Documentos de trabajo DE - ES Lan Gaiak

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Open Access
Equality of opportunities: cardinality-based criteria
(1998) Arlegi Pérez, Ricardo; Nieto Vázquez, Jorge; Economía; Ekonomia
In this paper we study possible rankings of opportunity profiles. An opportunity profile is a list of sets of alternative opportunities, one set for each agent in the society. We compare such opportunity profiles on the basis of the notion of “equality of opportunities”. Our main results show the necessary and sufficient conditions for this comparison to be made using exclusively the information provided by two cardinal measures: the number of common alternatives for all sets in a given profile and/or the difference between the number of alternatives of individual sets. We also show that, under given circumstances, the only way to solve conflicts between these two numbers is to combine them in a lexicographic procedure.
Open Access
Fair competition design
(2018) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Economía
We study the impact of two basic principles of fairness on the structure of competition systems and perform our analysis by focusing on sports competitions. The first principle states that equally strong players should have the same chances of being the final winner, while the second principle requires that the competition system should not favor weaker players. We apply these requirements to a class of competitions which includes, but is not limited to, the sport tournament systems that are most commonly used in practice, such as round-robin tournaments and different kinds of knockout competitions, and we characterize the structures satisfying these requirements. In our results, a new competition structure that we call an antler is found to play a referential role. Finally, we show that the class of fair competition systems becomes rather small when both fairness principles are jointly applied.
Open Access
Freedom of choice and conflict resolution
(2005) Arlegi Pérez, Ricardo; Economía; Ekonomia
This work is an output of my participation in the project 'Procedural Approaches to Conflict Resolution', coordinated by Professor Matthias Raith. The main goal of the project was making an interdisciplinary approach to the issue of conflicts resolution. The intention of the paper is providing an introductory survey to the emerging literature on ranking sets and freedom of choice as a theoretical source for its application in conflicts resolution.
Open Access
Freedom of choice: the leximax criterion in economic environments
(2000) Arlegi Pérez, Ricardo; Besada, M.; Nieto Vázquez, Jorge; Vázquez, C.; Economía; Ekonomia
Many recent works have investigated the question of extending a preference over a set of alternatives to its power set, as a way to provide a formal representation of the notion of freedom of choice. In general, the results are limited to the finite case, which excludes 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 of Bossert, Pattanaik and Xu (1994) on this more general framework. This characterization result opens the possibility of application of the literature on freedom of choice to standard economic environments.
Open Access
Freedom of choice: the leximax criterion in the infinite case
(2006) Arlegi Pérez, Ricardo; Besada, M.; Nieto Vázquez, Jorge; Vázquez, C.; Economía; Ekonomia
Many 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.
Open Access
Incomplete preferences and the preference for flexibility
(1998) Arlegi Pérez, Ricardo; Economía; Ekonomia
Sometimes individual agents display in their decisions a preference for having more opportunities to choose from. In this paper this fact is interpreted from a preference for flexibility approach, which links with the hypothesis that there is some uncertainty or vagueness in the decision maker’s preferences. We define an asymmetric (but not necessarily transitive, or complete) preference on a finite universe of alternatives, X, to express that vagueness. Taking this preference as a reference, the notion of preference for flexibility is described by means of the axiomatic characterization of a class of binary relations over the possible subsets of X, which are interpreted as opportunity sets. Subsequently, we demonstrate the relationship between the results and the representation theorem of preference for flexibility proposed by Kreps [10]. Finally, it is shown how some special orderings of the related literature could be interpreted as elements of the class characterized here.
Open Access
Note on Bossert, Pattanaik and Xu’s “Choice under complete uncertainty: axiomatic characterization of some decision rules”
(2002) Arlegi Pérez, Ricardo; Economía; Ekonomia
Recent work by Bossert, Pattanaik and Xu provides axiomatic characterizations of some decision rules for individual decision making under complete uncertainty. This note shows that, in the case of two of these rules, they do not satisfy one of the axioms used for their characterization. A counterexample illustrating this fact is provided, as well as an alternative way to characterize the two rules under consideration, mantaining as far as possible the original axioms proposed by Bossert, Pattanaik and Xu.
