Weighting individual opinions in group decision making

In this paper we introduce a multi-stage decision making procedure where decision makers sort the alternatives by means of a fixed set of linguistic categories, each one has associated a numerical score. First we average the scores obtained by each alternative and we consider the associated collective preference. Then, we obtain a distance between each individual preference and the collective one through the Euclidean distance among the individual and collective scoring vectors. Taking into account these distances, we measure the agreement in each subset of decision makers, and a weight is assigned to each decision maker: his/her overall contribution to the agreement. Those decision makers whose overall contribution to the agreement are not positive are expelled and we re-initiate the decision procedure with only the opinions of the decision makers which positively contribute to the agreement. The sequential process is repeated until it determines a final subset of decision makers where all of them positively contribute to the agreement. Then, we apply a weighted procedure where the scores each decision maker indirectly assigns to the alternatives are multiplied by the weight of the corresponding decision maker, and we obtain the final ranking of the alternatives.