Context and Decision: Utility on a Union of Mixture Spaces
Suppose a decision-maker is willing to make statements of the form : I prefer to choose alternative a when in context p, than to choose alternative b when in context q”. Contexts p and q may refer to given probability distributions over a set of states, and b and c to alternatives such as: “turn left” or “turn right” at a junction. In such decision problems, the set of alternatives is discrete and there is a continuum of possible contexts. I assume there is a is a mixture operation on the space of contexts (eg. convex combinations of lotteries), and propose a model that defines preferences over a collection of mixture spaces indexed by a discrete set. The model yields a spectrum of possibilities: some decision-makers are well represented by a standard von Neumann–Morgenstern type of utility function; whilst for others, utility across some or all the mixture spaces is only ordinally comparable. An application to the decision problem of Karni and Safra (2000) leads to a generalization, and shows that state-dependence and comparability are distinct concepts. A final application provides a novel way modeling incomplete preferences and explaining the Allais paradox.
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- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-87, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Hammond, Peter J, 1989. "Consistent Plans, Consequentialism, and Expected Utility," Econometrica, Econometric Society, vol. 57(6), pages 1445-49, November.
- Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
- repec:cup:cbooks:9780521789905 is not listed on IDEAS
- Morris, Stephen & Ui, Takashi, 2004.
"Best response equivalence,"
Games and Economic Behavior,
Elsevier, vol. 49(2), pages 260-287, November.
- Karni, Edi & Safra, Zvi, 2000. "An extension of a theorem of von Neumann and Morgenstern with an application to social choice theory," Journal of Mathematical Economics, Elsevier, vol. 34(3), pages 315-327, November.
- P. Mongin, 1997.
"A note on mixture sets in decision theory,"
THEMA Working Papers
97-24, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Vind, Karl, 1991.
Journal of Mathematical Economics,
Elsevier, vol. 20(1), pages 119-135.
- Itzhak Gilboa & David Schmeidler, 2001.
"A Derivation of Expected Utility Maximization in the Context of a Game,"
Cowles Foundation Discussion Papers
1342, Cowles Foundation for Research in Economics, Yale University.
- Gilboa, Itzhak & Schmeidler, David, 2003. "A derivation of expected utility maximization in the context of a game," Games and Economic Behavior, Elsevier, vol. 44(1), pages 172-182, July.
- Gilboa, I. & Schmeidler, D., 2001. "A Derivation of Expected Utility Maximization in the Context of a Game," Papers 2001-18, Tel Aviv.
- 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.
- Roberts, Kevin W S, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
- Fishburn, P. C., 1981. "An axiomatic characterization of skew-symmetric bilinear functionals, with applications to utility theory," Economics Letters, Elsevier, vol. 8(4), pages 311-313.
- Blackorby, Charles & Donaldson, David & Weymark, John A, 1984. "Social Choice with Interpersonal Utility Comparisons: A Diagrammatic Introduction," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 327-56, June.
- Hammond, P.J. & , ., 1987. "Consequentialist foundations for expected utility," CORE Discussion Papers 1987016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
- repec:cup:cbooks:9780521003117 is not listed on IDEAS
- repec:cup:cbooks:9780521593069 is not listed on IDEAS
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
- repec:cup:cbooks:9780521802345 is not listed on IDEAS
- Hammond, Peter J, 1981. "Ex-ante and Ex-post Welfare Optimality under Uncertainty," Economica, London School of Economics and Political Science, vol. 48(191), pages 235-50, August.
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