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...