A recursive group decision making procedure for choosing qualified individuals Miguel A. Ballester a Jos´ e Luis Garc´ ıa-Lapresta b a Dep. d’Economia i d’Hist`oria Econ`omica, Universitat Aut`onoma de Barcelona, 08193 Bellaterra (Barcelona), Spain. E-mail: miguelangel.ballester@uab.es. b Dep. de Econom´ ıa Aplicada (Matem´aticas), Universidad de Valladolid, Avda. Valle de Esgueva 6, 47011 Valladolid, Spain. E-mail: lapresta@eco.uva.es. Abstract In this paper we introduce a new group decision procedure that follows a recursive pattern. In the first stage, the members of a group show their opinions on all the individuals of that group, regarding a specific attribute, by means of assessments within the unit interval. Taking into account this information, some aggregation operators and a family of thresholds, a subgroup of individuals is selected: those members whose collective assessment reach a specific threshold. Now only the opinions of this qualified subgroup are taken into account and a new subgroup emerges in the implementation of the aggregation phase. We analyze when this recursive procedure converges providing a final subgroup of qualified members, taking into account some extended OWAs. Keywords: Group decision making; OWA operators; aggregation; qualification. 1 Introduction In some occasions a group of individuals has to select a subgroup for doing a task or regarding an attribute. This is the case of a group of experts that has to decide which members should participate in a concrete task. Another possibility consists on determining which members of a society are the best for constituting a committee. There exist in the literature some works where the problem arises in choosing the members of the society satisfying a social identity (see Kasher and Rubinstein [9]), or with respect to a general attribute (see Samet and Schmeidler [11]). We note that in these mentioned papers, only dichotomous assessments are allowed. Aggregation operators allow us to generate a collective assessment to each individual of the group taking into account the individual opinions (see Fodor and Roubens [5], Grabisch, Orlovski and Yager [6] and Calvo, Koles´arova, Komorn´ ıkov´ a and Mesiar [3], among others). A simple way of selecting a subgroup can be done by means of thresholds or quota: all the members reaching the quota have to be chosen. Typically, those members enrolled in this conformed category have more valuable opinions about the task or topic under discussion. It seems therefore reasonable to choose a stable group, i.e., a group such that when considering their assessments on all society members, they would select themselves, and only themselves, for the task. To analyze the possibility of arriving to stable subgroups, in this paper we consider a sequential procedure where in each stage a subgroup is selected, and taking the opinions of this subgroup a new subgroup 1