Intuitive probability of non-intuitive events

Knut Aase

No 2023/15, Discussion Papers from Norwegian School of Economics, Department of Business and Management Science

Abstract: Quantitative probability in the subjective theory is assumed to be finitely additive and defined on all the subsets of an underlying state space. Functions from this space into an Euclidian n-space create a new probability space for each such function. We point out that the associated probability measures, induced by the subjective probability, on these new spaces can not be finitely additive and defined on all the subsets of Euclidian n-space, for n ≥ 3. This is a consequence of the Banach-Tarski paradox. In the paper we show that subjective probability theory, including Savage’s theory of choice, can be reformulated to take this, and similar objections into account. We suggest such a reformulation which, among other things, amounts to adding an axiom to Savage’s seven postulates, and then use a version of Carathéodory’s extension theorem.

Keywords: The Banach-Tarski paradox; the axiom of choice; Savage’s theory of choice; monotone continuity; countable additivity; Carathéodory’s extension theorem; syndicates; contingent claims (search for similar items in EconPapers)
JEL-codes: C00 C10 C25 G10 G12 G13 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2023-09-29
New Economics Papers: this item is included in nep-ger, nep-mic and nep-upt
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://hdl.handle.net/11250/3093652 Full text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hhs:nhhfms:2023_015

Access Statistics for this paper

More papers in Discussion Papers from Norwegian School of Economics, Department of Business and Management Science NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway. Contact information at EDIRC.
Bibliographic data for series maintained by Stein Fossen ().