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Erscheinungsjahr: 
2019
Quellenangabe: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 14 [Issue:] 2 [Publisher:] The Econometric Society [Place:] New Haven, CT [Year:] 2019 [Pages:] 709-778
Verlag: 
The Econometric Society, New Haven, CT
Zusammenfassung: 
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.
Schlagwörter: 
Beliefs
qualitative probability
unlikely atoms
atom-swarming
JEL: 
D81
D83
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