and

We define a binary relation (qualitative uncertainty assessment (QUA)) to describe a decision-maker’s subjective assessment of likelihoods on a collection of events. To model ambiguity, we permit incompleteness. Our axioms yield a representation according to which A is more likely than B if an only if a capacity, called uncertainty measure (UM) as-signs a higher value to A than to B and a higher value A-complement than B-complement. We prove uniqueness, show that UMs are belief functions and describe how QUAs can be extended to utility functions on acts with a sophistication axiom. † This research was supported by grants from the National Science Foundation. 1