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

Andrew Mackenzie*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)67-74
Number of pages8
JournalEconomic Theory Bulletin
Issue number1
Early online date17 Sept 2020
Publication statusPublished - Apr 2021

JEL classifications

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


  • Qualitative probability
  • Atom-swarming

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