Preprint D110/2013
On the Axiom of Separability
Shilei Wang
Keywords: additivity | separability | Thomsen condition | 3-web

This work studies axiomatic systems for additive and separable preference structures on a product set, and explores the roles of different separability conditions in their corresponding utility representations. We show that the Thomsen condition is a necessary and sufficient condition for an independent preference structure is additive on a general two-dimensional domain. We develop a theorem to identify a large class of separable preference relations that can also admit additive utility representations, namely, a separable preference structure on a two-dimensional domain is additive if and only if its separability rule can represent an additive preference relation on the plane.

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