Multidimensional inequality comparisons: A compensation perspective

The aim of the paper is to provide criterions based on sound ethical grounds for inequality and welfare comparisons in a multi-dimensioned setting. We provide a unified treatment of multi-dimensional egalitarianism and of welfare analysis with needs using a compensation principle and encompassing the case of continuous and discrete distributions. Among the attributes of the individual utility, at least one, (in most cases the current period income) can be used to compensate attributes like past-income, income of the past generation, health, education, needs due to family size. Post-Rawlsian distributive justice (Dworkin, Roemer) argues for compensating an attribute, provided that persons should not be responsible for it. The main theorem exhibits two necessary and sufficient second degree stochastic dominance conditions for the comparison of bivariate distributions. In the case of a discrete compensated variable, the distributions of the compensating variable have to satisfy a condition which degenerates to the Sequential Generalized Lorenz test in case of identical marginal distributions of the compensating variable. Moreover, the distributions of the compensated variable must satisfy the Generalized Lorenz test. Extensions to the case of a trivariate distribution are provided, where we single out three configurations, the full compensation the chain compensation and the single compensation.