Representations of preorders by strong multi-objective functions
We introduce a new kind of representation of a not necessarily total preorder, called strong multi-utility representation, according to which not only the preorder itself but also its strict part is fully represented by a family of multi-objective functions. The representability by means of semicontinuous or continuous multi-objective functions is discussed, as well as the relation between the existence of a strong multi-utility representation and the existence of a Richter-Peleg utility function. We further present conditions for the existence of a semicontinuous or continuous countable strong multi-utility representation.
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- Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004.
"Expected utility theory without the completeness axiom,"
Journal of Economic Theory,
Elsevier, vol. 115(1), pages 118-133, March.
- Juan Dubra & Fabio Maccheroni & Efe Oki, 2001. "Expected utility theory without the completeness axiom," ICER Working Papers - Applied Mathematics Series 11-2001, ICER - International Centre for Economic Research.
- Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
- Schmeidler, David, 1971.
"A Condition for the Completeness of Partial Preference Relations,"
Econometric Society, vol. 39(2), pages 403-404, March.
- SCHMEIDLER, David, "undated". "A condition for the completeness of partial preference relations," CORE Discussion Papers RP 86, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Herden, Gerhard & Levin, Vladimir L., 2012. "Utility representation theorems for Debreu separable preorders," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 148-154.
- Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
- Herden, Gerhard & Pallack, Andreas, 2002. "On the continuous analogue of the Szpilrajn Theorem I," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 115-134, March.
- Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
- Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
- Kaminski, B., 2007. "On quasi-orderings and multi-objective functions," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1591-1598, March.
- Bergstrom, Theodore C., 1975. "Maximal elements of acyclic relations on compact sets," Journal of Economic Theory, Elsevier, vol. 10(3), pages 403-404, June.
- Bosi, Gianni & Caterino, Alessandro & Ceppitelli, Rita, 2009. "Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions," MPRA Paper 14808, University Library of Munich, Germany.
- Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563. Full references (including those not matched with items on IDEAS)
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