Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in...

In this paper a new numerical representation of preferences (by means of set-valued real functions) is proposed. Our representation extends the usual utility function (in case preferences are preorder-type) as well as the pairwise representation (in case preferences are interval-order type)....

This paper proposes a reform for school allocation procedures in order to help integration policies reach their objective. For this purpose, we suggest the use of a natural two-step mechanism. The (stable) first step is introduced as an adaptation of the deferred-acceptance algorithm designed by...

A new solution concept to monotonic cooperative games with nontransferable utility is introduced. This proposal, called the coalitional equal-loss solution, is based on the idea that players withing a coalition should have equal losses from a point of maximum expectations. The proposal...

A weaker than usual continuity condition for acyclic preferences is introduced. For preorders this condition turns out to be equivalent to lower continuity, but in general this is not true. By using this condition, a numerical representation which is upper semicontinuous is obtained. This fact...

Tournaments are complete and asymmetric binary relations. This type of binary relation rules out the possibility of ties or indifferences which are common in different contexts. In this work we generalize, from a normative point of view, some important tournaments solutions (top cycle, uncovered...

The existence of maximal elements for binary preference relations is analyzed without imposing transitivity or convexity conditions. From each preference relation a new acyclic relation is defined in such a way that some maximal elements of this new relation characterize maximal elements of the...

In this paper a numerical representation of preferences by means of subsets of the real line is proposed. This representation turns out to be natural for partial orderings. Some results on this representation, extending those for utility functions and pairwise representations, are provided for...

In this paper, it is shown that, under certain conditions on a preference relation defined on a set X, there exists a numerical representation by means of set-valued real functions. This kind of representation extends the usual utility function as well as the representation by means of two real...

In a choice situation, it is usually assumed that the agents select the maximal elements inaccordance with their preference relation. Nevertheless, there are situations in which a selectioninside this maximal set is needed. In such a situation we can select randomly some of thesemaximal...