Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
generalized lottery; preference relation; belief function; linear utility; Choquet expected utility; rationality conditions
generalized lottery; preference relation; belief function; linear utility; Choquet expected utility; rationality conditions
Summary:
A generalized notion of lottery is considered, where the uncertainty is expressed by a belief function. Given a partial preference relation on an arbitrary set of generalized lotteries all on the same finite totally ordered set of prizes, conditions for the representability, either by a linear utility or a Choquet expected utility are provided. Both the cases of a finite and an infinite set of generalized lotteries are investigated.
References:
[1] Chateauneuf, A.: Modeling attitudes towards uncertainty and risk through the use of Choquet integral. Ann. Oper. Res. 52 (1994), 3-20. DOI 10.1007/bf02032158 | MR 1293557 | Zbl 0823.90005
[2] Chateauneuf, A., Cohen, M.: Choquet expected utility model: a new approach to individual behavior under uncertainty and social choice welfare. In: Fuzzy Meas. and Int: Th. and Appl., Physica, Heidelberg 2000, pp. 289-314. MR 1767756
[3] Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5 (1954), 131-295. DOI 10.5802/aif.53 | MR 0080760 | Zbl 0679.01011
[4] Coletti, G., Petturiti, D., Vantaggi, B.: Choquet expected utility representation of preferences on generalized lotteries. In: IPMU 2014 (A. Laurent et al., eds.), Part II, CCIS 443, pp. 444-453. DOI 10.1007/978-3-319-08855-6_45
[5] Coletti, G., Regoli, G.: How can an expert system help in choosing the optimal decision?. Theory and Decision 33 (1992), 3, 253-264. DOI 10.1007/bf00133644 | MR 1196662 | Zbl 0769.90002
[6] Coletti, G., Scozzafava, R.: Toward a general theory of conditional beliefs. Int. J. Intell. Sys. 21 (2006), 229-259. DOI 10.1002/int.20133 | Zbl 1160.68582
[7] Coletti, G., Scozzafava, R., Vantaggi, B.: Inferential processes leading to possibility and necessity. Inform. Sci. 245 (2013), 132-145. DOI 10.1016/j.ins.2012.10.034 | MR 3095855
[8] Dempster, A. P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist. 38 (1967), 2, 325-339. DOI 10.1214/aoms/1177698950 | MR 0207001 | Zbl 0168.17501
[9] Denneberg, D.: Non-additive Measure and Integral. Theory and Decision Library: Series B, Vol. 27. Kluwer Academic, Dordrecht, Boston 1994. DOI 10.1007/978-94-017-2434-0 | MR 1320048 | Zbl 0968.28009
[10] Dubra, J., Maccheroni, F., Ok, E. A.: Expected utility theory without the completeness axiom. J. Econom. Theory 115 (2004), 118-133. DOI 10.1016/s0022-0531(03)00166-2 | MR 2036107 | Zbl 1062.91025
[11] Ellsberg, D.: Risk, ambiguity and the Savage axioms. Quart. J. Econ. 75 (1061), 643-669. DOI 10.2307/1884324 | Zbl 1280.91045
[12] Fagin, R., Halpern, J. Y.: Uncertainty, belief and probability. Comput. Intell. 7 (1991), 3, 160-173. DOI 10.1111/j.1467-8640.1991.tb00391.x | Zbl 0718.68066
[13] Gale, D.: The Theory of Linear Economic Models. McGraw Hill 1960. MR 0115801 | Zbl 0114.12203
[14] Gilboa, I., Schmeidler, D.: Maxmin expected utility with non-unique prior. J. Math. Econ. 18 (1989), 2, 141-153. DOI 10.1016/0304-4068(89)90018-9 | MR 1000102 | Zbl 0675.90012
[15] Gilboa, I., Schmeidler, D.: Additive representations of non-additive measures and the Choquet integral. Ann. Oper. Res. 52 (1994), 43-65. DOI 10.1007/bf02032160 | MR 1293559 | Zbl 0814.28010
[16] Herstein, I. N., Milnor, J.: An axiomatic approach to measurable utility. Econometrica 21 (1953), 2, 291-297. DOI 10.2307/1905540 | MR 0061356 | Zbl 0050.36705
[17] Jaffray, J. Y.: Linear utility theory for belief functions. Oper. Res. Let. 8 (1989), 2, 107-112. DOI 10.1016/0167-6377(89)90010-2 | MR 0995970 | Zbl 0673.90010
[18] Cord, M. Mc, Neufville, B. de: Lottery equivalents: Reduction of the certainty effect problem in utility assessment.
[19] Miranda, E., Cooman, G. de, Couso, I.: Lower previsions induced by multi-valued mappings. J. Stat. Plan. Inf. 133 (2005), 173-197. DOI 10.1016/j.jspi.2004.03.005 | MR 2162574 | Zbl 1101.68868
[20] Nau, R.: The shape of incomplete preferences. Ann. Statist. 34 (2006), 5, 2430-2448. DOI 10.1214/009053606000000740 | MR 2291506 | Zbl 1106.62001
[21] Quiggin, J.: A theory of anticipated utility. J. Econom. Beh. Org. 3 (1982), 323-343. DOI 10.1016/0167-2681(82)90008-7
[22] Savage, L.: The Foundations of Statistics. Wiley, New York 1954. MR 0063582 | Zbl 0276.62006
[23] Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press 1976. MR 0464340 | Zbl 0359.62002
[24] Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57 (1989), 3, 571-587. (First version: Subjective expected utility without additivity, Forder Institute Working Paper (1982)). DOI 10.2307/1911053 | MR 0999273 | Zbl 0672.90011
[25] Schmeidler, D.: Integral representation without additivity. Proc. Amer. Math. Soc. 97 (1986, 2, 255-261. DOI 10.1090/s0002-9939-1986-0835875-8 | MR 0835875 | Zbl 0687.28008
[26] Smets, P.: Decision making in the tbm: the necessity of the pignistic transformation. Int. J. Approx. Reas. 38 (2005), 2, 133-147. DOI 10.1016/j.ijar.2004.05.003 | MR 2116781 | Zbl 1065.68098
[27] Troffaes, M.: Decision making under uncertainty using imprecise probabilities. Int. J. Approx. Reas. 45 (2007), 1, 17-29. DOI 10.1016/j.ijar.2006.06.001 | MR 2321707 | Zbl 1119.91028
[28] Neumann, J. von, Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press 1944. DOI 10.2307/2572550 | MR 0011937
[29] Walley, P.: Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London 1991. DOI 10.1007/978-1-4899-3472-7 | MR 1145491 | Zbl 0732.62004
[30] Wakker, P.: Under stochastic dominance Choquet-expected utility and anticipated utility are identical. Theory and Decis. 29 (1990), 2, 119-132. DOI 10.1007/bf00126589 | MR 1064267 | Zbl 0722.90003
[31] Yaari, M.: The dual theory of choice under risk. Econometrica 55 (1987), 95-115. DOI 10.2307/1911158 | MR 0875518 | Zbl 0616.90005
Search
Partner of
