A Social Welfare Function Satisfying Anonymity and Almost Weak Pareto

2026-10-04

AI Summary

This study addresses whether social welfare functions (SWFs) over infinite utility streams can simultaneously satisfy anonymity and the approximate weak Pareto property. By integrating order isomorphism theory, set-theoretic analysis, and an axiomatic social choice framework, it precisely characterizes the one-period utility domains that permit the existence of such SWFs. The central contribution demonstrates that the existence conditions for SWFs under the approximate weak Pareto constraint coincide exactly with those in the classical weak Pareto setting. Building on this equivalence, the authors construct SWFs that are both invariant and stationary. Ultimately, this work establishes sharp boundaries for the existence of SWFs, providing a rigorous theoretical foundation for economic decision-making over infinite time horizons.

Abstract

We study the existence of real-valued social welfare functions (SWFs) on the set of infinite utility streams that satisfy anonymity and almost weak Pareto. We characterize the domains of one-period utilities, \(Y\subset \mathbb{R}\), for which such SWFs exist. We show that an SWF satisfying these two axioms exists if and only if \(Y\) contains no subset that is order-isomorphic to the set of negative and positive integers. Thus, the restrictions on \(Y\) required for the existence of an SWF satisfying anonymity and almost weak Pareto coincide with those required for an SWF satisfying anonymity and weak Pareto. Moreover, the SWF we construct is invariant under arbitrary permutations and satisfies stationarity, two properties that are particularly useful for decision making in infinite-horizon economies.

Problem

• social welfare function
• infinite utility streams
• anonymity
• almost weak Pareto

Innovation

• Social Welfare Function
• Anonymity
• Almost Weak Pareto
• Infinite Utility Streams
• Stationarity