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A simple hypergraph H with vertex set X and edge set 𝐄 is representable by Von Neumann-Morgenstern (VNM)-stable sets - or VNM - if there exists an irreflexive simple digraph D with vertex set X such that each edge of H is a VNM-stable set of D. It is shown that a simple hypergraph H is VNM if and only if each edge of H is a maximal clique of the conjugation graph of H. A related algorithm that identifies finite VNM hypergraphs is also provided.

When agents face incomplete information and their knowledge about the objects of choice is vague and imprecise, they tend to consider fewer choices and to process a smaller portion of the available information regarding their choices. This phenomenon is well-known as choice overload and is strictly related to the existence of a considerable amount of option-pairs that are not easily comparable. Thus, we use a finite partially-ordered set (poset) to model the subset of easily-comparable pairs within a set of options/items. The height ranking, a new ranking rule for menus, namely subposets of a finite poset, is then introduced and characterized. The height ranking rule ranks subsets of options in terms of the size of the longest chain that they include and is therefore meant to assess menus of available options in terms of the maximum number of distinct and easily-comparable alternative options that they offer.

A parameterized characterization of height-based total extensions of principal filtral opportunity rankings is provided and shown to include, as a special case, a version of the well-known Pattanaik-Xu characterization of the cardinality-based ranking.

Majority judgment as recently formulated and advocated by Balinski and Laraki in their influential monograph (Majority Judgment (2010)) is a method to aggregate profiles of judgments which are expressed in a common language consisting of a linearly ordered, and typically bounded, set of grades. It is shown that majority judgment thus defined is strategy-proof but not coalitionally strategy-proof on a very comprehensive class of rich single peaked preference domains. The proof relies on the key observation that a common bounded linear order of grades makes the set of gradings a product of bounded chains, which is a special instance of a bounded distributive lattice. Relying on the foregoing result, this paper also provides a simple characterization of majority judgment with an odd number of agents by anonymity, bi-idempotence and strategy-proofness on rich single peaked domains.

The di¤erent options people select from a set of non-rival alternatives are compared in terms of singularity. A criterion for ranking these choices on the basis of the number of other choices from which they di¤er is introduced and characterized. An axiomatic characterization of the ranking of choice pro…les based on the aggregation of the singularities of the chosen alternatives is also provided. JEL Classi…cation : D63 Keywords : Diversity, Freedom of choice, Orderings, Choice pro…les. \"The prosp ects of freedom in the contem p orary world m ay well lie in the recognition of the plurality of our identities, where p ersonal identity must b e understo o d as an extension of one's own choice of b eing som eone or doing som ething\" (A. K. Sen (2006))

It is shown that, under a very comprehensive notion of single peakedness, an aggregation rule on a bounded distributive lattice is strategy-proof on any rich domain of single peaked total preorders if and only if it admits one of three distinct and mutually equivalent representations by lattice-polynomials, namely whenever it can be represented as a generalized weak consensus rule, a generalized weak sponsorship rule, or an iterated median rule. The equivalence of individual and coalitional strategy-proofness that is known to hold for single peaked domains in bounded linearly ordered sets and in finite trees typically fails in such an extended setting. A related impossibility result concerning non-trivial anonymous and coalitionally strategy-proof aggregation rules is also obtained.

We study multidimensional inequality on integers. In such a setting, a Lorenz-like preorder and a suitably adapted version of the Muirhead-Pigou-Dalton transfers are defined, and a counterpart of some classic results on inequality measurement is established in this multivariate setting.

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 for the scientific output of authors which disallow endogenous reputation effects, including the Durfee- or h-number, the publication number and the citation number.

The lifetime incidence of deep vein thrombosis (DVT) is approximately 0.1% in general population and even more uncommon in subjects below 40 years of age. Thrombosis of the inferior ve cava (IVC) is an exceptiolly rare clinical condition, with etiological factors similar to lower limb DVT. We present a case of post-traumatic chronic obstruction of the IVC in 41 years-old man, caused by a prolonged squatted position, while he was working as a bricklayer. We visited the patient fifteen years after the onset of the first clinical setting showing a severe post thrombotic syndrome, as a consequence of the already diagnosticated thrombosis, involving predomintly the right inferior leg. Thrombophilia screening tests showed patient to be a heterozygous carrier of methylenetetrahydrofolate reductase (MTHFR) gene mutation. Computed tomography (CT) scan confirmed the thrombotic obstruction of the infrahepatic IVC, both common iliac veins, right exterl and interl iliac veins, with multiple collateral pathways. Because of thrombosis extension, inherited prothrombotic condition and the young age of the patient, we decided to continue life-long oral anticoagulant therapy.

It is argued that if a finite partially ordered population is given, and incomparability is taken as the relevant type of dissimilarity, then diversity comparisons between subpopulations may be conveniently based on widths namely on the maximum number of pairwise incomparable units they include. We introduce two width-based rankings. The first one is the plain width-ranking of subposets as induced by width computation. The second one is the undominated width-ranking of subposets namely the ranking induced by the sizes of undominated subposets. Simple axiomatic characterizations of the foregoing rankings are provided.