The Gini index and the Gini mean difference of a univariate distribution are extended to measure the disparity of a general d-variate distribution. We propose and investigate two approaches, one based on the distance of the distribution from itself, the other on the volume of a convex set in (d...

The paper presents an approach to the measurement of economic disparity in several commodities. We introduce a special view on the usual Lorenz curve and extend this view to the multivariate situation: Given a vector of shares of the total endowments in each commodity, the multivariate inverse...

We establish that the Pareto property is inconsistent with non-dictatorship for social choice rules defined on two-dimensional choice spaces. In addition, we consider applications of this result in higher dimensions. <p>We also establish the existence of Pareto rules with infinite populations, and...</p>

We consider an extension of the class of multi-utility hyper-relations, the class of semi-decent hyper-relations. A semi-decent hyper-relation satis…es monotonicity, stability with respect to contraction, and the union property. We analyze the class of semi-decent hyper-relations both...

We introduce a theory of marginal values and their core stability for cooperative games with transferable utility and arbitrary set systems representing the set of feasible coalitions. The theory is based on the notion of strictly nested sets in a set system. For each maximal strictly nested...

The distribution of d commodities among n individuals is described by an nþd row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The...

We introduce a new approach to showing existence of equilibrium in models of economies with unbounded short sales. Inspired by the pioneering works of Hart (1974) on asset market models, Grandmont (1977) on temporary economic equilibrium, and of Werner (1987) on general equilibrium exchange...

We consider an extension of the class of multi-utility hyper-relations, the class of semidecent hyper-relations. A semi-decent hyper-relation satisfies monotonicity, stability with respect to contraction, and the union property. We analyze the class of semi-decent hyper-relations both...

Even if its roots are much older, random sets theory has been considered as an academic area, part of stochastic geometry, since Matheron [7]. Random sets theory was first applied in some fields related to engineering sciences like geology, image analysis and expert systems (see Goutsias et al....