On multidimensional inequality with variable distribution mean

We compare alternative populations of individuals, who differ for many characteristics besides income, in terms of inequality. In order to achieve our aim, we extend the notion of Generalized Lorenz Preorder to a context of multivariate distributions with different marginals. Finally, we show, by using convex analysis, that some conditions, relevant in the analysis of multidimensional inequality, are equivalent to the ordering we introducedMultidimensional Inequality, Generalized Lorenz Preordering, Price-majorization

Multivariate Differences Ordering

A multivariate dispersion ordering is introduced as a natural extension of a well-known univariate inequality criterion. A characterization of this new ordering is provided.

On Multidimensional Inequality in Partitions of Multisets

We study multidimensional inequality in partitions of finite multisets with thresholds. In such a setting, a Lorenz-like preorder, a family of functions preserving such a preorder, and a counterpart of the Pigou-Dalton transfers are defined, and a version of the celebrated Hardy-Littlewood-Pölya characterization results is provided.Multisets, majorization, Lorenz preorder, Hardy-Littlewood-Polya theorem, transfers

On the Volume-Ranking of Opportunity Sets in Economic Environments

The domain of polyconvex sets, i.e. finite unions of convex, compact, Euclidean sets, is large enough to encompass most of the opportunity sets typically encountered in economic environments, including non-linear or even non-convex budget sets, and opportunity sets arising from production sets. We provide a characterization of the volume-ranking as defined on the set of all polyconvex sets, relying on a valuation-based volume-characterization theorem due to Klain and Rota (1997).Opportunity sets, valuation, volume total preordering

Poverty Rankings of Opportunity Profiles

We address the problem of ranking distributions of opportunity sets in terms of poverty. In order to accomplish this task, we identify a suitable notion of `multidimensional poverty line', extend the most widely used income poverty criteria to opportunity profiles, and provide characterizations of a few poverty rankings that rely on such criteria.Poverty, opportunity sets, head-count, poverty-gap.

Poverty rankings of opportunity profiles

We address the problem of ranking distributions of opportunity sets in terms of poverty. In order to accomplish this task, we identify a suitable notion of ‘multidimensional poverty line’ and we characterize axiomatically several poverty rankings of opportunity profiles. Among them, the Head-Count and the Opportunity-Gap poverty rankings, which are the natural counterparts of the most widely used income poverty indices.Poverty, opportunity sets, head-count, poverty-gap.

Ordering, equity and non-expected utility theory

According to Chateauneuf (1996), we compare some inequality criteria. We investigate their properties and characteristics. Then, following the approach that links different levels of deprivation with alternative values of social welfare, we look for a functional that evaluates the well-being of individuals with respect to their relative position in the distribution. After having criticized the approach to evaluate the social welfare using the expected utility theory or the rank dependent one respectively under a descriptive and normative point of view, we introduce an additive subjective utility functional in order to search the behavioral foundations of an equity concerned decision-maker

A note on inequality criteria

The absolute differentials ordering (ADO) and the relative differentials ordering (RDO) have been introduced as suitable alternative inequality criteria to Lorenz ordering (LO). We provide two new alternative proofs that ADO and RDO are sub-orderings of LO. Furthermore, we point out some paradoxical situations , where these two different partial orderings fail to rank alternative income distributions

Essays on economic inquality

Le travail suivant étudie certains problématiques qui concernent l'inégalité économique. L'analyse est réalisée en utilisant des instruments analytiques, qui par la suite sont traduits sous le profil économique. Dans la première partie nous établissons une comparaison entre la distribution des revenus au moyen de certains critères statiques. Apres avoir mis en évidence le contenu normatif et positif des critères considérés, nous soulignerons les limites et, dans un deuxième temps, nous effectuerons une représentation avec des fonctions convexes dans la même direction que Schur. La deuxième partie s'attache à la construction d'indices de mesure des inégalités à partir des fonctions d'évaluation sociale du genre utilité non attendu. La dernière partie étend l'analyse des problèmes des inégalités économiques du cas unidimensionnel (le revenu) au cas multidimensionnel (c'est-à-dire à la situation dans laquelle les individus diffèrent pour plus d'une caractéristique : revenu, santé, niveau de vie, etc.). Dans cette distribution multi variés apparaît alors un nouvel ordre qui sera analysé et caractérisé dans le contexte axiomatique.Doctorat en sciences économiques (ECON 3)--UCL, 200