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Expected utility theory with non-commutative probability theory

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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 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 (e.g., Allais paradox, etc.) to be solved or better understood.

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Correspondence to Dino Borie.

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Borie, D. Expected utility theory with non-commutative probability theory. J Econ Interact Coord 8, 295–315 (2013).

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  • Expected utility
  • Decision theory
  • Non-expected utility
  • Quantum decision theory

JEL Classification

  • C60
  • D03
  • D81