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Independence and indifferent points imply continuity

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  • Gerrit Bauch

Abstract

The expected utility theorem of von Neumann and Morgenstern (1947) has been a milestone in economics, describing rational behavior by two axioms on a weak preference on lotteries on a finite set of outcomes: the Independence Axiom and the Continuity Axiom. For a weak preference fulfilling the Independence Axiom, I prove that continuity is equivalent to the existence of a set indifferent lotteries spanning a hyperplane.

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  • Gerrit Bauch, 2024. "Independence and indifferent points imply continuity," Papers 2411.17883, arXiv.org.
    • Handle: RePEc:arx:papers:2411.17883
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