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On atom-swarming and Luce’s theorem for probabilistic beliefs

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  • Andrew Mackenzie

    (Maastricht University)

Abstract

For qualitative probability spaces, monotone continuity and third-order atom-swarming are together sufficient for a unique countably additive probability measure representation that may have atoms (Mackenzie in Theor Econ 14:709–778, 2019). We provide a new proof by appealing to a theorem of Luce (Ann Math Stat 38:780–786, 1967), highlighting the usefulness of extensive measurement theory (Krantz et al. in Foundations of Measurement Volume I: Additive and Polynomial Representations. Academic Press, New York, 1971) for economists.

Suggested Citation

  • Andrew Mackenzie, 2021. "On atom-swarming and Luce’s theorem for probabilistic beliefs," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 67-74, April.
    • Handle: RePEc:spr:etbull:v:9:y:2021:i:1:d:10.1007_s40505-020-00194-5
    DOI: 10.1007/s40505-020-00194-5
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    References listed on IDEAS

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    1. Mackenzie, Andrew, 2019. "A foundation for probabilistic beliefs with or without atoms," Theoretical Economics, Econometric Society, vol. 14(2), May.
    2. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
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    More about this item

    Keywords

    Qualitative probability; Atom-swarming;

    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

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