Résumé
When a group of agents is faced with collective decisional tasks, the agents may have to cooperate to establish which alternative appears to be a convenient con-sensus. The influence an agent may have upon the other ones may change the collective decision. Modelling of influence in a social network assumes that each player has an initial inclination for one of the alternative that may be different from his final decision. The point of departure of such studies is the concept of the Hoede-Bakker index, which computes the overall decisional power of a player in a social network when the decision is binary. We propose to extend the notions of decision power and influence indices when the decision is not simply binary, but associated with a scale of success: an indi-vidual can more or less adhere to the collective decision. Initially, the idea was moti-vated by the collective evaluation process in sensory analysis. Indeed, sensory analysis is a set of methods for measuring sensory perceptions. When the panel is made up of trained individuals who master the vocabulary of the domain, sensory analysis has been the subject of numerous evaluation protocols. On the other hand, when the evaluators are inexperienced evaluators not mastering the descriptors, the sensory characterization may strongly be impacted by influential panelists. In this paper, we are interested in measuring such a qualitative influence. Framing our work in game theory models, we propose to extend the notion of influence index to the qualitative process of graded decision in sensory analysis, justifying our choices on the basis of our feedback on the process of sensory analysis by a collective of panelists.