Inconclusive Quantum Measurements and Decisions under Uncertainty

Abstract

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory (QDT) has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in QDT, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.

Quantitative Predictions in Quantum Decision Theory

“…As is mentioned in the Introduction, the mathematical scheme is equally applicable to quantum decision theory as well as to the theory of quantum measurements [36]- [39]. An event can mean either the result of an estimation in the process of measurements, or a decision in decision making.…”

“…First, QDT is formulated as a general theory applicable to any variant of decision making, but not as a special model for a particular case. Second, the mathematical structure of QDT is common for both decision theory as well as for quantum measurements, which has been achieved by generalizing the von Neumann [35] theory of quantum measurements to the treatment of inconclusive measurements and composite events represented by noncommutative operators [36]- [39]. The third unique feature of QDT is the possibility to develop quantitative predictions without any fitting parameters, as has been shown for some simple choices in decision making [40].…”

Evaluation and hedonic value in mate choice

“…These properties of mate choice require us to go beyond sensory stimulation, and return to Darwin’s question about how choosers label stimuli as “good” or “bad”—that is, how they perform the task of evaluation . Yukalov and Sornette (2016) ’s recent model provides a good fit to Lea and Ryan’s (2015) demonstration of the so-called “decoy effect,” whereby an irrelevant option changes the direction of preferences. Their model borrows from quantum theory to incorporate unobservable “irrational effects describing the attractiveness of choice.” But although quantum entanglement may provide a useful metaphor for simulating the underlying dynamics, evaluative mechanisms are observable and can be modified through experience and selection.…”

Evolutionary Processes in Quantum Decision Theory

“…This approach was employed for explaining a number of paradoxes in classical decision making [ 46 , 63 , 64 , 71 , 72 , 81 , 82 ] and was found to be in good agreement with a variety of experimental observations [ 65 , 71 , 72 , 83 ].…”