- CHOICE FUNCTIONS: RATIONALITY RE-EXAMINED.

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 analyze solutions to the problem of choosing from a tournament (where maximalelements do not necessarily exist). So, in our opinion the notion of rationality must be discussed,not only in the traditional sense of external conditions (Sen, 1993) but in terms of the internalinformation provided by the binary relation.Rationality; Choice Functions; Maximal Elements.

CONDORCET CHOICE FUNCTIONS AND MAXIMAL ELEMENTS

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 weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Moreover, we compare these choice functions with those that already exist in the literature.choice functions, tournaments, maximal elements.

Choosing among maximals

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 elements, or we can choose among them according to the behaviour of these maximalelements. In order to illustrate this, let´s imagine a preference relation >=, defined on a finite setA={x1,x2,...,xn}, such that x1 is indifferent to each alternative and x2 is strictly preferred to everyxi,i >=3. Both x1 and x2 are maximal elements, but we can say that x2 is a better maximalthan x1. In this paper we define selections of the set of maximal elements of a preference relationby choosing the better ones among them.Binary relation, maximal elements

Numerical representation for lower quasi-continuous preferences

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 guarantees the existence of maxima of such a function, and therefore the existence of maximal elements of the binary relation.Numerical representation, maximal elements, lower quasi-continuous preferences

- FIXED AGENDA SOCIAL CHOICE CORRESPONDENCES

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, oligarchies or individuals with veto power can be proven ([7] and [10]); but no information about the social choice set is obtained. We now establish a relationship between the social choice set and the individual maximal sets which explicitly describes a fixed agenda social choice correspondence that satisfies theses rationality assumptions. Some of the results in [2] about the explicit representation of social decision functions are then translated and reinterpreted in the fixed agenda framework.fixed agenda, choice correspondences, explicit representation

VETO IN FIXED AGENDA SOCIAL CHOICE CORRESPONDENCES

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 neutrality). This enables us to translate known sesults of existence of individuals with veto from the social decision functions context into the fixed agenda framework, such as t.hose of Blau anad Deb (1977), Blair and Pollak (1982),. . .Veto; Fixed Agenda SSC; Acyclic SDF

ADJUSTING CORRELATION MATRICES

The article proposes a new algorithm for adjusting correlation matrices and for comparison with Finger's algorithm, which is used to compute Value-at-Risk in RiskMetrics for stress test scenarios. The solution proposed by the new methodology is always better than Finger's approach in the sense that it alters as little as possible those correlations that we do not wish to alter but they change in order to obtain a consistent Finger correlation matrix.Stochastic, Volatility, Skewness, Kurtosis, Pricing.

Maximal elements of non necessarily acyclic binary relations

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 original one. The result covers the case whereby the relation is acyclic.

A MECHANISM FOR META-BARGAINING PROBLEMS

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 kind of conflict. Furthermore, we characterize it axiomatically.Mechanism; Meta-Bargaining Problems.

A demand function for pseudotransitive preferences

This paper deals with the existence and properties of the demand correspondence when agents' preferences are pseudotransitive. It is shown that a consumption plan belongs to the demand mapping if and only if it is a maximizer of a real-valued weak utility function. Further properties, as hemicontinuity and convex-valuedness of the demand mapping, are also analyzed.Pseudotransitive preferences, demand function, weak utility function