IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1210.4853.html
   My bibliography  Save this paper

Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions

Author

Listed:
  • Joseph Y. Halpern
  • Samantha Leung

Abstract

We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a natural approach to determining the weights. We then show how this representation can be used in decision-making, by modifying a standard approach to decision making-minimizing expected regret-to obtain minimax weighted expected regret (MWER).We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case.

Suggested Citation

  • Joseph Y. Halpern & Samantha Leung, 2012. "Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions," Papers 1210.4853, arXiv.org.
    • Handle: RePEc:arx:papers:1210.4853
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1210.4853
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    3. 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.
    4. Chateauneuf, Alain & Faro, José Heleno, 2009. "Ambiguity through confidence functions," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 535-558, September.
    5. 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.
    6. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    7. 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.
    8. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    9. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    10. Jaffray, J.Y., 1992. "Dynamic Decision Making with belief Functions," Papiers d'Economie Mathématique et Applications 92.63, Université Panthéon-Sorbonne (Paris 1).
    11. 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.
    12. Todd Sarver, 2008. "Anticipating Regret: Why Fewer Options May Be Better," Econometrica, Econometric Society, vol. 76(2), pages 263-305, March.
    13. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
    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. Stoye, Jörg, 2015. "Choice theory when agents can randomize," Journal of Economic Theory, Elsevier, vol. 155(C), pages 131-151.
    16. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    17. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    18. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    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. Joseph Y. Halpern & Samantha Leung, 2016. "Maxmin weighted expected utility: a simpler characterization," Theory and Decision, Springer, vol. 80(4), pages 581-610, April.
    2. Joseph Y. Halpern & Samantha Leung, 2016. "Minimizing regret in dynamic decision problems," Theory and Decision, Springer, vol. 81(1), pages 123-151, June.
    3. Kaiwen Li & Yuanming Song & Rui Wang, 2022. "Multi-Objective Optimal Sizing of HRES under Multiple Scenarios with Undetermined Probability," Mathematics, MDPI, vol. 10(9), pages 1-19, May.
    4. Karmellos, M. & Georgiou, P.N. & Mavrotas, G., 2019. "A comparison of methods for the optimal design of Distributed Energy Systems under uncertainty," Energy, Elsevier, vol. 178(C), pages 318-333.

    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. Takashi Hayashi, 2008. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," KIER Working Papers 659, Kyoto University, Institute of Economic Research.
    2. Takashi Hayashi, 2011. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," Theory and Decision, Springer, vol. 70(4), pages 399-430, April.
    3. Faro, José Heleno & Lefort, Jean-Philippe, 2019. "Dynamic objective and subjective rationality," Theoretical Economics, Econometric Society, vol. 14(1), January.
    4. Heyen, Daniel, 2018. "Ambiguity aversion under maximum-likelihood updating," LSE Research Online Documents on Economics 80342, London School of Economics and Political Science, LSE Library.
    5. Spyros Galanis, 2021. "Dynamic consistency, valuable information and subjective beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1467-1497, June.
    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. Beauchêne, Dorian & Li, Jian & Li, Ming, 2019. "Ambiguous persuasion," Journal of Economic Theory, Elsevier, vol. 179(C), pages 312-365.
    8. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    9. Massimo Marinacci, 2015. "Model Uncertainty," Journal of the European Economic Association, European Economic Association, vol. 13(6), pages 1022-1100, December.
    10. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    11. Daniel Heyen, 2018. "Ambiguity aversion under maximum-likelihood updating," Theory and Decision, Springer, vol. 84(3), pages 373-386, May.
    12. Hill, Brian, 2020. "Dynamic consistency and ambiguity: A reappraisal," Games and Economic Behavior, Elsevier, vol. 120(C), pages 289-310.
    13. Lorenzo Bastianello & José Heleno Faro & Ana Santos, 2022. "Dynamically consistent objective and subjective rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 477-504, September.
    14. Li, Jian & Zhou, Junjie, 2016. "Blackwell's informativeness ranking with uncertainty-averse preferences," Games and Economic Behavior, Elsevier, vol. 96(C), pages 18-29.
    15. Konstantinos Georgalos, 2019. "An experimental test of the predictive power of dynamic ambiguity models," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 51-83, August.
    16. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    17. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    18. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
    19. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    20. 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.

    More about this item

    JEL classification:

    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:arx:papers:1210.4853. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.