Abstract
A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intended actions. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. The self-consistent procedure of decision making, in the frame of the quantum decision theory, takes into account both the available objective information as well as subjective contextual effects. This quantum approach avoids any paradox typical of classical decision theory. Conditional maximization of entropy, equivalent to the minimization of an information functional, makes it possible to connect the quantum and classical decision theories, showing that the latter is the limit of the former under vanishing interference terms.
Highlights
A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable Hilbert spaces
We show that the method of conditional entropy maximization, which is equivalent to the minimization of an information functional, yields an explicit relation between the quantum decision theory and the classical decision theory based on the standard notion of expected utility
We have presented a quantum theory of decision making
Summary
A survey is given summarizing the state of the art of describing information processing in Quantum Decision Theory, which has been recently advanced as a novel variant of decision making, based on the mathematical theory of separable Hilbert spaces. The self-consistent procedure of decision making, in the frame of the quantum decision theory, takes into account both the available objective information as well as subjective contextual effects. This quantum approach avoids any paradox typical of classical decision theory. Many paradoxes remain unexplained or are sometimes rationalized on an ad hoc basis, which does not provide much predictive power Another approach to decision theory can be proposed, being part of the mathematical theory of Hilbert spaces [11] and employing the mathematical techniques that are used in quantum theory. No self-consistent quantum theory of decision making has been developed, which would have predictive power
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