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....

The concept lattice of a coalitional game form is introduced and advocated as a structural classificatory tool. The basic properties of such lattices are studied. Sufficient concept-latticial properties for convexity of the underlying coalitional game form are identified. Spectral issues...

It is shown that concept lattices can be attached in a natural way to any voting protocol. The concept lattices of some voting protocols that are solvable with respect to some prominnent solution concepts and outcome-efficient are studied: it is proved that they typically amount to chains

This paper studies Collective Identification Procedures in a finite lattice when the standard Independence axiom is dropped and replaced with an Independent Qualified Certification requirement

It is argued that if the population of options is a finite poset, diversity comparisons may be conveniently based on widths i.e. on the respective maximum numbers of pairwise incomparable options included in the relevant subposets. The width-ranking and the undominated width-ranking are...

The choice functions that are consistent with selections of VNM-stable sets of an underlying revealed dominance digraph are characterized both under VNM-perfection of the latter and in the general case.

We introduce the dominance dimension principle and the parameterized family of criteria for the assessment of publication/citation profiles it generates. We show that by a suitable choice of parameters dominance dimension may specialize to the most widely known and used of those impact scores...

A clutter on a set X is a simple hypergraph with pairwise not-comparable hyperedges, hence in particular any set of Von Neumann-Morgenstern (VNM) -stable sets of an irreflexive simple digraph is a clutter. A clutter (X,E) is representable by VNM-stable sets or VNM if there exists an irreflexive...

Characterizations of the choice functions that select the cores or the externally stable cores induced by an underlying revealed dominance digraph are provided. Relying on such characterizations, the basic order-theoretic structure of the corresponding sets of revealed cores is also analyzed