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Subjective expected utility on orthomodular lattices

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  • 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05398789, HAL.
    • Handle: RePEc:hal:cesptp:hal-05398789
    DOI: 10.2139/ssrn.5048137
    Note: View the original document on HAL open archive server: https://hal.science/hal-05398789v1
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Marcus Pivato, 2025. "Global subjective expected utility representations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05415430, HAL.
    2. Marcus Pivato, 2025. "Polyvalent decision theory," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-05415427, HAL.

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