Necessary and possible preference structures
A classical approach to model a preference on a set A of alternatives uses a reflexive, transitive and complete binary relation, i.e. a total preorder. Since the axioms of a total preorder do not usually hold in many applications, preferences are often modeled by means of weaker binary relations, dropping either completeness (e.g. partial preorders) or transitivity (e.g. interval orders and semiorders). We introduce an alternative approach to preference modeling, which uses two binary relations–the necessary preference ≿N and the possible preference ≿P–to fulfill completeness and transitivity in a mixed form. Formally, a NaP-preference (necessary and possible preference) on A is a pair (≿N,≿P) such that ≿N is a partial preorder on A and ≿P is an extension of ≿N satisfying mixed properties of transitivity and completeness. We characterize a NaP-preference (≿N,≿P) by the existence of a nonempty set R of total preorders such that ⋂R=≿N and ⋃R=≿P. In order to analyze the representability of NaP-preferences via families of utility functions, we generalize the notion of a multi-utility representation of a partial preorder by that of a modal utility representation of a pair of binary relations. Further, we give a dynamic view of the family of all NaP-preferences on a fixed set A by endowing it with a relation of partial order, which is defined according to the stability of the information represented by each NaP-preference.
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- Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
- Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
- Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008.
"Objective and Subjective Rationality in a Multiple Prior Model,"
Carlo Alberto Notebooks
73, Collegio Carlo Alberto, revised 2008.
- Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, 03.
- Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Post-Print hal-00537082, HAL.
- 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.
- 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 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.
- Herden, Gerhard & Levin, Vladimir L., 2012. "Utility representation theorems for Debreu separable preorders," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 148-154.
- Itzhak Gilboa & David Schmeidler, 1989.
"Maxmin Expected Utility with Non-Unique Prior,"
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
- Back, Kerry, 1986. "Concepts of similarity for utility functions," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 129-142, April.
- Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
- Michael Mandler, 2006. "Cardinality versus Ordinality: A Suggested Compromise," American Economic Review, American Economic Association, vol. 96(4), pages 1114-1136, September.
- Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2010. "Multiple criteria sorting with a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1455-1470, December.
- Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, 07.
- Mukul Majumdar & Amartya Sen, 1976. "A Note on Representing Partial Orderings," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 543-545.
- 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.
- Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
- Angilella, Silvia & Greco, Salvatore & Matarazzo, Benedetto, 2010. "Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral," European Journal of Operational Research, Elsevier, vol. 201(1), pages 277-288, February.
- Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
- Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001.
"A Subjective Spin on Roulette Wheels,"
1127, California Institute of Technology, Division of the Humanities and Social Sciences.
- Ehud Lehrer & Roee Teper, 2014. "Extension Rules or What Would the Sage Do?," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 5-22, February.
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