Open Access
On freedom of choice, ambiguity, and the preference for easy choices
(2006) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia
This paper is devoted to the study of opportunity set comparisons when the characteristics of the options within the sets in question may be ambiguous. We assume that agents display a preference for freedom of choice, but also aversion to the presence of ambiguous options. We propose a suitable environment for approaching this problem, and provide axiomatic characterizations of several rules for ranking sets in such a context.
Unknown
On procedural freedom of choice
(2004) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia
Numerous works in the last decade have analyzed the question of how to compare opportunity sets as a way to measure and evaluate individual freedom of choice. This paper defends that, in many contexts, external procedural aspects that are associated to an opportunity set should be taken into account when making judgements about the freedom of choice an agent enjoys. We propose criteria for comparing procedure-based opportunity sets that are consistent with both the procedural aspect of freedom and most of the standard theories of ranking opportunity sets.
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; Ekonomia
Using 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.
Open Access
Ranking sets additively in decisional contexts: an axiomatic characterization
(2006) Arlegi Pérez, Ricardo; Rodríguez Alcantud, José Carlos; Economía; Ekonomia
Ranking finite subsets of a given set X of elements is the formal object of analysis in this paper. This problem has found a wide range of economic interpretations in the literature. The focus of the paper is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn [13] showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this paper proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s [21] characterization of the cardinality based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms.
Open Access
Rational evaluation of actions under complete uncertainty
(2001) Arlegi Pérez, Ricardo; Economía; Ekonomia
This work analyzes the problem of individual choice of actions under complete uncertainty. In this context, each action consists of a set of different possible outcomes with no probability distribution associated with them. The work examines and defines a class of choice procedures in which: a): the evaluation of sets (actions) is element-induced; and b): certain assumption of rationality, which is an adaptation of Sen's condition, is satisfied. Some results of characterization show that different well-known rules can be reinterpreted as particular cases within the defined class, each of them responding to different attitudes towards uncertainty by the agent.
Unknown
A theory of choice under internal conflict
(2012) Arlegi Pérez, Ricardo; Teschl, Miriam; Economía; Ekonomia
In this paper we discuss, inspired by some psychological literature, that choices are the outcome of the interplay of different, potentially conflicting motivations. We propose an axiomatic approach with two motivations, which we assume to be single-peaked over a certain given dimension. We first consider the case in which motivations are given and stable, and then introduce the possibility for motivations to change. We show first that in the no-motivation change case, certain choice behaviours that appear to be inconsistent from the standard rational choice point of view may be explained in our framework as the outcome of conflicting motivations. Afterwards, in the case of motivation change, we present two psychologically-flavoured assumptions about how motivations are influenced by choices. We show that, with some additional weak assumptions of rationality, motivation change leads to a smaller range of potentially inconsistent choices and not to a larger one as one may think. In particular, conflicts between two motivations can eventually be resolved by choosing different actions and consequently a definite and final preference for an action be revealed.
Open Access
Uncertainty with ordinal likelihood information
(2007) Alcalde Unzu, Jorge; Arlegi Pérez, Ricardo; Economía; Ekonomia
This paper proposes a new framework of choice under uncertainty, where the only information available to the decision maker is about the the ordinal likelihood of the different outcomes each action generates. This contrasts both with the classical models where the potential outcomes of each action have an associated probability distribution, and with the more recent complete uncertainty models, where the agent has no information whatever about the probability of the outcomes, even of an ordinal nature. We present an impossibility result in our framework, and some ways to circumvent it that result in different ranking rules.
Open Access
Variable population egalitarian ethics and the critical-level: a note
(2000) Arlegi Pérez, Ricardo; Ballester Oyarzun, Miguel Ángel; Nieto Vázquez, Jorge; Economía; Ekonomia
This paper explores the introduction of a variable critical-level in a variable population context. We focus the attention on the “Critical-Level Egalitarian Rule”, a social evaluation procedure which compares two social states as follows: (i) It reproduces the leximin criterion when applied to vectors of identical dimension and (ii) otherwise, it completes the small one with so many times a variable critical-level as to make the two vectors equal in size and applies the leximin criterion again. We prove that the use of a strict monotonic critical-level leads to the intransitivity of the social evaluation rule. This problem disappears when a weak monotonicity condition is required.

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