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An experimental investigation of violations of transitivity in choice under uncertainty

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  • Michael Birnbaum
  • Ulrich Schmidt

Abstract

Several models of choice under uncertainty imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by these models. To distinguish "true" violations from those produced by "error", a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that does not need to be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of the same choice. Our results showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants.
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Suggested Citation

  • Michael Birnbaum & Ulrich Schmidt, 2008. "An experimental investigation of violations of transitivity in choice under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 37(1), pages 77-91, August.
  • Handle: RePEc:kap:jrisku:v:37:y:2008:i:1:p:77-91
    DOI: 10.1007/s11166-008-9043-z
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    1. Michael Birnbaum, 2005. "A Comparison of Five Models that Predict Violations of First-Order Stochastic Dominance in Risky Decision Making," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 263-287, December.
    2. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    3. Robert Bordley & Gordon B. Hazen, 1991. "SSB and Weighted Linear Utility As Expected Utility with Suspicion," Management Science, INFORMS, vol. 37(4), pages 396-408, April.
    4. Steven Humphrey, 2001. "Non‐transitive Choice: Event‐Splitting Effects or Framing Effects?," Economica, London School of Economics and Political Science, vol. 68(269), pages 77-96, February.
    5. Enrica Carbone & John D. Hey, 2018. "Which Error Story is Best?," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 16, pages 365-380, World Scientific Publishing Co. Pte. Ltd..
    6. Iverson, G. & Falmagne, J. -C., 1985. "Statistical issues in measurement," Mathematical Social Sciences, Elsevier, vol. 10(2), pages 131-153, October.
    7. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    8. Loomes, Graham & Starmer, Chris & Sugden, Robert, 1991. "Observing Violations of Transitivity by Experimental Methods," Econometrica, Econometric Society, vol. 59(2), pages 425-439, March.
    9. Michael H. Birnbaum, 2005. "Three New Tests of Independence That Differentiate Models of Risky Decision Making," Management Science, INFORMS, vol. 51(9), pages 1346-1358, September.
    10. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    11. Schoemaker, Paul J. H. & Hershey, John C., 1992. "Utility measurement: Signal, noise, and bias," Organizational Behavior and Human Decision Processes, Elsevier, vol. 52(3), pages 397-424, August.
    12. Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
    13. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    14. Loomes, Graham & Starmer, Chris & Sugden, Robert, 1989. "Preference Reversal: Information-Processing Effect or Rational Non-transitive Choice?," Economic Journal, Royal Economic Society, vol. 99(395), pages 140-151, Supplemen.
    15. Ulrich Schmidt & Stefan Traub (ed.), 2005. "Advances in Public Economics: Utility, Choice and Welfare," Theory and Decision Library C, Springer, number 978-0-387-25706-8, September.
    16. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-824, December.
    17. Chris Starmer, 1999. "Cycling with Rules of Thumb: An Experimental Test for a new form of Non-Transitive Behaviour," Theory and Decision, Springer, vol. 46(2), pages 139-157, April.
    18. Jonathan W. Leland, 1998. "Similarity Judgments in Choice Under Uncertainty: A Reinterpretation of the Predictions of Regret Theory," Management Science, INFORMS, vol. 44(5), pages 659-672, May.
    19. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    20. repec:bla:econom:v:65:y:1998:i:259:p:347-61 is not listed on IDEAS
    21. Viscusi, W Kip, 1989. "Prospective Reference Theory: Toward an Explanation of the Paradoxes," Journal of Risk and Uncertainty, Springer, vol. 2(3), pages 235-263, September.
    22. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
    23. Loomes, Graham & Taylor, Caron, 1992. "Non-transitive Preferences over Gains and Losses," Economic Journal, Royal Economic Society, vol. 102(411), pages 357-365, March.
    24. Birnbaum, Michael H & Navarrete, Juan B, 1998. "Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence," Journal of Risk and Uncertainty, Springer, vol. 17(1), pages 49-78, October.
    25. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
    26. Pavlo Blavatskyy, 2006. "Axiomatization of a Preference for Most Probable Winner," Theory and Decision, Springer, vol. 60(1), pages 17-33, February.
    27. Bordley, Robert F, 1992. "An Intransitive Expectations-Based Bayesian Variant of Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 5(2), pages 127-144, May.
    28. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    29. Sugden, Robert, 2003. "Reference-dependent subjective expected utility," Journal of Economic Theory, Elsevier, vol. 111(2), pages 172-191, August.
    30. Camerer, Colin F, 1989. "An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 61-104, April.
    31. Peter Fishburn, 1980. "A simple model for the utility of gambling," Psychometrika, Springer;The Psychometric Society, vol. 45(4), pages 435-448, December.
    32. Pavlo R. Blavatskyy, "undated". "Axiomatization of a Preference for Most Probable Winner," IEW - Working Papers 230, Institute for Empirical Research in Economics - University of Zurich.
    33. Leland, Jonathan W, 1994. "Generalized Similarity Judgments: An Alternative Explanation for Choice Anomalies," Journal of Risk and Uncertainty, Springer, vol. 9(2), pages 151-172, October.
    34. Han Bleichrodt & Ulrich Schmidt, 2002. "A Context-Dependent Model of the Gambling Effect," Management Science, INFORMS, vol. 48(6), pages 802-812, June.
    35. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    36. Michael Birnbaum & Ulrich Schmidt, 2010. "Testing transitivity in choice under risk," Theory and Decision, Springer, vol. 69(4), pages 599-614, October.
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    More about this item

    Keywords

    Choice; Decision making; Errors; Regret theory; Transitivity; C91; D81;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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