Open Access
July, 1975 Unbounded Expected Utility
Peter C. Fishburn
Ann. Statist. 3(4): 884-896 (July, 1975). DOI: 10.1214/aos/1176343189


Let P be a convex set of finitely additive probability measures defined on a Boolean algebra of subsets of a set X of consequences. Axioms are specified for a preference relation $\prec$ on P which are necessary and sufficient for the existence of a real-valued utility function u on X for which expected utility E (u, p) is finite for all p in P and for which $p\precq$ iff E (u, p) > E (u, q), for all p and q in P. A slightly simpler set of axioms yields the same results when the algebra is a Borel algebra and every measure in P is countably additive. The axioms allow P to contain nonsimple probability measures without necessarily implying that the utility function u is bounded.


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Peter C. Fishburn. "Unbounded Expected Utility." Ann. Statist. 3 (4) 884 - 896, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0311.62001
MathSciNet: MR381638
Digital Object Identifier: 10.1214/aos/1176343189

Primary: 62C05
Secondary: 06A75 , 60A05 , 90A10 , 90D35

Keywords: convex sets of probability measures , Expected utility , preference axioms , unbounded utility

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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