IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-05398789.html

Subjective expected utility on orthomodular lattices

Author

Listed:
  • Marcus Pivato

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne)

Abstract

In recent work, the author has developed a general category-theoretic framework for decision theory. This paper applies this to the category of orthomodular lattices. Every Boolean algebra is an orthomodular lattice, so this yields a new ("syntactic") model of decision-making with classical uncertainty. The lattice of closed subspaces of a Hilbert space is also an orthomodular lattice, so this also yields a new model of decision-making with quantum uncertainty.

Suggested Citation

  • Marcus Pivato, 2025. "Subjective expected utility on orthomodular lattices," Post-Print hal-05398789, HAL.
    • Handle: RePEc:hal:journl:hal-05398789
    DOI: 10.2139/ssrn.5048137
    Note: View the original document on HAL open archive server: https://hal.science/hal-05398789v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-05398789v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.2139/ssrn.5048137?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Blume, Lawrence & Easley, David & Halpern, Joseph Y., 2021. "Constructive decision theory," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Rozen, Victor & Zhitomirski, Grigori, 2006. "A category theory approach to derived preference relations in some decision making problems," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 257-273, May.
    3. John Broome, 1990. "Bolker-Jeffrey Expected Utility Theory and Axiomatic Utilitarianism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 477-502.
    4. Diederik Aerts & Emmanuel Haven & Sandro Sozzo, 2018. "A proposal to extend expected utility in a quantum probabilistic framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 1079-1109, June.
    5. de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    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. Marcus Pivato, 2025. "Global subjective expected utility representations," Working Papers hal-05415430, HAL.
    2. Marcus Pivato, 2025. "Polyvalent decision theory," Working Papers hal-05415427, HAL.

    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. Marcus Pivato, 2025. "Polyvalent decision theory," Working Papers hal-05415427, HAL.
    2. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    3. Mark Whitmeyer & Cole Williams, 2024. "Strong Dominance for Dynamic Signals," Papers 2407.16648, arXiv.org, revised May 2026.
    4. Mark Whitmeyer & Cole Williams, 2024. "Comparisons of Sequential Experiments for Additively Separable Problems," Papers 2405.13709, arXiv.org.
    5. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    6. Pierfrancesco Guarino, 2025. "Topology-free type structures with conditioning events," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(4), pages 1107-1166, June.
    7. Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2025. "A simple proof of Blackwell’s theorem on the comparison of experiments for a general state space," Economics Letters, Elsevier, vol. 247(C).
    8. Richard Bradley, 2003. "Axiomatic Bayesian Utilitarianism," Working Papers hal-00242956, HAL.
    9. Blackorby, Charles & Donaldson, David & Weymark, John A., 1999. "Harsanyi's social aggregation theorem for state-contingent alternatives1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 365-387, November.
    10. Denant-Boèmont, L. & Petiot, R., 2003. "Information value and sequential decision-making in a transport setting: an experimental study," Transportation Research Part B: Methodological, Elsevier, vol. 37(4), pages 365-386, May.
    11. Agastya, Murali & Slinko, Arkadii, 2015. "Dynamic choice in a complex world," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 232-258.
    12. Nicolas Gravel, 2019. "Richard Bradley, Decision Theory with a Human Face," Post-Print hal-02471153, HAL.
    13. Piermont, Evan, 2017. "Introspective unawareness and observable choice," Games and Economic Behavior, Elsevier, vol. 106(C), pages 134-152.
    14. 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.
    15. Aerts, Diederik & Geriente, Suzette & Moreira, Catarina & Sozzo, Sandro, 2018. "Testing ambiguity and Machina preferences within a quantum-theoretic framework for decision-making," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 176-185.
    16. Khan, M. Ali & Yu, Haomiao & Zhang, Zhixiang, 2024. "On comparisons of information structures with infinite states," Journal of Economic Theory, Elsevier, vol. 218(C).
    17. Wang, Zichang, 2024. "Informativeness orders over ambiguous experiments," Journal of Economic Theory, Elsevier, vol. 222(C).
    18. Evan Piermont & Marcus Pivato, 2024. "Coarse Descriptions and Cautious Preferences," Papers 2409.06054, arXiv.org.
    19. Chady Jabbour & Anis Hoayek & Jean-Michel Salles, 2022. "Formalizing a Two-Step Decision-Making Process in Land Use: Evidence from Controlling Forest Clearcutting Using Spatial Information," Land, MDPI, vol. 12(1), pages 1-17, December.
    20. Wei Ma, 2025. "Random Discounting and Assessment of Intertemporal Projects: a Non-expected Utility Approach," Papers 2508.17978, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;

    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:hal:journl:hal-05398789. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.