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>

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...