Expected Utility Without Assuming Continuity
arXiv:2411.17883
summary
The paper proposes a new axiomatization of expected utility that replaces the usual continuity assumption with a geometric axiom involving a finite set of indifferent lotteries spanning a hyperplane.
Abstract
I provide an axiomatization of expected utility in which topological continuity is replaced by a geometric axiom. The axiom requires a finite set of indifferent lotteries that span a hyperplane. In the case of three prizes, two indifferent lotteries suffice. The axiom is weaker than Solvability, as well as logically independent of Weak Continuity and the Archimedean axiom.
Topics & keywords
#expected utility#decision theory#axiomatization#continuity#geometric axiom#lotteriesexpected utilitycontinuitysolvabilityweak continuityArchimedean axiomhyperplaneindifferent lotteries