Expected utility theory with noncommutative proba

Authors: Dino Borie

Publish Date: 2012/07/21

Volume: 8, Issue: 2, Pages: 295-315

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Abstract

In this paper we extend von Neumann and Morgenstern’s expected utility approach to a noncommutative probability theory We introduce a new representation of the decision maker’s set of events which extends the canonical representation We reformulate von Neumann and Morgenstern’s approach to modeling decision maker behavior by noncommutative probability theory We introduce a set of preference axioms similar to von Neumann and Morgenstern’s axioms and show that they lead to a generalization of the expected utility theorem Our generalization allows for decision makers to make an intuitive distinction between representations of a set of events We find that this methodology enables several paradoxes and inconsistencies in traditional expected utility theory eg Allais paradox etc to be solved or better understood

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