Letter to the Editor - Additive Utilities with Incomplete Product Sets: Application to Priorities and Assignments
A previous paper discusses the notion of additive utilities in the expected-utility context when the set of consequences X can be written as the product of n other sets: X = X 1 × X 2 × ⋯ × X n . The present paper continues this investigation for cases where X is a subset of the product of n other sets: X ⊂ X 1 × X 2 × ⋯ × X n . Under a finiteness restriction, an additivity axiom leads to an additive utility representation for the elements in X. The potential usefulness of the theory in connection with incomplete product sets is demonstrated with priority orderings and assignments.