Asymptotic properties of welfare relations

Abstract

We introduce and discuss notions of efficiency in the aggregation of infinite utility streams. For any utility streams x and y, our efficiency criteria roughly require this: If a utility stream x dominates another utility stream y and if the asymptotic density of the set of coordinates in favor of x is strictly positive, then x is socially preferred to y. As a robustness check of the proposed efficiency axioms we explore the consistency of the axioms with notions of equity. Our main results characterize one period utility domains, i.e., the set of utilities Y attainable by each generation, admitting a social welfare aggregator with the desired properties.

On social welfare orders satisfying anonymity and asymptotic density-one Pareto

“…Theorem 1 is a handy characterization result whose range of applicability may be appreciated by noting that part 1 of Proposition 4.4 in Petri (2019) obtains as an immediate corollary of our Theorem 1. In terms of the analytical techniques employed to prove Theorem 1, we mention, in passing, that the proof of the latter hinges on Lemma 1 below, which asserts that there does not exist any social welfare function satisfying ADP and AN if Y is the set of natural numbers.…”

I–Convergence of Arithmetical Functions

“…The notion of statistical convergence was introduced independently by Fast and Schoenberg in [1,2], and the notion of I-convergence introduced by Kostyrko et al in the paper [3] coresponds to the natural generalization of statistical convergence (see also [4] where I-convergence is defined by means of filterthe dual notion to ideal). These notions have been developed in several directions in [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and have been used in various parts of mathematics, in particular in Number Theory and Ergodic Theory, for example [15,[19][20][21][22][23][24][25][26][27][28] also in Economic Theory [29,30] and Political Science [31]. Many authors deal with average and normal order of the wellknown arithmetical functions (see [20,21,23,24,26,28,32,33] and the monograph [34] for basic properties of the well-known arithmetical functions).…”

On the Representation and Construction of Equitable Social Welfare Orders

“…In a pioneering paper, Ramsey (1928) observed that discounting one generation's utility relative to another's is "ethically indefensible", and something that "arises merely from the weakness of the imagination". Following in Ramsey's footsteps, Diamond (1965) introduced the concept of anonymity (as an axiom imposed on preferences over infinite utility streams) to formalize the principle of equitable preferences ("equal treatment" of present and future generations).…”

“…In the wake of Svensson's result, Fleurbaey and Michel (2003) conjectured that "there exists no explicit description (that is, avoiding the axiom of choice or similar contrivances) of an ordering which satisfies the Anonymity and Weak Pareto axioms". As shown by Lauwers (2010) and Zame (2007), it turns out that the axiom of choice is unavoidable for the existence of a social welfare order satisfying the anonymity and Pareto axioms. The proof of their result relies on the existence of non-Ramsey sets and non-measurable sets, respectively.…”