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Countably Additive Subjective Probabilities

Author

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  • Maxwell B. Stinchcombe

Abstract

The subjective probabilities implied by Savage's (1954, 1972) Postulates are finitely but not countably additive. The failure of countable additivity leads to two known classes of dominance paradoxes, money pumps and indifference between an act and one that pointwise dominates it. There is a common resolution to these classes of paradoxes and to any others that might arise from failures of countably additivity. It consists of reinterpreting finitely additive probabilities as the "traces" of countably additive probabilities on larger state spaces. The new and larger state spaces preserve the essential decision-theoretic structures of the original spaces.

Suggested Citation

  • Maxwell B. Stinchcombe, 1997. "Countably Additive Subjective Probabilities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 125-146.
    • Handle: RePEc:oup:restud:v:64:y:1997:i:1:p:125-146.
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    File URL: http://hdl.handle.net/10.2307/2971743
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    Citations

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    Cited by:

    1. Stinchcombe, Maxwell B., 2011. "Correlated equilibrium existence for infinite games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 146(2), pages 638-655, March.
    2. Pivato, Marcus & Vergopoulos, Vassili, 2018. "Subjective expected utility with topological constraints," MPRA Paper 85749, University Library of Munich, Germany.
    3. Martin Dumav & Maxwell B. Stinchcombe, 2021. "The multiple priors of the open-minded decision maker," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 663-692, March.
    4. Stinchcombe, Maxwell B., 2005. "Nash equilibrium and generalized integration for infinite normal form games," Games and Economic Behavior, Elsevier, vol. 50(2), pages 332-365, February.
    5. João Correia-da-Silva, 2010. "Agreeing to disagree in a countable space of equiprobable states of nature," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 291-302, October.
    6. Pivato, Marcus & Vergopoulos, Vassili, 2020. "Subjective expected utility with imperfect perception," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 104-122.
    7. Khan, M. Ali & Qiao, Lei & Rath, Kali P. & Sun, Yeneng, 2020. "Modeling large societies: Why countable additivity is necessary," Journal of Economic Theory, Elsevier, vol. 189(C).
    8. Pivato, Marcus & Vergopoulos, Vassili, 2017. "Subjective expected utility representations for Savage preferences on topological spaces," MPRA Paper 77359, University Library of Munich, Germany.
    9. Dumav, Martin & Stinchcombe, Maxwell B., 2014. "The von Neumann/Morgenstern approach to ambiguity," Center for Mathematical Economics Working Papers 480, Center for Mathematical Economics, Bielefeld University.
    10. João Correia-da-Silva, 2008. "Agreeing to disagree in a countable space of equiprobable states," FEP Working Papers 260, Universidade do Porto, Faculdade de Economia do Porto.
    11. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.

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