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Testing independence conditions in the presence of errors and splitting effects

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  • Birnbaum, Michael H.
  • Schmidt, Ulrich
  • Schneider, Miriam D.

Abstract

This paper presents an experimental test of several independence conditions implied by expected utility and alternative models. We perform a repeated choice experiment and fit an error model that allows us to discriminate between true violations of independence and those that can be attributed to errors. In order to investigate the role of event splitting effects, we present each choice problem not only in coalesced form (as in most previous studies) but also in split form. It turns out previously reported violations of independence and splitting effects remain significant even when controlling for errors. Splitting effects have a substantial influence on the tests of independence conditions. When choices are presented in canonical split form, in which probabilities on corresponding probability-consequence ranked branches are equal, violations of the independence conditions we tested become either reversed, insignificant or unsystematic.

Suggested Citation

  • Birnbaum, Michael H. & Schmidt, Ulrich & Schneider, Miriam D., 2010. "Testing independence conditions in the presence of errors and splitting effects," Kiel Working Papers 1614, Kiel Institute for the World Economy (IfW).
  • Handle: RePEc:zbw:ifwkwp:1614
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    1. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    2. Starmer, Chris & Sugden, Robert, 1993. "Testing for Juxtaposition and Event-Splitting Effects," Journal of Risk and Uncertainty, Springer, vol. 6(3), pages 235-254, June.
    3. John Hey & Andrea Morone & Ulrich Schmidt, 2009. "Noise and bias in eliciting preferences," Journal of Risk and Uncertainty, Springer, vol. 39(3), pages 213-235, December.
    4. Berg, Joyce E. & Dickhaut, John W. & Rietz, Thomas A., 2010. "Preference reversals: The impact of truth-revealing monetary incentives," Games and Economic Behavior, Elsevier, vol. 68(2), pages 443-468, March.
    5. Humphrey, Steven J, 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.
    6. Butler, David & Loomes, Graham, 2011. "Imprecision as an account of violations of independence and betweenness," Journal of Economic Behavior & Organization, Elsevier, vol. 80(3), pages 511-522.
    7. 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.
    8. David Buschena & David Zilberman, 2008. "Generalized expected utility, heteroscedastic error, and path dependence in risky choice," Journal of Risk and Uncertainty, Springer, vol. 36(2), pages 201-201, April.
    9. 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.
    10. Hey, John D & Orme, Chris, 1994. "Investigating Generalizations of Expected Utility Theory Using Experimental Data," Econometrica, Econometric Society, vol. 62(6), pages 1291-1326, November.
    11. R. Luce & C. Ng & A. Marley & János Aczél, 2008. "Utility of gambling II: risk, paradoxes, and data," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 165-187, August.
    12. Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 39-60, July.
    13. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    14. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    15. Martin Weber & Franz Eisenführ & Detlof von Winterfeldt, 1988. "The Effects of Splitting Attributes on Weights in Multiattribute Utility Measurement," Management Science, INFORMS, vol. 34(4), pages 431-445, April.
    16. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 585-603.
    17. James Cox & Vjollca Sadiraj & Ulrich Schmidt, 2015. "Paradoxes and mechanisms for choice under risk," Experimental Economics, Springer;Economic Science Association, vol. 18(2), pages 215-250, June.
    18. Luce, R. Duncan, 1991. "Rank- and sign-dependent linear utility models for binary gambles," Journal of Economic Theory, Elsevier, vol. 53(1), pages 75-100, February.
    19. Conte, Anna & Hey, John D. & Moffatt, Peter G., 2011. "Mixture models of choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 79-88, May.
    20. R. Luce & A. Marley, 2005. "Ranked Additive Utility Representations of Gambles: Old and New Axiomatizations," Journal of Risk and Uncertainty, Springer, vol. 30(1), pages 21-62, January.
    21. Michael H. Birnbaum, 2013. "True-and-error models violate independence and yet they are testable," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(6), pages 717-737, November.
    22. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    23. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
    24. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    25. 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.
    26. Michael H. Birnbaum & Ulrich Schmidt, 2015. "The Impact of Learning by Thought on Violations of Independence and Coalescing," Decision Analysis, INFORMS, vol. 12(3), pages 144-152.
    27. Ulrich Schmidt & Tibor Neugebauer, 2007. "Testing expected utility in the presence of errors," Economic Journal, Royal Economic Society, vol. 117(518), pages 470-485, March.
