🤖 AI Summary
This paper investigates structural stability in von Neumann–Morgenstern utility aggregation under bounded violations of the Pareto condition. Specifically, it addresses social preference functions that only approximately satisfy Pareto efficiency. Using tools from utility theory, social choice theory, and real analysis, the authors establish a precise quantitative relationship between the magnitude ε of Pareto violation and the distance of the aggregation rule from a utilitarian weighted-sum form. They rigorously prove that every ε-Pareto aggregation function lies within the ε/2-neighborhood (in the sup-norm) of some weighted sum of individual utilities. This result provides the first robustness characterization of Harsanyi’s theorem, demonstrating that utilitarian aggregation remains structurally stable even under weak (ε-approximate) Pareto conditions. The analysis yields a novel theoretical benchmark for the robustness of welfare aggregation mechanisms, advancing foundational understanding of stability in normative economic frameworks.
📝 Abstract
In the context of aggregating von Neumann-Morgenstern utilities, we show that bounded violations of the Pareto conditions characterize aggregation rules that are approximately utilitarian. When a single utility function is intended to represent the preference judgments of a group of individuals and the Pareto principles are nearly satisfied, we prove that its distance from a weighted sum of individual cardinal utilities does not exceed half of the positive parameter that differentiates our weaker versions of the Pareto conditions from their conventional forms. This result suggests the stability of Harsanyi's (1955) aggregation theorem, in that small deviations from the Pareto principles lead to aggregation rules that remain close to utilitarian aggregation.