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A test of (weak) certainty independence

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  • König-Kersting, Christian
  • Kops, Christopher
  • Trautmann, Stefan T.

Abstract

We provide a test of the axioms of certainty and weak certainty independence in models of decision-making under subjective uncertainty. We show that it is through these two weakenings of the classic independence axiom that prominent ambiguity models retain properties that stand in conflict with the ambiguity-sensitive behavior that is revealed in our experiment. Our findings suggest that this conflict may be of a more fundamental nature than what most of these models can accommodate. Our results call for the use of ambiguity models that can accommodate an ambiguity attitude which depends on the chances of winning.

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  • König-Kersting, Christian & Kops, Christopher & Trautmann, Stefan T., 2023. "A test of (weak) certainty independence," Journal of Economic Theory, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:jetheo:v:209:y:2023:i:c:s0022053123000194
    DOI: 10.1016/j.jet.2023.105623
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    1. Olivier L’Haridon & Lætitia Placido, 2010. "Betting on Machina’s reflection example: an experiment on ambiguity," Theory and Decision, Springer, vol. 69(3), pages 375-393, September.
    2. David Kelsey & Sara Roux, 2015. "An experimental study on the effect of ambiguity in a coordination game," Theory and Decision, Springer, vol. 79(4), pages 667-688, December.
    3. Aurelien Baillon & Olivier L'Haridon & Laetitia Placido, 2011. "Ambiguity Models and the Machina Paradoxes," American Economic Review, American Economic Association, vol. 101(4), pages 1547-1560, June.
    4. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    5. Aurélien Baillon & Yoram Halevy & Chen Li, 2022. "Experimental elicitation of ambiguity attitude using the random incentive system," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 1002-1023, June.
    6. Mohammed Abdellaoui & Peter Klibanoff & Lætitia Placido, 2015. "Experiments on Compound Risk in Relation to Simple Risk and to Ambiguity," Management Science, INFORMS, vol. 61(6), pages 1306-1322, June.
    7. Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
    8. Camerer, Colin F & Hogarth, Robin M, 1999. "The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework," Journal of Risk and Uncertainty, Springer, vol. 19(1-3), pages 7-42, December.
    9. Robin M. Hogarth & Hillel J. Einhorn, 1990. "Venture Theory: A Model of Decision Weights," Management Science, INFORMS, vol. 36(7), pages 780-803, July.
    10. Larry G. Epstein & Martin Schneider, 2008. "Ambiguity, Information Quality, and Asset Pricing," Journal of Finance, American Finance Association, vol. 63(1), pages 197-228, February.
    11. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    12. Aurélien Baillon & Yoram Halevy & Chen Li, 2022. "Randomize at Your Own Risk: On the Observability of Ambiguity Aversion," Econometrica, Econometric Society, vol. 90(3), pages 1085-1107, May.
    13. 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.
    14. David J. Freeman & Yoram Halevy & Terri Kneeland, 2019. "Eliciting risk preferences using choice lists," Quantitative Economics, Econometric Society, vol. 10(1), pages 217-237, January.
    15. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    16. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    17. H. Henry Cao & Tan Wang & Harold H. Zhang, 2005. "Model Uncertainty, Limited Market Participation, and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1219-1251.
    18. Luciano Castro & Alain Chateauneuf, 2011. "Ambiguity aversion and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 243-273, October.
    19. Kajii, Atsushi & Ui, Takashi, 2006. "Agreeable bets with multiple priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 299-305, May.
    20. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(4), pages 883-904.
    21. Roee Teper, 2015. "Subjective Independence and Concave Expected Utility," Working Paper 5865, Department of Economics, University of Pittsburgh.
    22. Chateauneuf, Alain & Faro, José Heleno, 2009. "Ambiguity through confidence functions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 535-558, September.
    23. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    24. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    25. Larry G. Epstein & Martin Schneider, 2010. "Ambiguity and Asset Markets," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 315-346, December.
    26. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    27. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    28. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    29. Mark J. Machina, 2009. "Risk, Ambiguity, and the Rank-Dependence Axioms," American Economic Review, American Economic Association, vol. 99(1), pages 385-392, March.
    30. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    31. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    32. Prokosheva, Sasha, 2016. "Comparing decisions under compound risk and ambiguity: The importance of cognitive skills," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 64(C), pages 94-105.
    33. Scott Condie & Jayant Ganguli, 2011. "Informational efficiency with ambiguous information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 229-242, October.
    34. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    35. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    36. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    37. Bryan Routledge & Stanley Zin, 2009. "Model Uncertainty and Liquidity," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(4), pages 543-566, October.
