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An empirical test of ordinal independence

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Abstract

In this article, we test Green and Jullien's (1988) Ordinal Independence (OI) Axiom, an axiom necessary for any rank-dependent expected utility (RDEU) model, including Cumulative Prospect Theory (Tversky and Kahneman, 1992). We observe systematic violations of OI (some within-subject violation rates of over 50%). These patterns of choice cannot be explained by any RDEU theory alone. We suggest that subjects are employing an editing operation prior to evaluation: if an outcome-probability pair is common to both gambles, it is cancelled when the commonality is transparent; otherwise, it is not cancelled. We interpret the results with respect to both original and cumulative prospect theory and the known empirical properties of the weighting function.

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References

  • Camerer, Colin. (1989). “An Experimental Test of Several Generalized Utility Theories,”Journal of Risk and Uncertainty 2, 61–104.

    Google Scholar 

  • Camerer, Colin. (1992). “Recent Tests of Generalizations of Expected Utility Theory.” In Ward Edwards (ed.),Utility: Theories, Measurement, and Applications. Boston: Kluwer Academic, pp. 207–251.

    Google Scholar 

  • Camerer, Colin, and Teck-Hua Ho. (1994). “Violations of the Betweenness Axiom and Nonlinearity in Probability,” Journal of Risk and Uncertainty 8, 167–196.

    Google Scholar 

  • Chew, Soo-Hong and Kenneth R. MacCrimmon (1979). “Alpha-nu Choice Theory: An Axiomatization of Expected Utility,” Faculty of Commerce Working Paper No. 669, University of British Columbia.

  • Conlisk, John. (1989). “Three Variants on the Allais Example,”American Economic Review 79, 392–407.

    Google Scholar 

  • Gonzalez, Richard (1993). “Estimating the weighting function,” paper presented at the 26th Annual Mathematical Psychology Meeting.

  • Gonzalez, Richard and George Wu (1994). “New Directions in Modeling Risky Choice,” paper presented at the 37th TIMS/ORSA meeting, Boston, MA.

  • Green, Jerry R., and Bruno Jullien. (1988). “Ordinal Independence in Nonlinear Utility Theory,”Journal of Risk and Uncertainty 1, 355–387.

    Google Scholar 

  • Huber, Joel, John W. Payne, and Christopher Puto. (1982). “Adding Asymmetrically Dominated Alternatives: Violations of Regularity and the Similarity Hypothesis,”Journal of Consumer Research 9, 90–98.

    Google Scholar 

  • Kahneman, Daniel, and Amos Tversky. (1979). “Prospect Theory: An Analysis of Decision under Risk,”Econometrica 47, 263–291.

    Google Scholar 

  • Luce, R. Duncan, and Peter C. Fishburn. (1991). “Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles,”Journal of Risk and Uncertainty 4, 29–59.

    Google Scholar 

  • Machina, Mark (1982). “‘Expected Utility’ Analysis without the Independence Axiom,”Econometrica 50, 277–323.

    Google Scholar 

  • Machina, Mark J. (1987). “Choice under Uncertainty: Problems Solved and Unsolved,”Journal of Economic Perspectives 1, 121–154.

    Google Scholar 

  • Pratt, John W. (1964). “Risk Aversion in the Small and in the Large,”Econometrica 32, 122–136.

    Google Scholar 

  • Prelec, Drazen. (1990). “A ‘Pseudo-endowment’ Effect, and its Implications for Some Recent Nonexpected Utility Models,”Journal of Risk and Uncertainty 3, 247–259.

    Google Scholar 

  • Prelec, Drazen. (1993). “The Probability Weighting Function,” unpublished paper.

  • Quiggin, John. (1982). “A Theory of Anticipated Utility,”Journal of Economic Behavior and Organization, 323–343.

  • Simonson, Itamar and Amos Tversky (1992). “Choice in Context:Tradeoff Contrast and Extremeness Aversion,”Journal of Marketing Research 29, 281–295.

    Google Scholar 

  • Starmer, Chris and Robert Sugden. (1989). “Violations of the Independence Axiom in Common Ratio Problems: An Experimental Test of Some Competing Hypotheses,”Annals of Operations Research 19, 79–101.

    Google Scholar 

  • Starmer, Chris, and Robert Sugden. (1993). “Testing for Juxtaposition and Event-Splitting Effects,”Journal of Risk and Uncertainty 6, 235–254.

    Google Scholar 

  • Tversky, Amos (1969). “The Intransitivity of Preferences,”Psychological Review 76, 31–48.

    Google Scholar 

  • Tversky, Amos, and Daniel Kahneman (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,”Journal of Risk and Uncertainty 5, 297–323.

    Google Scholar 

  • Wakker, Peter P., Ido Erev, and Elke U. Weber (1993). “Comonotonic Independence: The Critical Test between Classical and Rank-dependent Utility Theories,” unpublished paper.

  • Wakker, Peter P., and Amos Tversky. (1993). “An Axiomatization of Cumulative Prospect Theory,”Journal of Risk and Uncertainty 8, 147–176.

    Google Scholar 

  • Yaari, Menahem E. (1987). “The Dual Theory of Choice Under Risk,”Econometrica 55, 95–117.

    Google Scholar 

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Wu, G. An empirical test of ordinal independence. J Risk Uncertainty 9, 39–60 (1994). https://doi.org/10.1007/BF01073402

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  • DOI: https://doi.org/10.1007/BF01073402

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