Context and Decision: Utility on a Union of Mixture Spaces
AbstractSuppose 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 973.
Date of creation: 2011
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-03 (All new papers)
- NEP-MIC-2012-01-03 (Microeconomics)
- NEP-UPT-2012-01-03 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
- Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
- Rubinstein, A., 1998.
"Economics and Language,"
14-98, Tel Aviv.
- Rubinstein,Ariel, 2000. "Economics and Language," Cambridge Books, Cambridge University Press, number 9780521789905, December.
- Ariel Rubinstein, 2000. "Economics and Language," Online economics textbooks, SUNY-Oswego, Department of Economics, number lang1.
- Rubinstein,Ariel, 2000. "Economics and Language," Cambridge Books, Cambridge University Press, number 9780521593069, December.
- Gilboa, I. & Schmeidler, D., 2001.
"A Derivation of Expected Utility Maximization in the Context of a Game,"
2001-18, Tel Aviv.
- 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.
- 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.
- 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.
- 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.
- Morris, Stephen Morris & Takashi Ui, 2002.
"Best Response Equivalence,"
Cowles Foundation Discussion Papers
1377, Cowles Foundation for Research in Economics, Yale University.
- Vind, Karl, 1991.
Journal of Mathematical Economics,
Elsevier, vol. 20(1), pages 119-135.
- Roberts, Kevin W S, 1980. "Interpersonal Comparability and Social Choice Theory," Review of Economic Studies, Wiley Blackwell, vol. 47(2), pages 421-39, January.
- Hammond, Peter J, 1989. "Consistent Plans, Consequentialism, and Expected Utility," Econometrica, Econometric Society, vol. 57(6), pages 1445-49, November.
- Gilboa,Itzhak & Schmeidler,David, 2001.
"A Theory of Case-Based Decisions,"
Cambridge University Press, number 9780521003117, December.
- 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.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- 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.
- 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.
- Hammond, P.J. & , ., 1987. "Consequentialist foundations for expected utility," CORE Discussion Papers 1987016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Helen Neal).
If references are entirely missing, you can add them using this form.