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
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.
Open Access
An axiomatic analysis of ranking sets under simple categorization
(Springer, 2012) Alcantud, José Carlos R.; Arlegi Pérez, Ricardo; Economía; Ekonomia
This paper contributes to the axiomatization of additive rules for ranking sets of objects under the psychological principle of categorization. Firstly we proceed with the case where the elements in the sets are categorized into at most three groups, namely good (with value 1), neutral (with value 0), and bad (with value−1). Secondly, we solve the case where there are only good and neutral elements. In both instances the evaluation of the sets is purely additive. Lastly, we show that dropping one of the axioms in our general characterization produces an axiomatization of the more general class of evaluations where good and bad elements are weighted differently. Areas of research in Economics such as committee selection problems, hedonic games and matching are among the ranking sets models where our results could potentially be applied.
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
Attitudes toward choice with incomplete preferences: an experimental study
(Elsevier, 2022) Arlegi Pérez, Ricardo; Bourgeois-Gironde, Sacha; Hualde Vidaurre, Mikel; Economía; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Gobierno de Navarra / Nafarroako Gobernua; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA19-2022
We present an experiment to test different individual attitudes toward choice, such as preference for flexibility, choice aversion, betweenness and choice neutrality. Unlike other related experimental papers, we want to analyze whether different choice attitudes can coexist for the same subject, depending on the characteristics of the choice set she is facing. In particular, our main hypothesis is that the presence of incomparability among the alternatives in the choice set, and the time at which such incomparability is solved, affect crucially the kind of attitude towards choice that the subject will exhibit. We find that, indeed, choice attitudes are not homogeneous across choice sets, yet they are conditional on the preferences over the alternatives. We also find some evidence supporting that subjects tend to value heuristically sets as a whole.
Open Access
Fair elimination-type competitions
(Elsevier, 2020) 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 elimination-type competitions and perform our analysis by focusing on sports competitions. The first principle states that stronger players should have a larger chance of winning than weaker players, while the second principle provides equally strong players the same chances of being the final winner. We apply these requirements to different kinds of knockout competitions, and characterise the structures satisfying them. In our results, a new competition structure that we call an antler is found to play a referential role.
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
League competitions and fairness
(Springer, 2023) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE
We formulate two fairness principles and characterize the league competition systems that satisfy them. The first principle requires that all players should have the same chance of being the final winner if all players are equally strong, while the second states that the league competition should not favor weaker players. We apply these requirements to a class of systems which includes round-robin tournaments as a particular case.
Open Access
Power set extensions of dichotomous preferences
(Elsevier, 2016) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Economía; Ekonomia
This paper is devoted to the study of how to extend a dichotomous partition of a universal set X into good and bad objects to an ordering on the power set of X. We introduce a family of rules that naturally take into account the number of good objects and the number of bad objects, and provide axiomatic characterizations of two rules that are particularly appealing when it comes to compating sets in which the good
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.