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Savage's Theorem Under Changing Awareness

Author

Listed:
  • Franz Dietrich

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper proposes a simple unified framework of choice under changing awareness, addressing both outcome awareness and (nature) state awareness, and both how fine and how exhaustive the awareness is. Six axioms characterize an (essentially unique) expected-utility rationalization of preferences, in which utilities and probabilities are revised according to three revision rules when awareness changes: (R1) utilities of unaffected outcomes are transformed affinely; (R2) probabilities of unaffected events are transformed proportionally; (R3) enough probabilities ‘objectively' never change (they represent revealed objective risk). Savage's Theorem is a special case of the theorem, namely the special case of fixed awareness, in which our axioms reduce to Savage's axioms while R1 and R2 hold trivially and R3 reduces to Savage's requirement of atomless probabilities. Rule R2 parallels Karni and Viero's (2013) ‘reverse Bayesianism' and Ahn and Ergin's (2010) ‘partition-dependence'. The theorem draws mathematically on Kopylov (2007), Niiniluoto (1972) and Wakker (1981).

Suggested Citation

  • Franz Dietrich, 2018. "Savage's Theorem Under Changing Awareness," PSE-Ecole d'économie de Paris (Postprint) halshs-01743898, HAL.
    • Handle: RePEc:hal:pseptp:halshs-01743898
    DOI: 10.1016/j.jet.2018.01.015
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01743898v1
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    Cited by:

    1. Wesley H. Holliday, 2024. "A partial-state space model of unawareness," Papers 2412.00897, arXiv.org, revised Dec 2024.
    2. Vierø, Marie-Louise, 2021. "An intertemporal model of growing awareness," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Boissonnet, Niels & Ghersengorin, Alexis & Gleyze, Simon, 2020. "Revealed Deliberate Preference Changes," MPRA Paper 101756, University Library of Munich, Germany.
    4. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org, revised Feb 2025.
    5. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    6. Christoph K. Becker & Tigran Melkonyan & Eugenio Proto & Andis Sofianos & Stefan T. Trautmann, 2020. "Reverse Bayesianism: Revising Beliefs in Light of Unforeseen Events," CESifo Working Paper Series 8662, CESifo.
    7. Holliday, Wesley H., 2025. "A partial-state space model of unawareness," Journal of Mathematical Economics, Elsevier, vol. 116(C).
    8. Grant Simon & Guerdjikova Ani & Quiggin John, 2021. "Ambiguity and Awareness: A Coherent Multiple Priors Model," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 571-612, June.
    9. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    10. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    11. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    12. Marcus Pivato, 2025. "Polyvalent decision theory," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05415427, HAL.
    13. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).

    More about this item

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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