IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v80y2025i3d10.1007_s00199-025-01637-5.html

An exchangeability-based finite-state axiomatization of subjective probability

Author

Listed:
  • Soo Hong Chew

    (Southwestern University of Finance and Economics
    National University of Singapore)

  • Jacob S. Sagi

    (University of North Carolina)

  • Wenqian Wang

    (Southwestern University of Finance and Economics
    Hong Kong University of Science and Technology (Guangzhou))

Abstract

We axiomatize subjective probabilities on finite domains without requiring richness in the outcome space or restrictions on risk preference through event exchangeability, defined in Chew and Sagi (Econometrica, 74:771–786, 2006), which was implicit in the prior literature (Savage in The Foundations of Statistics, Weily, NewYork, 1954; Machina and Schmeidler in Econometrica, 60:745–780, 1992; Grant in Econometrica, 63:159–189, 1995). We characterize the unique subjective probability representing the underlying exchangeability relation and apply this subjective probability to characterize finite-state probabilistic sophistication.

Suggested Citation

  • Soo Hong Chew & Jacob S. Sagi & Wenqian Wang, 2025. "An exchangeability-based finite-state axiomatization of subjective probability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(3), pages 685-702, November.
    • Handle: RePEc:spr:joecth:v:80:y:2025:i:3:d:10.1007_s00199-025-01637-5
    DOI: 10.1007/s00199-025-01637-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-025-01637-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-025-01637-5?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    3. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    4. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-189, January.
    5. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
    6. Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469-479, April.
    7. Marina Agranov & Pietro Ortoleva, 2022. "Revealed Preferences for Randomization: An Overview," AEA Papers and Proceedings, American Economic Association, vol. 112, pages 426-430, May.
    8. Gul, Faruk, 1992. "Savagés theorem with a finite number of states," Journal of Economic Theory, Elsevier, vol. 57(1), pages 99-110.
    9. 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.
    10. Mackenzie, Andrew, 2019. "A foundation for probabilistic beliefs with or without atoms," Theoretical Economics, Econometric Society, vol. 14(2), May.
    11. Marina Agranov & Pietro Ortoleva, 2017. "Stochastic Choice and Preferences for Randomization," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 40-68.
    12. Alon, Shiri & Lehrer, Ehud, 2014. "Subjective multi-prior probability: A representation of a partial likelihood relation," Journal of Economic Theory, Elsevier, vol. 151(C), pages 476-492.
    13. Chew Soo Hong & Jacob S. Sagi, 2006. "Event Exchangeability: Probabilistic Sophistication Without Continuity or Monotonicity," Econometrica, Econometric Society, vol. 74(3), pages 771-786, May.
    14. Green, Jerry R & Jullien, Bruno, 1989. "Ordinal Independence in Nonlinear Utility Theory: Erratum," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 119-119, April.
    15. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    16. 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.
    17. Ramsey, Frank P., 1926. "Truth and Probability," Histoy of Economic Thought Chapters, in: Braithwaite, R. B. (ed.),The Foundations of Mathematics and other Logical Essays, chapter 7, pages 156-198, McMaster University Archive for the History of Economic Thought.
    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. Soo Chew & Richard Ebstein & Songfa Zhong, 2012. "Ambiguity aversion and familiarity bias: Evidence from behavioral and gene association studies," Journal of Risk and Uncertainty, Springer, vol. 44(1), pages 1-18, February.
    2. Chew, Soo Hong & Wang, Wenqian, 2020. "On the robustness of indeterminacy in subjective probability," Economics Letters, Elsevier, vol. 188(C).
    3. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
    5. Camerer, Colin & Weber, Martin, 1992. "Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-370, October.
    6. Alain J. Chateauneuf & Fabio A. Maccheroni & Horst Zank, 2026. "A Separation of Utility and Beliefs Through Betting Consistency," Management Science, INFORMS, vol. 72(3), pages 1987-2005, March.
    7. Sandroni Alvaro & Ludwig Sandra & Kircher Philipp, 2013. "On the Difference between Social and Private Goods," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 151-177, June.
    8. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    9. Qiyan Ong & Jianying Qiu, 2023. "Paying for randomization and indecisiveness," Journal of Risk and Uncertainty, Springer, vol. 67(1), pages 45-72, August.
    10. Grant, Simon & Kajii, Atsushi & Polak, Ben, 2000. "Decomposable Choice under Uncertainty," Journal of Economic Theory, Elsevier, vol. 92(2), pages 169-197, June.
    11. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).
    12. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    13. Sara Arts & Qiyan Ong & Jianying Qiu, 2024. "Measuring decision confidence," Experimental Economics, Springer;Economic Science Association, vol. 27(3), pages 582-603, July.
    14. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic Information," Management Science, INFORMS, vol. 67(7), pages 4310-4326, July.
    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. 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.
    17. Monet, Benjamin & Vergopoulos, Vassili, 2022. "Subjective probability and stochastic independence," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    18. Hengjie Ai, 2005. "Smooth nonexpected utility without state independence," Working Papers 637, Federal Reserve Bank of Minneapolis.
    19. Tomasz, Strzalecki, 2011. "Probabilistic sophistication and variational preferences," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2117-2125, September.
    20. Karni, Edi, 2020. "On the indeterminacy of the representation of beliefs by probabilities," Economics Letters, Elsevier, vol. 196(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:spr:joecth:v:80:y:2025:i:3:d:10.1007_s00199-025-01637-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.