfare should be treated equally. By contrast, Arrow (1999a, b) accepted, perhaps rather reluctantly, the logical force of Koopmans’ argument that no satisfactory preference ordering on a sufficiently unrestricted domain of infinite utility streams satisfies equal treatment. In this paper, we first derive an equitable utilitarian objective based on a version of the Vickrey–Harsanyi original position, extended to allow a variable and uncertain population with no finite bound. Following the work of Chichilnisky and others on sustainability, slightly weakening the conditions of Koopmans and co-authors allows intergenerational equity to be satisfied. In fact, assuming that the expected total number of individuals who ever live is finite, and that each individual’s utility is bounded both above and below, there is a coherent equitable objective based on expected total utility. Moreover, it implies the “extinction discounting rule” advocated by, inter alia, the Stern Review on climate change

The Possibility of Ordering Infinite Utility Streams

This paper revisits Diamond’s classical impossibility result regarding the ordering of infinite utility streams. We show that if no representability condition is imposed, there do exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams with attractive additional properties. We extend a possibility theorem due to Svensson to a characterization theorem and we provide characterizations of all strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. In addition, infinite horizon extensions of leximin and of utilitarianism are characterized by adding an equity preference axiom and finite translation-scale measurability, respectively, to strong Pareto and finite anonymity