IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v109y2023ics0304406823001088.html
   My bibliography  Save this article

The Sure-Thing Principle

Author

Listed:
  • Baccelli, Jean
  • Hartmann, Lorenz

Abstract

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe-Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance.

Suggested Citation

  • Baccelli, Jean & Hartmann, Lorenz, 2023. "The Sure-Thing Principle," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    • Handle: RePEc:eee:mateco:v:109:y:2023:i:c:s0304406823001088
    DOI: 10.1016/j.jmateco.2023.102915
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406823001088
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2023.102915?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ivan Moscati, 2016. "Retrospectives: How Economists Came to Accept Expected Utility Theory: The Case of Samuelson and Savage," Journal of Economic Perspectives, American Economic Association, vol. 30(2), pages 219-236, Spring.
    2. Samet, Dov, 2022. "The impossibility of agreeing to disagree: An extension of the sure-thing principle," Games and Economic Behavior, Elsevier, vol. 132(C), pages 390-399.
    3. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    4. Marc Fleurbaey, 2010. "Assessing Risky Social Situations," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 649-680, August.
    5. Alex Bara & Gift Mugano & Pierre Le Roux, 2017. "Financial Development and Economic Growth in SADC: Cross Country Spatial Spill-Over Effects," Working Papers 97, Economic Research Southern Africa.
    6. Franz Dietrich & Antonios Staras & Robert Sugden, 2021. "Savage’s response to Allais as Broomean reasoning," Journal of Economic Methodology, Taylor & Francis Journals, vol. 28(2), pages 143-164, April.
    7. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    8. Lorenz Hartmann, 2020. "Savage's P3 Is Redundant," Econometrica, Econometric Society, vol. 88(1), pages 203-205, January.
    9. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    10. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, November.
    11. Zimper Alexander, 2008. "Revisiting Independence and Stochastic Dominance for Compound Lotteries," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-11, April.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. Luyao Zhang & Dan Levin, 2017. "Bounded Rationality and Robust Mechanism Design: An Axiomatic Approach," American Economic Review, American Economic Association, vol. 107(5), pages 235-239, May.
    14. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    15. 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.
    16. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    17. Hong, Chew Soo & Wakker, Peter, 1996. "The Comonotonic Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 12(1), pages 5-27, January.
    18. Grant, Simon & Kajii, Atsushi & Polak, Ben, 2000. "Decomposable Choice under Uncertainty," Journal of Economic Theory, Elsevier, vol. 92(2), pages 169-197, June.
    19. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804, November.
    20. Milton Friedman & L. J. Savage, 1952. "The Expected-Utility Hypothesis and the Measurability of Utility," Journal of Political Economy, University of Chicago Press, vol. 60(6), pages 463-463.
    21. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    Full references (including those not matched with items on IDEAS)

    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. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    2. Echenique, Federico & Miyashita, Masaki & Nakamura, Yuta & Pomatto, Luciano & Vinson, Jamie, 2022. "Twofold multiprior preferences and failures of contingent reasoning," Journal of Economic Theory, Elsevier, vol. 202(C).
    3. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    4. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    5. Monet, Benjamin & Vergopoulos, Vassili, 2022. "Subjective probability and stochastic independence," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    6. Xiangyu Qu, 2015. "Purely subjective extended Bayesian models with Knightian unambiguity," Theory and Decision, Springer, vol. 79(4), pages 547-571, December.
    7. Bommier, Antoine, 2017. "A dual approach to ambiguity aversion," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 104-118.
    8. Nobuo Koida, 2012. "Nest-monotonic two-stage acts and exponential probability capacities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 99-124, May.
    9. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    10. 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.
    11. Mayumi Horie, 2016. "Bayesian Updating for Complementarily Additive Beliefs under Ambiguity," KIER Working Papers 935, Kyoto University, Institute of Economic Research.
    12. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    13. Craig Webb, 2013. "Bargaining with subjective mixtures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 15-39, January.
    14. Baillon, Aurélien & Driesen, Bram & Wakker, Peter P., 2012. "Relative concave utility for risk and ambiguity," Games and Economic Behavior, Elsevier, vol. 75(2), pages 481-489.
    15. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2012. "Probabilistic sophistication, second order stochastic dominance and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 271-283.
    16. Junyi Chai & Zhiquan Weng & Wenbin Liu, 2021. "Behavioral Decision Making in Normative and Descriptive Views: A Critical Review of Literature," JRFM, MDPI, vol. 14(10), pages 1-14, October.
    17. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    18. Yoram Halevy & Vincent Feltkamp, 2005. "A Bayesian Approach to Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 449-466.
    19. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    20. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.

    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:eee:mateco:v:109:y:2023:i:c:s0304406823001088. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.