NCJ Number
94730
Date Published
1984
Length
12 pages
Annotation
The use of additive value models when attributes have overlapping dependencies is analyzed.
Abstract
According to Krantz, et al. (1971), an additive conjoint structure in relation to a designated component set is a binary relation on the component set that satisfies five specific conditions: (1) weak ordering, (2) independence, (3) restricted solvability, (4) the Archimedean property, and (5) essentialism. The weak-ordering axiom implies that the component set satisfies connectedness and the concept of transitivity. A proof that connectedness and transitivity imply a weak ordering is provided in Krantz et al. (1971). The implications of the axioms are considered, and it is pointed out that in problems where a decisionmaker is attempting to evaluate riskless alternatives described over multiple attributes, it is possible to infer the existence of an additive preference function if the attribute set satisfies the requirements for an component additive conjoint structure. Thus, the interdependent additive formulation due to Fishburn (1967) is adapted to Krantz et al.'s axiomatic system definition of an additive conjoint structure. This is accomplished by replacing the independence condition defined within the additive conjoint structure with a conditional independence condition. The interdependent additive formulation is shown to be the appropriate form for value functions defined over attribute sets when certain conditions hold.