Equivalences and Continuity in Multivalent Preference Structures

In assessing multiattribute utility functions, the valence approach partitions the elements of each attribute into equivalence classes. Since attribute interactions are reflected by these equivalence classes, the functional forms of the utility representations are kept simple. This paper establishes equivalence relations for multivalent forms of additive independence, utility independence, and fractional independence, which lead to several new representation theorems. We show also that some simple partitions are not possible multivalent structures when the utility function is continuous. These results should simplify the assessment of utility functions when the attributes are interdependent.