IDEAS home Printed from https://ideas.repec.org/p/igi/igierp/632.html
   My bibliography  Save this paper

The Rational Core of Preference Relations

Author

Listed:
  • Simone Cerreia-Vioglio
  • Efe A. Ok

Abstract

We consider revealed preference relations over risky (or uncertain) prospects, and allow them to be nontransitive and/or fail the classical Independence Axiom. We identify the ?rational part ?of any such preference relation as its largest transitive subrelation that satis?fies the Independence Axiom and that exhibits some coherence with the original relation. It is shown that this subrelation, which we call the rational core of the given revealed preference, exists in general, and under fairly mild conditions, it is continuous. We obtain various representation theorems for the rational core, and decompose it into other core concepts for preferences. These theoretical results are applied to compute the rational cores of a number of well-known preference models (such as Fishburn?s SSB model, justi?fiable preferences, and variational and multiplier modes of rationalizable preferences). As for applications, we use the rational core operator to develop a theory of risk aversion for nontransitive nonexpected utility modals (which may not even be complete). Finally, we show that, under a basic monotonicity hypothesis, the Preference Reversal Phenomenon cannot arise from the rational core of one?s preferences. JEL Classifi?cation: D11, D81. Keywords: Transitive core, affine core, nontransitive nonexpected utility, justi?fiable preferences, comparative risk aversion, preference reversal phenomenon.

Suggested Citation

  • Simone Cerreia-Vioglio & Efe A. Ok, 2018. "The Rational Core of Preference Relations," Working Papers 632, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    • Handle: RePEc:igi:igierp:632
    as

    Download full text from publisher

    File URL: https://repec.unibocconi.it/igier/igi/wp/2018/632.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    2. Kazuhiro Hara & Efe A. Ok & Gil Riella, 2019. "Coalitional Expected Multi‐Utility Theory," Econometrica, Econometric Society, vol. 87(3), pages 933-980, May.
    3. 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.
    4. 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.
    5. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    6. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    7. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 163-172.
    8. Nishimura, Hiroki, 2018. "The transitive core: inference of welfare from nontransitive preference relations," Theoretical Economics, Econometric Society, vol. 13(2), May.
    9. Lehrer, Ehud & Teper, Roee, 2011. "Justifiable preferences," Journal of Economic Theory, Elsevier, vol. 146(2), pages 762-774, March.
    10. 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.
    11. 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.
    12. ,, 2016. "Objective rationality and uncertainty averse preferences," Theoretical Economics, Econometric Society, vol. 11(2), May.
    13. 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..
    14. Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
    15. Grether, David M & Plott, Charles R, 1979. "Economic Theory of Choice and the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 69(4), pages 623-638, September.
    16. 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.
    17. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    18. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    19. 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.
    20. Yuval Salant & Ariel Rubinstein, 2008. "(A, f): Choice with Frames -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1287-1296.
    21. Fishburn, P.C., 1984. "SSB Utility theory: an economic perspective," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 63-94, August.
    22. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    23. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    24. 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.
    25. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Uyanik, Metin & Khan, M. Ali, 2022. "The continuity postulate in economic theory: A deconstruction and an integration," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    2. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    3. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    4. Borie, Dino, 2023. "Purely subjective revealed ambiguity," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    5. Uyanık, Metin & Khan, M. Ali, 2019. "On the consistency and the decisiveness of the double-minded decision-maker," Economics Letters, Elsevier, vol. 185(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    2. Faro, José Heleno, 2015. "Variational Bewley preferences," Journal of Economic Theory, Elsevier, vol. 157(C), pages 699-729.
    3. Andrew J. Keith & Darryl K. Ahner, 2021. "A survey of decision making and optimization under uncertainty," Annals of Operations Research, Springer, vol. 300(2), pages 319-353, May.
    4. Elena Cettolin & Arno Riedl, 2015. "Revealed Incomplete Preferences under Uncertainty," CESifo Working Paper Series 5359, CESifo.
    5. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. 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.
    7. Ilke AYDOGAN & Loïc BERGER & Valentina BOSETTI & Ning LIU, 2022. "Three layers of uncertainty," Working Papers 2022-iRisk-01, IESEG School of Management.
    8. Guo, Liang, 2021. "Contextual deliberation and the choice-valuation preference reversal," Journal of Economic Theory, Elsevier, vol. 195(C).
    9. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2019. "Boolean Representations of Preferences under Ambiguity," Rationality and Competition Discussion Paper Series 173, CRC TRR 190 Rationality and Competition.
    10. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    11. Madhav Chandrasekher & Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2022. "Dual‐Self Representations of Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(3), pages 1029-1061, May.
    12. Nobuo Koida, 2021. "Intransitive indifference with direction-dependent sensitivity," KIER Working Papers 1061, Kyoto University, Institute of Economic Research.
    13. repec:hal:journl:hal-03031751 is not listed on IDEAS
    14. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    15. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    16. Ghirardato, Paolo & Pennesi, Daniele, 2020. "A general theory of subjective mixtures," Journal of Economic Theory, Elsevier, vol. 188(C).
    17. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2019. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2180, Cowles Foundation for Research in Economics, Yale University.
    18. Heller, Yuval, 2012. "Justifiable choice," Games and Economic Behavior, Elsevier, vol. 76(2), pages 375-390.
    19. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    20. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Stochastic Dominance Analysis Without the Independence Axiom," Management Science, INFORMS, vol. 63(4), pages 1097-1109, April.
    21. Robert G. Chambers & Tigran Melkonyan & John Quiggin, 2022. "Incomplete preferences, willingness to pay, and willingness to accept," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 727-761, October.

    More about this item

    Keywords

    transitive core; affine core; nontransitive nonexpected utility; justi?fiable preferences; comparative risk aversion; preference reversal phenomenon.;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:igi:igierp:632. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.igier.unibocconi.it/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.