A Joint-Receipt Conjoint Structure and its Additive Representation

Abstract

This paper introduces a componentwise joint receipt operation ⊕ on an n -component product set Πⁿ_i=1 g_i, and develops an axiom system to justify an additive representation for a binary relation succsim on Πⁿ_i=1 g_i. Basically, our axiom system is similar to the n -component (n≥ 3), additive conjoint structure. However, the introduction of the operation ⊕ yields two new axioms – additive solvability and invariance under multiplication – and hence we can weaken the independence axiom of the conjoint structure. The weakened independence axiom requires the independence of the order for each single factor from fixed levels of the other factors, while the conjoint structure involves the independence of the order for two or more factors. Finally, it is shown by a brief experimental test that the weakened independence axiom is sustained.