M. Carmen Sánchez

Rationality of bargaining solutions

We analyze the rationality of two person bargaining solutions by considering conditions which are weaker than those used by Peters and Wakker (1991) or Bossert (1994). As a particular consequence of their results, the rationality of the Nash solution is obtained, although they can not be applied to other well known bargaining solutions. The aim of this paper is, on the one hand, lo prove that a choice function defined on the usual bargaining domain which satisfies Independence of Irrelevant Alternatives, Weak Pareto Optimality and Pareto Continuity is also rationalized by a preorder (reflexive, complete and transitive binary relation). Moreover, the representability of this relation is analyzed. These results can be applied, in particular, lo the Nash solution and moreover to the egalitarian (Kalai, 1977), monotone path solutions and their lexicographic extensions. On the other hand, and by substituting Pareto Continuity for Monotonicity assumptions, rationality IS al so analyzed. As a consequence, a result along the same lines as Bosserts (1994) is obtained.

Non-binary choice functions on non-compact sets

Abstract We provide sufficient conditions to ensure the non-emptiness of non-binary choice functions on a family of subsets larger than compact sets. This result generalizes Nehrings one [Nehring, 1996, Economics Letters, 50, 337–340] and, therefore, the Bergstrom–Walker theorem.

Rational choice on non-finite sets by means of expansion-contraction axioms

The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartzs results (1976), stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented.The rationalization of a choice function, in terms of assumptions that involve expansion or contraction properties of the feasible set, over non-finite sets is analyzed. Schwartzs results (1976), stated in the finite case, are extended to this more general framework. Moreover, a characterization result when continuity conditions are imposed on the choice function, as well as on the binary relation that rationalizes it, is presented.

An oligarchy theorem in fixed agenda without Pareto conditions

Abstract We prove the existence of oligarchies and individuals with different degrees of veto power in the context of fixed agenda social choice correspondences by dropping Pareto Optimality assumptions and by imposing only Weak Independence.

Numerical representation of choice functions

In the social sciences, the most common description of individual choice consistsof assuming that the agent has an a priori ordering, or a ranking over the differentalternatives, that is, the agent knows his preference relation. Then, rational behaviorrequires choosing the best elements, according to this criterion, in every feasibleset presented for choice (i.e., to choose the maximal elements).A different approach is given by removing the assumption that the agent knowsa priori his preference relation. In this case, the way of analyzing the rationality ofthe choice function consists of observing the different choices individuals make whendifferent subsets of alternatives are presented for choice, and comparing them. Thus,rationality is based on the analysis of some coherent properties between the differentchoices individuals make when the feasible set changes.

A New Multidimensional Measurement of Educational Poverty. An Application to PISA 2012

The consequences that educational underperforming has on both individuals and the society as a whole lead policy makers and planners to focus on how to measure properly the extent of educational poverty. The main aim of this paper is to propose a multidimensional adjusted poverty index (α-MAPI) by considering explicitly not only the individual deprivations, but also the non-deprivation attributes of the poor. It permits to set a precise valuation on school poverty. We apply α-MAPI to the measurement of educational poverty in the OECD countries by using data from PISA 2012 report.

Revealed preference axioms for continuous rational choice

Abstract In this paper, we analyze the relationship between the upper hemicontinuity of the choice function and the continuity of the revealed preference which rationalizes this choice function. Moreover, we obtain that, under standard conditions, it is possible to express this choice function as the set of alternatives maximizing a real valued function.