General nesting relation between EBUU and utility-level-dependent capacity representations

Establish whether Expected Balanced Uncertain Utility and the certainty-equivalent-indexed capacity representation admit a general nesting relation, despite their different primitive objects and organizational structures.

Background

The paper compares its certainty-equivalent-indexed capacity representation with Expected Balanced Uncertain Utility (EBUU), which ranks acts through a balancing value and a balancing-value-dependent outcome-set utility. The two frameworks differ in their primitive objects: EBUU is organized around a prior on decomposable events and a balancing-value-dependent utility of outcome sets, whereas the present representation assigns a capacity on subjective events at each certainty-equivalent level.

The authors explicitly state that they do not establish a general nesting relation between the two representation classes and explain that such a relation is not immediate. Determining whether one class contains the other, or characterizing their intersection and relative expressive power, remains unresolved within the paper.