    38. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    39. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    40. Kajii, Atsushi & Ui, Takashi, 2009. "Interim efficient allocations under uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 337-353, January.
    41. David Kelsey & Sara le Roux, 2018. "Strategic ambiguity and decision-making: an experimental study," Theory and Decision, Springer, vol. 84(3), pages 387-404, May.
    42. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    43. Kocher, Martin G. & Lahno, Amrei Marie & Trautmann, Stefan T., 2018. "Ambiguity aversion is not universal," European Economic Review, Elsevier, vol. 101(C), pages 268-283.
    44. Smith, Vernon L & Walker, James M, 1993. "Monetary Rewards and Decision Cost in Experimental Economics," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 245-261, April.
    45. Lehrer, Ehud & Teper, Roee, 2015. "Subjective independence and concave expected utility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 33-53.
    46. Ben Gillen & Erik Snowberg & Leeat Yariv, 2019. "Experimenting with Measurement Error: Techniques with Applications to the Caltech Cohort Study," Journal of Political Economy, University of Chicago Press, vol. 127(4), pages 1826-1863.
    47. Roee Teper, 2015. "Subjective Independence and Concave Expected Utility," Working Paper 5866, Department of Economics, University of Pittsburgh.
    48. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.
    49. Oechssler, Jörg & Roomets, Alex, 2015. "A test of mechanical ambiguity," Journal of Economic Behavior & Organization, Elsevier, vol. 119(C), pages 153-162.
    50. Alain Chateauneuf & Luciano De Castro, 2011. "Ambiguity Aversion and Absence of Trade," Discussion Papers 1535, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    51. Aurélien Baillon & Han Bleichrodt, 2015. "Testing Ambiguity Models through the Measurement of Probabilities for Gains and Losses," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 77-100, May.
    52. Stephen G. Dimmock & Roy Kouwenberg & Peter P. Wakker, 2016. "Ambiguity Attitudes in a Large Representative Sample," Management Science, INFORMS, vol. 62(5), pages 1363-1380, May.
    53. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    54. Casey, Jeff T. & Scholz, John T., 1991. "Boundary effects of vague risk information on taxpayer decisions," Organizational Behavior and Human Decision Processes, Elsevier, vol. 50(2), pages 360-394, December.
    55. Dimmock, Stephen G. & Kouwenberg, Roy & Mitchell, Olivia S. & Peijnenburg, Kim, 2016. "Ambiguity aversion and household portfolio choice puzzles: Empirical evidence," Journal of Financial Economics, Elsevier, vol. 119(3), pages 559-577.
    56. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    57. Baillon, Aurélien & Placido, Lætitia, 2019. "Testing constant absolute and relative ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 181(C), pages 309-332.
    58. Bade, Sophie, 2015. "Randomization devices and the elicitation of ambiguity-averse preferences," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 221-235.
    59. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    60. Oechssler, Jörg & Roomets, Alex, 2014. "Unintended hedging in ambiguity experiments," Economics Letters, Elsevier, vol. 122(2), pages 243-246.
    61. Oechssler, Jörg & Rau, Hannes & Roomets, Alex, 2019. "Hedging, ambiguity, and the reversal of order axiom," Games and Economic Behavior, Elsevier, vol. 117(C), pages 380-387.
    62. Han Ozsoylev & Jan Werner, 2011. "Liquidity and asset prices in rational expectations equilibrium with ambiguous information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 469-491, October.
    63. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    64. Bock, Olaf & Baetge, Ingmar & Nicklisch, Andreas, 2014. "hroot: Hamburg Registration and Organization Online Tool," European Economic Review, Elsevier, vol. 71(C), pages 117-120.
    65. W. Viscusi & Harrell Chesson, 1999. "Hopes and Fears: the Conflicting Effects of Risk Ambiguity," Theory and Decision, Springer, vol. 47(2), pages 157-184, October.
    66. Curley, Shawn P. & Yates, J. Frank, 1985. "The center and range of the probability interval as factors affecting ambiguity preferences," Organizational Behavior and Human Decision Processes, Elsevier, vol. 36(2), pages 273-287, October.
    67. Mukerji, Sujoy, 1998. "Ambiguity Aversion and Incompleteness of Contractual Form," American Economic Review, American Economic Association, vol. 88(5), pages 1207-1231, December.
    68. Cettolin, Elena & Riedl, Arno, 2019. "Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization," Journal of Economic Theory, Elsevier, vol. 181(C), pages 547-585.
    69. Timothy N. Cason & Charles R. Plott, 2014. "Misconceptions and Game Form Recognition: Challenges to Theories of Revealed Preference and Framing," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1235-1270.
    70. Holt, Charles A, 1986. "Preference Reversals and the Independence Axiom," American Economic Review, American Economic Association, vol. 76(3), pages 508-515, June.
    71. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
    72. Kahn, Barbara E & Sarin, Rakesh K, 1988. "Modeling Ambiguity in Decisions under Uncertainty," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 15(2), pages 265-272, September.
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    More about this item

    Keywords

    Ellsberg paradox; Ellsberg urn; Machina paradox; Certainty independence; Weak certainty independence;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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