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Comparative Incompleteness: Measurement, Behavioral Manifestations and Elicitation

Author

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  • Edi Karni

    (Johns Hopkins University)

  • Marie-Louise Vierø

    (Department of Economics and Business Economics, Aarhus University)

Abstract

This paper introduces measures of overall incompleteness of preference relations under risk and uncertainty, as well as measures of incompleteness of beliefs and tastes. These measures are used to define 'more incomplete' than relations among different preference relations. We show how greater incompleteness is manifested in the representations of decision makers’ preferences and illustrate its behavioral implications in a simple portfolio choice problem. In addition, the paper introduces incentive compatible schemes of eliciting the degrees of overall incompleteness and those of beliefs and tastes.

Suggested Citation

  • Edi Karni & Marie-Louise Vierø, 2022. "Comparative Incompleteness: Measurement, Behavioral Manifestations and Elicitation," Economics Working Papers 2022-05, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:aarhec:2022-05
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    References listed on IDEAS

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    1. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
    2. Gil Riella, 2015. "On the representation of incomplete preferences under uncertainty with indecisiveness in tastes and beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 571-600, April.
    3. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    4. Karni, Edi, 2011. "Continuity, completeness and the definition of weak preferences," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 123-125, September.
    5. Edi Karni, 2020. "A mechanism for the elicitation of second-order belief and subjective information structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 217-232, February.
    6. 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.
    7. Massimiliano Amarante & Fabio Maccheroni, 2006. "When an Event Makes a Difference," Theory and Decision, Springer, vol. 60(2), pages 119-126, May.
    8. Robert Chambers & Tigran Melkonyan, 2020. "Incomplete Preferences and Equilibrium in Contingent Markets," Economica, London School of Economics and Political Science, vol. 87(345), pages 108-131, January.
    9. Arthur E. Attema & Han Bleichrodt & Olivier l’Haridon & Stefan A. Lipman, 2020. "A comparison of individual and collective decision making for standard gamble and time trade-off," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 21(3), pages 465-473, April.
    10. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.
    11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    12. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    13. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    14. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    15. Brian Hill & Mohammed Abdellaoui & Philippe Colo, 2021. "Eliciting Multiple Prior Beliefs," Working Papers hal-03503996, HAL.
    16. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    17. Abdellaoui, Mohammed & Colo, Philippe & Hill, Brian, 2021. "Eliciting Multiple Prior Beliefs," HEC Research Papers Series 1426, HEC Paris.
    18. 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.
    19. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, January.
    20. Chambers, Christopher P. & Lambert, Nicolas S., 2014. "Dynamically Eliciting Unobservable Information," Research Papers 3036, Stanford University, Graduate School of Business.
    21. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    22. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    23. Karni, Edi, 2020. "Probabilistic sophistication without completeness," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 8-13.
    24. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    25. Luca Rigotti & Chris Shannon, 2005. "Uncertainty and Risk in Financial Markets," Econometrica, Econometric Society, vol. 73(1), pages 203-243, January.
    26. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    27. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
    28. Eric Danan & Anthony Ziegelmeyer, 2006. "Are preferences complete? An experimental measurement of indecisiveness under risk," Papers on Strategic Interaction 2006-01, Max Planck Institute of Economics, Strategic Interaction Group.
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    Cited by:

    1. Edi Karni, 2024. "Irresolute choice behavior," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(1), pages 70-87, March.

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    More about this item

    Keywords

    Incomplete preferences; Knightian uncertainty; Comparative incompleteness; Elicitation mechanisms;
    All these keywords.

    JEL classification:

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

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