Decomposition of Utility Functions on Subsets of Product Sets
The standard decomposition theorem for additive and multiplicative utility functions (Pollak 1967, Keeney 1974) assumes that the outcome set is a whole product set. In this paper this assumption is relaxed, and the question of whether or not a natural revision of this theorem necessarily holds is in...
| Veröffentlicht in: | Operations Research. - Institute for Operations Research and the Management Sciences, 1956. - 44(1996), 4, Seite 609-616 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1996
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| Zugriff auf das übergeordnete Werk: | Operations Research |
| Schlagworte: | Utility/preference, multiattribute: utility theory on subsets of product sets Utility/preference, theory: utility theory on subsets of product sets Decision Analysis, Bargaining, and Negotiation Economics Philosophy Mathematics Biological sciences Applied sciences Law |
| Zusammenfassung: | The standard decomposition theorem for additive and multiplicative utility functions (Pollak 1967, Keeney 1974) assumes that the outcome set is a whole product set. In this paper this assumption is relaxed, and the question of whether or not a natural revision of this theorem necessarily holds is investigated. This paper proves that two additional conditions are needed for the decomposition theorem to hold in the context where the outcome set is a subset of a Cartesian product. It is argued that these two new conditions are satisfied by a large family of subsets corresponding to significant real-world problems. Further research avenues are suggested including a generalization of this new decomposition result to nonexpected utility theories. |
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| ISSN: | 15265463 |