A model of procedural decision making in the presence of risk

We introduce a procedural model of risky choice in which an individual is endowed with a core preference relation that may be highly incomplete. She can, however, derive further rankings of alternatives from her core preferences by means of a procedure based on the independence axiom. We find that the preferences. that are generated from an initial set of rankings according to this procedure can be represented by means of a set of von Neumann-Morgenstern utility functions, thereby allowing for incompleteness of preference relations. The proposed theory also yields new characterizations of the stochastic dominance orderings.