On the multi-utility representation of preference relations
We develop the ordinal theory of (semi)continuous multi-utility representation for incomplete preference relations. We investigate the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the maps contained in these sets are required to be (semi)continuous. With the exception of the case where the representing set is required to be finite, we find that the requirements of such representations are surprisingly weak, pointing to a wide range of applicability of the representation theorems reported here. Some applications to decision theory under uncertainty and consumer theory are also considered.
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- José Apesteguía & Miguel A. Ballester, 2004.
"A Theory Of Reference-Dependent Beavior,"
Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra
0402, Departamento de Economía - Universidad Pública de Navarra.
- Jose Apesteguia & Miguel Angel Ballester, 2007. "A Theory of Reference-Dependent Behavior," Working Papers 323, Barcelona Graduate School of Economics.
- Jose Apesteguia & Miguel A. Ballester, 2007. "A theory of reference-dependent behavior," Economics Working Papers 1056, Department of Economics and Business, Universitat Pompeu Fabra.
- Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
- Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
- Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
- Schmeidler, David, 1971.
"A Condition for the Completeness of Partial Preference Relations,"
Econometric Society, vol. 39(2), pages 403-04, March.
- SCHMEIDLER, David, . "A condition for the completeness of partial preference relations," CORE Discussion Papers RP -86, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Eric Danan, 2010.
"Randomization vs. selection: How to choose in the absence of preference?,"
- Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
- Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001.
"A subjective spin on roulette wheels,"
ICER Working Papers - Applied Mathematics Series
17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
- Jyrki Wallenius & James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Stanley Zionts & Kalyanmoy Deb, 2008. "Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead," Management Science, INFORMS, vol. 54(7), pages 1336-1349, July.
- Sagi, Jacob S., 2006. "Anchored preference relations," Journal of Economic Theory, Elsevier, vol. 130(1), pages 283-295, September.
- Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
- Campbell, Donald E. & Walker, Mark, 1990. "Maximal elements of weakly continuous relations," Journal of Economic Theory, Elsevier, vol. 50(2), pages 459-464, April.
- Eric Danan & Anthony Ziegelmeyer, 2006. "Are preferences complete? An experimental measurement of indecisiveness under risk," Papers on Strategic Interaction 2006-01, Max Planck Institute of Economics, Strategic Interaction Group.
- Sophie Bade, 2005. "Nash equilibrium in games with incomplete preferences," Economic Theory, Springer, vol. 26(2), pages 309-332, 08.
- John E. Roemer, 1997.
"The Democratic Political Economy of Progressive Income Taxation,"
97-03, University of Copenhagen. Department of Economics.
- John E. Roemer, 1999. "The Democratic Political Economy of Progressive Income Taxation," Econometrica, Econometric Society, vol. 67(1), pages 1-20, January.
- John Roemer, 2003. "The Democratic Political Economy Of Progressive Income Taxation," Working Papers 9711, University of California, Davis, Department of Economics.
- John E. Roemer, . "The Democratic Political Economy Of Progressive Income Taxation," Department of Economics 97-11, California Davis - Department of Economics.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- 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.
- Jaffray, Jean-Yves, 1975. "Semicontinuous extension of a partial order," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 395-406, December.
- Gilat Levy, 2004.
"A model of political parties,"
LSE Research Online Documents on Economics
540, London School of Economics and Political Science, LSE Library.
- Sondermann, Dieter, 1980. "Utility representations for partial orders," Journal of Economic Theory, Elsevier, vol. 23(2), pages 183-188, October.
- Rigotti, Luca & Shannon, Chris, 2001.
"Uncertainty and Risk in Financial Markets,"
Department of Economics, Working Paper Series
qt6m42r5rr, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
- Luca Rigotti & Chris Shannon=20, 2002. "Uncertainty and Risk in Financial Markets," Game Theory and Information 0201001, EconWPA.
- Rigotti, Luca & Shannon, Chris, 2001. "Uncertainty and Risk in Financial Markets," Department of Economics, Working Paper Series qt7pp7113z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
- Majumdar, Mukul & Sen, Amartya K, 1976. "A Note on Representing Partial Orderings," Review of Economic Studies, Wiley Blackwell, vol. 43(3), pages 543-45, October.
- 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.
- Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
- Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, March.
- Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
- Kopylov, Igor, 2009. "Choice deferral and ambiguity aversion," Theoretical Economics, Econometric Society, vol. 4(2), June.
- Michael Mandler, 2006. "Cardinality versus Ordinality: A Suggested Compromise," American Economic Review, American Economic Association, vol. 96(4), pages 1114-1136, September.
- Masatlioglu, Yusufcan & Ok, Efe A., 2005. "Rational choice with status quo bias," Journal of Economic Theory, Elsevier, vol. 121(1), pages 1-29, March.
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