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.).

This paper investigates the problem of finding a preference relation on a set of acts from the knowledge of an ordering on events (subsets of states of the world) describing the decision-maker (DM)s uncertainty and an ordering of consequences of acts, describing the DMs preferences. However, contrary to classical approaches to decision theory, we try to do it without resorting to any numerical representation of utility nor uncertainty, and without even using any qualitative scale on which both uncertainty and preference could be mapped. It is shown that although many axioms of Savage theory can be preserved and despite the intuitive appeal of the method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty, but leads to the kind of uncertainty theory encountered in non-monotonic reasoning (especially preferential and rational inference), closely related to possibility theory. Moreover the method turns out to be either very little decisive or to lead to very risky decisions, although its basic principles look sound. This paper raises the question of the very possibility of purely symbolic approaches to Savage-like decision-making under uncertainty and obtains preliminary negative results.

This paper relates comparative belief structures and a general view of belief management in the setting of deductively closed logical representations of accepted beliefs. We show that the range of compatibility between the classical deductive closure and uncertain reasoning covers precisely the nonmonotonic 'preferential' inference system of Kraus, Lehmann and Magidor and nothing else. In terms of uncertain reasoning any possibility or necessity measure gives birth to a structure of accepted beliefs. The classes of probability functions and of Shafer's belief functions which yield belief sets prove to be very special ones.

This paper investigates a purely qualitative version of Savage's theory for decision making under uncertainty. Until now, most representation theorems for preference over acts rely on a numerical representation of utility and uncertainty where utility and uncertainty are commensurate. Disrupting the tradition, we relax this assumption and introduce a purely ordinal axiom requiring that the Decision Maker (DM) preference between two acts only depends on the relative position of their consequences for each state. Within this qualitative framework, we determine the only possible form of the decision rule and investigate some instances compatible with the transitivity of the strict preference. Finally we propose a mild relaxation of our ordinality axiom, leaving room for a new family of qualitative decision rules compatible with transitivity.