It is shown that a social choice rule f : X^N ? X as defined on a bounded distributive lattice (X, ) is strategy-proof on the set of all profiles of unimodal total preorders on X if and only if it can be represented as an iterated median of projections and constants. The equivalence of individual...

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...

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 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...

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,...

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.

We introduce and characterize axiomatically a diversity criterion, capturing individual dissimilarity as `revealed' by the different best-choices that members of a society select from a set of opportunities. Diversity ordering is induced by a class of frequency-based evaluation functions, the...

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...

We establish the multidimensional couterpart of the fundamental theorem on the inequality measurement due to Hardy, Littlewood and Polya (HLP, 1934) for the case of household with different weights

It is shown that the median voter theorem for committee-decisions holds over a full unimodal preference domain whenever (i) the underlying median interval space satisfi?es interval antiexchange and (ii) unimodality is defi?ned with respect to the incidence-geometry of the relevant outcome space...