Necessary and possible preference structures

Journal of Mathematical Economics

Volumn 49, Issue 2, 2013, Pages 163-172

  Giarlotta, Alfio ^a   Greco, Salvatore ^a  

^a Palazzo delle Scienze   (Italy)

Author keywords

Incomplete preference; Interval order; Intransitive indifference; Modal utility representation; NaP preference; Partial preorder; Preference resolution; Semiorder; Total preorder

Indexed keywords

EID: 84875088582     PISSN: 03044068     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmateco.2013.01.001     Document Type: Article

References (42)

1. Aleskerov F., Bouyssou D., Monjardet B. Utility Maximization, Choice and Preference 2007, Springer, Berlin.
2. Angilella S., Greco S., Matarazzo B. Non-additive robust ordinal regression: a multiple criteria decision model based on the Choquet integral. European J. Oper. Res. 2010, 201(1):277-288.
3. Anscombe F.J., Aumann R.J. A definition of subjective probability. Ann. Math. Statist. 1963, 34(1):199-295.
4. Aumann R.J. Utility theory without the completeness axiom. Econometrica 1962, 30:445-462.
5. Back K. Concepts of similarity for utility functions. J. Math. Econom. 1986, 15:129-142.
6. Bewley, T., 1986. Knightian uncertainty theory: part I. Cowles Foundation. Discussion Paper no. 807.
7. Bridges D., Mehta G.B. Representations of Preference Orderings. Lecture Notes in Economics and Mathematical Systems 1995, vol. 422. Springer, Berlin.
8. Debreu G. Representation of a preference ordering by a numerical function. Decision Processes 1954, 159-166. Wiley, New York. R.M. Thrall, C.H. Coombs, R.L. Davies (Eds.).
9. Dubra J., Maccheroni F., Ok E.A. Expected utility theory without the completeness axiom. J. Econom. Theory 2004, 115:118-133.
10. Eliaz K., Ok E.A. Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences. Games Econom. Behav. 2006, 56:61-86.
11. Evren O., Ok E.A. On the multi-utility representation of preference relations. J. Math. Econom. 2011, 47:554-563.
12. Figueira J., Greco S., Ehrgott M. Multiple Criteria Decision Analysis: State of the Art Surveys 2005, Springer, Berlin.
13. Fishburn P.C. Semiorders and risky choices. J. Math. Psych. 1968, 5:358-361.
14. Fishburn P.C. Intransitive indifference with unequal indifference intervals. J. Math. Psych. 1970, 7:144-149.
15. Fishburn P.C. Interval representations for interval orders and semiorders. J. Math. Psych. 1973, 10:91-105.
16. Fishburn P.C. Interval Orders and Interval Graphs 1985, Wiley, New York.
17. Ghirardato P., Maccheroni F., Marinacci M. Differentiating ambiguity and ambiguity attitude. J. Econom. Theory 2004, 118:133-173.
18. Ghirardato P., Maccheroni F., Marinacci M., Siniscalchi M. A subjective spin on roulette wheels. Econometrica 2003, 71:1897-1908.
19. Giarlotta, A., A genesis of interval orders and semiorders: transitive NaP-preorders. Order (submitted for publication).
20. Giarlotta, A., Watson, S., 2012. Minimally resolvable NaP-preferences. Preprint.
21. Gilboa I., Maccheroni F., Marinacci F., Schmeidler D. Objective and subjective rationality in a multiple prior model. Econometrica 2010, 78(2):755-770.
22. Gilboa I., Schmeidler D. Maxmin expected utility with a non-unique prior. J. Math. Econom. 1989, 18:141-153.
23. Greco S., Mousseau V., Słowiński R. Ordinal regression revisited: multiple criteria ranking with a set of additive value functions. European J. Oper. Res. 2008, 191:415-435.
24. Greco S., Mousseau V., Słowiński R. Multiple criteria sorting with a set of additive value functions. European J. Oper. Res. 2010, 207(3):1455-1470.
25. Greco S., Słowiński R., Mousseau V., Figueira J. Robust ordinal regression. New Advances in Multiple Criteria Decision Analysis 2010, 273-320. Springer, Berlin. M. Ehrgott, J. Figueira, S. Greco (Eds.).
26. Herden G., Levin V.L. Utility representation theorems for Debreu separable preorders. J. Math. Econom. 2012, 48(3):148-154.
27. Krantz D.H. Extensive measurement in semiorders. Philos. Sci. 1967, 34:348-362.
28. Lehrer E., Teper R. Justifiable preferences. J. Econom. Theory 2011, 146:762-774.
29. Lehrer, E., Teper, R., 2011b. Extension rules or what would the sage do? Mimeo.
30. Lehrer K., Wagner C. Intransitive indifference: the semi-order problem. Synthese 1985, 65:249-256.
31. Luce R.D. Semiorders and a theory of utility discrimination. Econometrica 1956, 24:178-191.
32. Majumdar M., Sen A. A note on representing partial orderings. Rev. Econ. Stud. 1976, 43:543-545.
33. Mandler M. Incomplete preferences and rational intransitivity of choice. Games Econom. Behav. 2005, 50:255-277.
34. Mandler M. Cardinality versus ordinality: a suggested compromise. Amer. Econ. Rev. 2006, 96:1114-1136.
35. Ok E.A. Utility representation of an incomplete preference relation. J. Econom. Theory 2002, 104:429-449.
36. Ok E.A., Ortoleva P., Riella G. Incomplete preferences under uncertainty: indecisiveness in beliefs vs. tastes. Econometrica 2012, 80(4):1791-1808.
37. Peleg B. Utility functions for partially ordered topological spaces. Econometrica 1970, 38:93-96.
38. Pirlot M., Vincke P. Semiorders: Properties, Representations, Applications 1997, Kluwer, Dordrecht.
39. Richter M.K. Revealed preference theory. Econometrica 1966, 34:635-645.
40. Rubinstein A. Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox)?. J. Econom. Theory 1988, 46:145-153.
41. Steiner A.K. The lattice of topologies: structure and complementation. Trans. Amer. Math. Soc. 1966, 122(2):379-398.
42. von Neumann J., Morgenstern O. Theory of Games and Economic Behavior 1944, Princeton University Press, Princeton.