Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/217064
Authors: 
Mackenzie, Andrew
Year of Publication: 
2019
Citation: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 14 [Year:] 2019 [Issue:] 2 [Pages:] 709-778
Abstract: 
We propose two novel axioms for qualitative probability spaces (Bernstein, 1917; de Finetti, 1937; Koopman, 1940; Savage, 1954): (i) unlikely atoms, which requires that there is an event containing no atoms that is at least as likely as its complement; and (ii) third-order atom-swarming, which requires that for each atom, there is a countable pairwise-disjoint collection of less-likely events that can be partitioned into three groups, each with union at least as likely as the given atom. We prove that under monotone continuity (Villegas, 1964; Arrow, 1970), each of these axioms is sufficient to guarantee a unique countably additive probability measure representation, generalizing Villegas (1964) to allow atoms. Unlike previous contributions that allow atoms, we impose no cancellation or solvability axiom.
Subjects: 
Beliefs
qualitative probability
unlikely atoms
atom-swarming
JEL: 
D81
D83
Persistent Identifier of the first edition: 
Creative Commons License: 
https://creativecommons.org/licenses/by-nc/4.0/
Document Type: 
Article

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