Distributive justice and the Nash bargaining solution

Suppes-Sen dominance or SS-proofness (SSP) is a commonly accepted criterion of impartiality in distributive justice. Mariotti (Review of Economic Studies, 66, 733–741, 1999) characterized the Nash bargaining solution using Nash’s (Econometrica, 18, 155–162, 1950) scale invariance (SI) axiom and SSP. In this article, we introduce equity dominance (E-dominance). Using the intersection of SS-dominance and E-dominance requirements, we obtain a weaker version of SSP (WSSP). In addition, we consider α − SSP, where α measures the degree of minimum acceptable inequity aversion; α − SSP is weaker than weak Pareto optimality (WPO) when α = 1. We then show that it is still possible to characterize the Nash solution using WSSP and SI only or using α -SSP, SI, and individual rationality (IR) only for any \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha \in [0,1)}$$\end{document}. Using the union of SS-dominance and E-dominance requirements, we obtain a stronger version of SSP (SSSP). It turns out that there is no bargaining solution that satisfies SSSP and SI, but the Egalitarian solution turns out to be the unique solution satisfying SSSP.