Arlegi Pérez, Ricardo
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Arlegi Pérez
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Ricardo
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Economía
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INARBE. Institute for Advanced Research in Business and Economics
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Publication Open Access Freedom of choice: the leximax criterion in the infinite case(2006) Arlegi Pérez, Ricardo; Besada, M.; Nieto Vázquez, Jorge; Vázquez, C.; Economía; EkonomiaMany recent works have investigated the problem of extending a preference over a set of alternatives to its power set, in an attempt to provide a formal representation of the notion of freedom of choice. In general, results are limited to the finite case, which excludes, for instance, the case of economic environments. This paper deals with the possibility of extending those results to the context where the basic set of alternatives is the n-dimensional Euclidean space. We present an extension of the leximax criterion described by Bossert, Pattanaik and Xu (1994) to this more general framework.Publication Open Access On the equivalence of the two existing extensions of the leximax criterion to the infinite case(2006) Arlegi Pérez, Ricardo; Ballester Oyarzun, Miguel Ángel; Besada, M.; Miguel Velasco, Juan Ramón de; Nieto Vázquez, Jorge; Vázquez, C.; Economía; EkonomiaUsing a common framework, we consider the two existing extensions of the leximax criterion to infinite environments (Arlegi et al. (2005) and Ballester and De Miguel (2003), and show that, though the respective definitions of the rules and their axiomatic characterizations appear to differ considerably, they actually propose the same extension of the leximax criterion to the infinite case.Publication Open Access Uncertainty with ordinal likelihood information(Springer-Verlag, 2013) Alcalde Unzu, Jorge; Arlegi Pérez, Ricardo; Ballester Oyarzun, Miguel Ángel; Economía; EkonomiaWe present a model that is closely related to the so-called models of choice under complete uncertainty, in which the agent has no information about the probability of the outcomes. There are two approaches within the said models: the state space-based approach, which takes into account the possible states of nature and the correspondence between states and outcomes; and the set-based approach, which ignores such information, and solves certain difficulties arising from the state space-based approach. Kelsey (Int Econ Rev 34:297–308, 1993) incorporates into a state space-based framework the assumption that the agent has ordinal information about the likelihood of the states. This paper incorporates this same assumption into a set-based framework, thus filling a theoretical gap in the literature. Compared to the set-based models of choice under complete uncertainty we introduce the information about the ordinal likelihood of the outcomes while, compared to Kelsey’s approach, we incorporate the advantages of describing uncertainty environments from the set-based perspective. We present an axiomatic study that includes adaptations of some of the axioms found in the related literature and we characterize some rules featuring different combinations of information about the ordinal likelihood of the outcomes and information about their desirability.