Procedural Group Identification

In this paper we axiomatically characterize two recursive procedures for defining a social group.The first procedure starts with the set of all individuals who define themselves as members of the social group, while the starting point of the second procedure is the set of all individuals who are defined by everyone in the society as group members.Both procedures expand these initial sets by adding individuals who are considered to be appropriate group members by someone in the corresponding initial set, and continue inductively until there is no possibility of expansion any more.identification;social groups;social identity

Procedural group identification

In this paper we axiomatically characterize two recursive procedures for defining a social group. The first procedure starts with the set of all individuals who are defined by everyone in the society as group members, while the starting point of the second procedure is the set of all individuals who define themselves as members of the social group. Both procedures expand these initial sets by adding individuals who are considered to be appropriate group members by someone in the corresponding initial set, and continue inductively un- til there is no possibility of expansion any more.consensus, liberalism, procedure, social identity

Procedural Group Identification

In this paper we axiomatically characterize two recursive procedures for defining a social group.The first procedure starts with the set of all individuals who define themselves as members of the social group, while the starting point of the second procedure is the set of all individuals who are defined by everyone in the society as group members.Both procedures expand these initial sets by adding individuals who are considered to be appropriate group members by someone in the corresponding initial set, and continue inductively until there is no possibility of expansion any more

Separability and aggregation of equivalence relations

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability and unanimity characterize the family of meet aggregators. We show another characterization of the family of meet aggregators using conjunctive separability and two Pareto axioms, Pareto+ and Pareto−. If we drop Pareto−, then conjunctive separability and Pareto+ characterize the family of meet aggregators along with a trivial aggregator

The problem of collective identity in a fuzzy environment

Producción CientíficaWe define the problem of group identication in a fuzzy environment. We concentrate on the case where the society is required to self-determine the belongingness of each member to a speci_c group, characterized by a single attribute. In general terms, this case consists of a collective identity issue that can be regarded as an aggregation problem of individual assessments within a group. Here we introduce the possibility that both the original assessments and the resulting output attach partial memberships to the collectivity, for each potential member. We propose relevant classes of rules, and some are axiomatically characterized. Our new approach provides a way to circumvent classical impossibility results like Kasher and Rubinstein's.Ministerio de Economía, Industria y Competitividad (Project ECO2012-32178

Separation of Decisions in Group Identification

We study a model of group identification in which individuals’ opinions as to the membership of a group are aggregated to form a list of the group’s members. Potential aggregation rules are studied through the axiomatic approach. We introduce two axioms, meet separability and join separability, each of which requires the list of members generated by the aggregation rule to be independent of whether the question of membership in a group is separated into questions of membership in two other groups. We use these axioms to characterize a class of “one vote” rules, in which one opinion determines whether an individual is considered to be a member of a group. We then use this characterization to provide new axiomatizations of the liberal rule, in which each individual determines for himself whether he is a member of the group, as the only non-degenerate anonymous rule satisfying the meet separability and join separability axioms

SELECCIÓN ENDÓGENA DE EXPERTOS

El problema de la cualificación e identificación de los individuos pertenecientes a ungrupo es uno de los más recientes problemas abordados desde la Teoría de la Elección Social. En este trabajo hemos tratado un problema similar: el de la selección endógena de un grupo de expertos dentro de un colectivo a partir de las opiniones de cada individuo sobre el resto de los agentes y de la que cada agente tiene sobre sí mismo. Hemos supuesto que los individuos gradúan sus valoraciones en el intervalo unidad y que a través de ellas se obtiene una valoración colectiva para cada uno de los posibles expertos. Para agregar las opiniones individuales en una valoración colectiva sobre cada uno de los posibles expertos se ha utilizado una clase de medias cuasiaritméticas ponderadas. Hemos considerado reglas de decisión que, a partir de las valoraciones colectivas, permiten seleccionar los expertos en función de diferentes niveles de cualificación. En el trabajo se demuestran las principales propiedades de las reglas de decisión propuestas. Palabras clave: toma de decisiones colectivas, selección de individuos, valoraciones difusas, medias cuasiaritméticas ponderadas. Abstract The problem of qualification and identification of individuals belonging to a group is one of the most recent problems analyzed in the Social Choice Theory. In this paper we deal with a similar problem: the endogenous selection of experts in a group taking into account the opinions of each individual over every member of the group, including himself. We have supposed that individuals grade their assessments in the unit interval and we aggregate these opinions in order to obtain a collective assessment for each agent. This aggregation procedure is based on a class of weighted quasi-arithmetic means. We have considered decision rules which select the final set of experts taking into account the collective assessments obtained for each individual by using different qualification levels. In the paper we prove the main properties of the proposed decision rules. Keywords: group decision-making, individuals’ selection, fuzzy assessments, weighted quasi-arithmetic means