Qualitative Models for Decision Under Uncertainty without the
  Commensurability Assumption
  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.
