Expected utility theory with non-commutative probability theory

Dino Borie ()

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Abstract: In this paper, we extend von Neumann and Morgenstern's expected utility approach to a non-commutative 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 non-commutative probability theory. We introduce a set of preference axi- oms 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 (e.g., Allais paradox, etc.) to be solved or better understood.

Keywords: Expected utility; Decision theory; Non-expected utility; Quantum decision theory (search for similar items in EconPapers)
Date: 2013-10
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Citations: View citations in EconPapers (1)

Published in Journal of Economic Interaction and Coordination, 2013, ⟨10.1007/s11403-012-0098-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01341722

DOI: 10.1007/s11403-012-0098-1

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