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

Andrew Mackenzie

doi:10.1007/s40505-020-00194-5

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

Andrew Mackenzie^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

For qualitative probability spaces,monotone continuityandthird-order atom-swarmingare 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.

Original language	English
Pages (from-to)	67-74
Number of pages	8
Journal	Economic Theory Bulletin
Volume	9
Issue number	1
Early online date	17 Sept 2020
DOIs	https://doi.org/10.1007/s40505-020-00194-5
Publication status	Published - Apr 2021

JEL classifications

d81 - Criteria for Decision-Making under Risk and Uncertainty
d83 - "Search; Learning; Information and Knowledge; Communication; Belief"

Keywords

Qualitative probability
Atom-swarming
EXISTENCE

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10.1007/s40505-020-00194-5Licence: CC BY

Cite this

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

Abstract

JEL classifications

Keywords

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Cite this