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.
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I am very grateful to Peter Wakker, who suggested that I investigate the relationship between my theorem and Luce’s.
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Mackenzie, A. On atom-swarming and Luce’s theorem for probabilistic beliefs. Econ Theory Bull 9, 67–74 (2021). https://doi.org/10.1007/s40505-020-00194-5
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DOI: https://doi.org/10.1007/s40505-020-00194-5