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 a distribution problem, and specifically in bankruptcy issues, the Proportional (P) and theEgalitarian (EA) divisions are two of the most popular ways to resolve the conflict. TheConstrained Equal Awards rule (CEA) is introduced in bankruptcy literature to ensure that noagent receives more...

Consider a two-person bargaining problem, where both agents have a particular notion of what would be a just solution outcome. In case their opinions differ, a procedure which leads to a compromise between t,he two different views is needed. In this paper we propose a mechanism to solve this...

In this paper we analyze the explicit representation of fixed agenda social choice correspondence under different rationality assumptions (independence, neutrality, monotonicity, ...). It is well know in the literature that, under some of theses assumptions, the existence of dictators,...

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...

On analyzing the problem that arises whenever the set of maximal elements is large, and aselection is then required (see Peris and Subiza, 1998), we realize that logical ways of selectingamong maximals violate the classical notion and axioms of rationality. We arrive at the sameconclusion if we...

In this paper we analyze the existence of three different kinds of continuous numerical representations for binary relations by using a finite measure defined on the space of alternatives. Each one of these kinds of representation is suitable for a different class of binary relations. Thus we...

In this paper we analyze the relationship between acyclic social decision functions and fixed agenda social choice correspondences which verify some rationality conditions (such as Pareto, independence, monotonicity or neutrality). This enables us to translate known sesults of monlotonicity or...