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

Andrew Mackenzie

Economic Theory Bulletin, 2021, vol. 9, issue 1, No 7, 67-74

Abstract: 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.

Keywords: Qualitative probability; Atom-swarming (search for similar items in EconPapers)
JEL-codes: D81 D83 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s40505-020-00194-5

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