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
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.
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
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
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
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
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
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
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.