Additive difference models without additivity and subtractivity

This paper studies conjoint measurement models tolerating intransitivities that closely resemble Tversky's additive difference model while replacing additivity and subtractivity by mere decomposability requirements. We offer a complete axiomatic characterisation of these models without having recourse to unnecessary structural assumptions on the set of objects. This shows the pure consequences of several cancellation conditions that have often been used in the analysis of more traditional conjoint measurement models. Our models contain as particular cases many aggregation rules that have been proposed in the literature.