A Social Welfare Function Satisfying Anonymity and Almost Weak Pareto
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.