Following Fleming (1952), Harsanyi (1955) showed that if the collective preference satisfies von Neumann and Morgenstern's Prade's axioms (1995), and particularly risk aversion, The present paper raises the question of collective resorts on (i) the identification of a theory of decision decision making under possibilistic uncertainty. The making under uncertainty (DMU) that captures the decision next Section recalls the basic notions on which our work relies makers' behaviour with respect to uncertainty and (ii) the (decision under possibilistic uncertainty, collective utility specification of a collective utility function (CUF) as it may functions, etc.).

Starting from a general characterization of roles, we focus on the ways in which roles are specified, we examine the formal constraints on their definitions, and propose definitional schemas motivating different kinds of roles. This classification, in addition to clarify the notion of role itself, helps us to reconsider the two standard solutions that have been proposed for the famous counting problem, and to suggest that a third mixed approach may be considered.