The utility efficient set and its interactive reduction

We assume a decision situation under risk with incomplete information on preferences modelled as a vector utility function. We consider an additive aggregation of its components and partial information on the scaling constants. We develop the concept of utility efficiency to identify efficient strategies in discrete problems when the information about the scaling constants of the decision maker is in the form of a polyhedral cone. A characterization of the utility efficient set provides a practical way to compute such efficient strategies. We then discuss an interactive method based on the assessment of the scaling constants via an interactive paired comparison with its convergence. The method is complemented by a procedure to reduce the utility efficient set to aid in the process of reaching a final strategy.