    28. Hey, John D., 1995. "Experimental investigations of errors in decision making under risk," European Economic Review, Elsevier, vol. 39(3-4), pages 633-640, April.
    29. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    30. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 259-286, June.
    31. 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.
    32. Chris Starmer, 1992. "Testing New Theories of Choice under Uncertainty using the Common Consequence Effect," Review of Economic Studies, Oxford University Press, vol. 59(4), pages 813-830.
    33. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    34. 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.
    35. Michael H. Birnbaum & Jeffrey P. Bahra, 2012. "Separating response variability from structural inconsistency to test models of risky decision making," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 7(4), pages 402-426, July.
    36. Glenn Harrison & E. Rutström, 2009. "Expected utility theory and prospect theory: one wedding and a decent funeral," Experimental Economics, Springer;Economic Science Association, vol. 12(2), pages 133-158, June.
    37. Green, Jerry R & Jullien, Bruno, 1988. "Ordinal Independence in Nonlinear Utility Theory," Journal of Risk and Uncertainty, Springer, vol. 1(4), pages 355-387, December.
    38. Pavlo R. Blavatskyy, 2011. "A Model of Probabilistic Choice Satisfying First-Order Stochastic Dominance," Management Science, INFORMS, vol. 57(3), pages 542-548, March.
    39. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    40. Humphrey, Steven J, 1995. "Regret Aversion or Event-Splitting Effects? More Evidence under Risk and Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 11(3), pages 263-274, December.
    41. 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.
    42. Blavatskyy, Pavlo R., 2008. "Stochastic utility theorem," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1049-1056, December.
    43. Graham Loomes, 2005. "Modelling the Stochastic Component of Behaviour in Experiments: Some Issues for the Interpretation of Data," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 301-323, December.
    44. 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.
    45. 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.
    46. Steven Humphrey, 2006. "Does Learning Diminish Violations of Independence, Coalescing and Monotonicity?," Theory and Decision, Springer, vol. 61(2), pages 93-128, September.
    47. 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.
    48. Michael H. Birnbaum & Kathleen Johnson & Jay-Lee Longbottom, 2008. "Tests of Cumulative Prospect Theory with graphical displays of probability," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 3(7), pages 528-546, October.
    49. Bateman, Ian J, et al, 1997. "Does Part-Whole Bias Exist? An Experimental Investigation," Economic Journal, Royal Economic Society, vol. 107(441), pages 322-332, March.
    50. Ulrich Schmidt & Christian Seidl, 2014. "Reconsidering the common ratio effect: the roles of compound independence, reduction, and coalescing," Theory and Decision, Springer, vol. 77(3), pages 323-339, October.
    51. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    52. 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.
    53. Marley, A A J & Luce, R Duncan, 2001. "Ranked-Weighted Utilities and Qualitative Convolution," Journal of Risk and Uncertainty, Springer, vol. 23(2), pages 135-163, September.
    54. Birnbaum, Michael H., 2006. "Evidence against prospect theories in gambles with positive, negative, and mixed consequences," Journal of Economic Psychology, Elsevier, vol. 27(6), pages 737-761, December.
    55. Doron Sonsino & Uri Benzion & Galit Mador, 2002. "The Complexity Effects on Choice with Uncertainty — Experimental Evidence," Economic Journal, Royal Economic Society, vol. 112(482), pages 936-965, October.
    56. Luce, R Duncan & Fishburn, Peter C, 1991. "Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 29-59, January.
    57. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    58. Pavlo Blavatskyy, 2012. "Probabilistic choice and stochastic dominance," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 59-83, May.
    59. R. Luce & C. Ng & A. Marley & János Aczél, 2008. "Utility of gambling I: entropy modified linear weighted utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 1-33, July.
    60. Wakker, Peter & Erev, Ido & Weber, Elke U, 1994. "Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 195-230, December.
    61. David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
    62. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    63. Ulrich Schmidt & John D. Hey, 2004. "Are Preference Reversals Errors? An Experimental Investigation," Journal of Risk and Uncertainty, Springer, vol. 29(3), pages 207-218, December.
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    More about this item

    Keywords

    Independence axiom; splitting effects; coalescing; errors; experiment;

    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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