IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4946.html
   My bibliography  Save this article

∀ or ∃?

Author

Listed:
  • Segal, Uzi

    (Department of Economics, Boston College)

Abstract

This paper shows that in some axioms regarding the mixture of random variables, the requirement that the conclusions hold for all values of the mixture parameter can be replaced by requiring the existence of only one non-trivial value of the parameter, which needs not be fixed. This is the case for the independence, betweenness, and the mixture symmetry axioms. Unlike the standard axioms, these weaker versions cannot be refuted by experimental methods.

Suggested Citation

  • Segal, Uzi, 2023. "∀ or ∃?," Theoretical Economics, Econometric Society, vol. 18(1), January.
    • Handle: RePEc:the:publsh:4946
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20230001/35720/1052
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. Christopher P. Chambers & Federico Echenique & Eran Shmaya, 2014. "The Axiomatic Structure of Empirical Content," American Economic Review, American Economic Association, vol. 104(8), pages 2303-2319, August.
    3. Mongin, Philippe, 1986. "Are “All-and-Some” Statements Falsifiable After All?: The Example of Utility Theory," Economics and Philosophy, Cambridge University Press, vol. 2(2), pages 185-195, October.
    4. Epstein, Larry G & Segal, Uzi, 1992. "Quadratic Social Welfare Functions," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 691-712, August.
    5. 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.
    6. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    7. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
    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. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    2. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    3. Uzi Segal, 2021. "For all or exists?," Boston College Working Papers in Economics 1034, Boston College Department of Economics.
    4. Kemal Ozbek, 2024. "Expected utility, independence, and continuity," Theory and Decision, Springer, vol. 97(1), pages 1-22, August.
    5. Bikhchandani, Sushil & Segal, Uzi, 2014. "Transitive regret over statistically independent lotteries," Journal of Economic Theory, Elsevier, vol. 152(C), pages 237-248.
    6. Bin Miao & Songfa Zhong, 2018. "Probabilistic social preference: how Machina’s Mom randomizes her choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 1-24, January.
    7. Kam Yu, 2009. "Measuring the Output and Prices of the Lottery Sector: An Application of Implicit Expected Utility Theory," NBER Chapters, in: Price Index Concepts and Measurement, pages 405-425, National Bureau of Economic Research, Inc.
    8. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    9. 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.
    10. Xi Zhi Lim, 2021. "Ordered Reference Dependent Choice," Papers 2105.12915, arXiv.org, revised Feb 2024.
    11. Ma, Sinong & Safra, Zvi, 2016. "Fairness and Utilitarianism without Independence," CRETA Online Discussion Paper Series 20, Centre for Research in Economic Theory and its Applications CRETA.
    12. Christina Letsou & Shlomo Naeh & Uzi Segal, 2022. "All probabilities are equal, but some probabilities are more equal than others," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 423-445, September.
    13. Syngjoo Choi & Raymond Fisman & Douglas Gale & Shachar Kariv, 2007. "Consistency, Heterogeneity, and Granularity of Individual Behavior under Uncertainty," Economics Working Papers 0076, Institute for Advanced Study, School of Social Science.
    14. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. Daniel R. Burghart, 2020. "The two faces of independence: betweenness and homotheticity," Theory and Decision, Springer, vol. 88(4), pages 567-593, May.
    16. Aluma Dembo & Shachar Kariv & Matthew Polisson & John Quah, 2021. "Ever since Allais," IFS Working Papers W21/15, Institute for Fiscal Studies.
    17. Michele Bernasconi, 2002. "How should income be divided? questionnaire evidence from the theory of “Impartial preferences”," Journal of Economics, Springer, vol. 9(1), pages 163-195, December.
    18. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 193-232, August.
    19. Bernasconi, Michele, 1992. "Different Frames for the Independence Axiom: An Experimental Investigation in Individual Decision Making under Risk," Journal of Risk and Uncertainty, Springer, vol. 5(2), pages 159-174, May.
    20. Pavlo R. Blavatskyy & Francesco Feri, 2018. "Violations of betweenness and choice shifts in groups," Theory and Decision, Springer, vol. 85(3), pages 321-331, October.

    More about this item

    Keywords

    Betweenness; independence axiom; mixture symmetry;
    All these keywords.

    JEL classification:

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

    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:the:publsh:4946. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.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.