Rank Dependent Weighted Average Utility Models for Decision Making under Ignorance or Objective Ambiguity

The paper provides an axiomatic characterization of a family of rank dependent weighted average utility criteria applicable to decision making under ignorance or objective ambiguity. Decision making under ignorance compares finite sets of final consequences while decision making under objective ambiguity compares finite sets of probability distributions over those final consequences. The criteria characterized assign to every element in a set a weight that depends upon the rank of this element if it was available for sure (non-ambiguously) and that compare sets on the basis of their weighted utility for some utility function. We also discuss the implication of comparative attitudes to ignorance or ambiguity on the form of the weights and the utility functions and provide an additional characterization of a subfamily of these criteria that requires the rank-dependent weights to result from a probability weighting function.