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Preferences with grades of indecisiveness

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  • Minardi, Stefania
  • Savochkin, Andrei

Abstract

Departing from the traditional approach of modeling indecisiveness based on the weakening of the completeness axiom, we introduce the notion of graded preferences: The agent is characterized by a binary relation over (ordered) pairs of alternatives, which allows her to express her inclination to prefer one alternative over another and her confidence in the relative superiority of the indicated alternative. In the classical Anscombe–Aumann framework, we derive a representation of a graded preference by a measure of the set of beliefs that rank one option better than the other. Our model is a refinement of Bewley's [6] model of Knightian uncertainty: It is based on the same object of representation — the set of beliefs — but provides more information about how the agent compares alternatives.

Suggested Citation

  • Minardi, Stefania & Savochkin, Andrei, 2015. "Preferences with grades of indecisiveness," Journal of Economic Theory, Elsevier, vol. 155(C), pages 300-331.
  • Handle: RePEc:eee:jetheo:v:155:y:2015:i:c:p:300-331
    DOI: 10.1016/j.jet.2014.11.009
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    1. Basu, Kaushik, 1987. "Axioms for a fuzzy measure of inequality," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 275-288, December.
    2. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    3. James S. Dyer & Rakesh K. Sarin, 1979. "Measurable Multiattribute Value Functions," Operations Research, INFORMS, vol. 27(4), pages 810-822, August.
    4. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    5. 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.
    6. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    7. Bruno S. Frey & Alois Stutzer, 2002. "What Can Economists Learn from Happiness Research?," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 402-435, June.
    8. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: A Study of Response Times," Economic Journal, Royal Economic Society, vol. 117(523), pages 1243-1259, October.
    9. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
    10. 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.
    11. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    12. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    13. Danan, Eric, 2008. "Revealed preference and indifferent selection," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 24-37, January.
    14. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    15. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    16. Faro, José Heleno, 2015. "Variational Bewley preferences," Journal of Economic Theory, Elsevier, vol. 157(C), pages 699-729.
    17. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2008. "Objective and Subjective Rationality," Levine's Working Paper Archive 122247000000001950, David K. Levine.
    18. John R. Hauser & Steven M. Shugan, 1980. "Intensity Measures of Consumer Preference," Operations Research, INFORMS, vol. 28(2), pages 278-320, April.
    19. Patrick Suppes & Muriel Winet, 1955. "An Axiomatization of Utility Based on the Notion of Utility Differences," Management Science, INFORMS, vol. 1(3-4), pages 259-270, 04-07.
    20. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    21. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    22. Basu, Kaushik, 1984. "Fuzzy revealed preference theory," Journal of Economic Theory, Elsevier, vol. 32(2), pages 212-227, April.
    23. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, January.
    24. Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
    25. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
    26. 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.
    27. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
    28. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    29. Ariel Rubinstein, 2007. "Instinctive and Cognitive Reasoning: Response Times Study," Levine's Bibliography 321307000000001011, UCLA Department of Economics.
    30. 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:

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    2. McClellon, Morgan, 2016. "Confidence models of incomplete preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 30-34.
    3. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    4. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," SIRE Discussion Papers 2015-17, Scottish Institute for Research in Economics (SIRE).
    5. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    6. Nobuo Koida, 2021. "Intransitive indifference with direction-dependent sensitivity," KIER Working Papers 1061, Kyoto University, Institute of Economic Research.
    7. Costa-Gomes, Miguel & Cueva, Carlos & Gerasimou, Georgios, 2014. "Choice, Deferral and Consistency," SIRE Discussion Papers 2015-17, Scottish Institute for Research in Economics (SIRE).
    8. Patrick Schmidt, 2019. "Eliciting ambiguity with mixing bets," Papers 1902.07447, arXiv.org, revised Jul 2022.

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    More about this item

    Keywords

    Incomplete preferences; Knightian uncertainty; Graded preferences; Confidence; Decisiveness;
    All these keywords.

    JEL classification:

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

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