Collective decision making under possibilistic uncertainty. Principles and characterization

This paper raises the question of collective decisionmaking under possibilistic uncertainty. We study several egalitarian decision rules and show that in the context of a possibilistic representation of uncertainty the use of an egalitarian collective utility function allows us to get rid of the Timing Effect. Making a step further, we prove that if both the agents' preferences and the collective ranking of the decisions satisfy Dubois and Prade's axioms (Dubois, Prade, 1995), and particularly risk aversion, and Pareto unanimity, then the egalitarian collective aggregation is compulsory. This result can be seen as an ordinal counterpart of Harsanyi's theorem (Harsanyi, 1955). The picture is then completed by the proposition and the characterization of an optimistic counterpart of this pessimistic decision rule. © 2015 Lavoisier.