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'Additive difference' models without additivity or subtractivity

Pirlot, Marc; Bouyssou, Denis (2004), 'Additive difference' models without additivity or subtractivity, Journal of Mathematical Psychology, 48, 4, p. 263-291. http://dx.doi.org/10.1016/j.jmp.2004.04.002

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Type
Article accepté pour publication ou publié
Date
2004
Journal name
Journal of Mathematical Psychology
Volume
48
Number
4
Publisher
Elsevier
Pages
263-291
Publication identifier
http://dx.doi.org/10.1016/j.jmp.2004.04.002
Metadata
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Author(s)
Pirlot, Marc
Bouyssou, Denis cc
Abstract (EN)
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.
Subjects / Keywords
Cancellation conditions; Additive difference model; Nontransitive preferences; Conjoint measurement

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