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
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
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
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
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
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
Manipulative agendas in four-candidate elections
(Elsevier, 2020) Arlegi Pérez, Ricardo; Dimitrov, Dinko; Ekonomia; Institute for Advanced Research in Business and Economics - INARBE; Economía
We consider a setting where it is known for an electorate what probability a given candidate has of beating another in a pairwise ballot. An agenda assigns candidates to the leaves of a binary tree and is called manipulative if it inverts the final winning probabilities for two candidates. We compare standard and symmetric agendas in four-candidate elections and show that in monotone environments the former are more manipulative.
Open Access
Uncertainty with ordinal likelihood information
(Springer-Verlag, 2013) Alcalde Unzu, Jorge; Arlegi Pérez, Ricardo; Ballester Oyarzun, Miguel Ángel; Economía; Ekonomia
We 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.
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
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.