Decision-making Under Ordinal Preferences and Comparative Uncertainty
  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.
