McCarthy, David and Mikkola, Kalle (2017): Continuity and completeness of strongly independent preorders.
This is the latest version of this item.
Preview 
PDF
MPRA_paper_79755.pdf Download (288kB)  Preview 
Abstract
A strongly independent preorder on a possibly infinite dimensional convex set that satisfies two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfies two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii) mixture continuity; and (iii') completeness. Applications to decision making under conditions of risk and uncertainty are provided.
Item Type:  MPRA Paper 

Original Title:  Continuity and completeness of strongly independent preorders 
Language:  English 
Keywords:  Continuity Completeness Archimedean Strong independence Expected utility 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty 
Item ID:  79757 
Depositing User:  Dr David McCarthy 
Date Deposited:  19 Jun 2017 14:29 
Last Modified:  26 Sep 2019 18:34 
References:  Aumann, R., 1962. `Utility theory without the completeness axiom.' Econometrica 30, 455462. Baucells, M. and Shapley, L. 2008. `Multiperson utility.' Games and Economic Behavior 62: 329347. Bewley, T., 2002.`Knightian decision theory: Part I.' Decisions in Economics and Finance 25(2): 79110. Blackwell, D. and Girshick, M., 1954. Theory of Games and Statistical Decisions. New York, John Wiley. Broome, J., 1999. `Is incommensurability vagueness?' In Ethics out of Economics Cambridge University Press, Cambridge, 123161. Danan, E., Guerdjikova, A. and Zimper, A., 2012. `Indecisiveness aversion and preference for commitment.' Theory and Decision 72: 113. Dubra, J., 2011.`Continuity and completeness under risk.' Mathematical Social Sciences 61, 8081. Dubra, J., Maccheroni, F., and Ok, E., 2004. `Expected utility theory without the completeness axiom.' Journal of Economic Theory 115: 118133. Evren, Ö., 2008. `On the existence of expected multiutility representations.' Economic Theory 35: 575592. Evren, Ö., 2014. `Scalarization methods and expected multiutility representations.' Journal of Economic Theory 151: 3063. Galaabaatar, T. and Karni, E., 2012. `Expected multiutility representations.' Mathematical Social Sciences 64: 242246. Galaabaatar, T. and Karni, E., 2013. `Subjective expected utility with incomplete preferences.' Econometrica 81: 255284. Ghirardato, P., Maccheroni, F., Marinacci, M., and Siniscalchi, M., 2003. `A subjective spin on roulette wheels.' Econometrica 71: 18971908. Gilboa, I., Maccheroni, F., Marinacci, M. and Schmeidler, D., 2010. `Objective and subjective rationality in a multiple prior model.' Econometrica 78: 755770. Hausner, M., Wendel, J., 1952 `Ordered vector spaces.' Proceedings of the American Mathematical Society 3, 977982. Herstein, I. and Milnor, J., 1953. `An axiomatic approach to measurable utility.' Econometrica 21: 291297. Karni, E., 2007.`Archimedean and continuity.' Mathematical Social Sciences 53: 332334. Kopylov, I., 2009. `Choice deferral and ambiguity aversion.' Theoretical Economics 4: 199225. Manzini, P. and Mariotti, M., 2008. `On the representation of incomplete preferences over risky alternatives.' Theory and Decision 65: 303323. McCarthy, D., Mikkola, K., Thomas, T., 2017a. `Representation of strongly independent preorders by sets of scalarvalued functions.' MPRA Paper No. 79284 https://mpra.ub.unimuenchen.de/79284/ McCarthy, D., Mikkola, K., Thomas, T., 2017b.`Representation of strongly independent strict partial orders by scalarvalued utility functions.' Mimeo. McCarthy, D., Mikkola, K., Thomas, T., 2017c. `Representation of strongly independent preorders by vectorvalued functions.' Mimeo Nau, R., 2006. `The shape of incomplete preferences' Annals of Statistics} 34; 24302448. Ok, E., 2007. Real Analysis with Economic Applications. Princeton, Princeton University Press. Ok, E., Ortoleva, P. and Riella, G., 2012. `Incomplete preferences under uncertainty: Indecisiveness in beliefs vs. tastes.' Econometrica 80: 17911808. Schmeidler, D., 1971. `A condition for the completeness of partial preference relations.' Econometrica 39: 403404. Seidenfeld, T., Schervish, M. and Kadane, J., 1995. `A representation of partially ordered preferences.' Annals of Statistics 23: 21682217. Shapley, L. and Baucells, M., 1998. `Multiperson utility.' UCLA Working Paper 779. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/79757 
Available Versions of this Item

Continuity and completeness of strongly independent preorders. (deposited 19 Jun 2017 13:13)
 Continuity and completeness of strongly independent preorders. (deposited 19 Jun 2017 14:29) [Currently Displayed]