A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform measure.
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Expected Utility Theory Under Non-Classical Uncertainty.V. I. Danilov & A. Lambert-Mogiliansky - 2010 - Theory and Decision 68 (1-2):25-47.
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