Inconclusive quantum measurements and decisions under uncertainty

TL;DR

This paper introduces a mathematical framework for inconclusive quantum measurements and applies it to quantum decision theory, explaining decision-making under uncertainty and irrational influences with predictions matching experimental data.

Contribution

It develops a formal definition of inconclusive quantum measurements and integrates them into quantum decision theory, providing a novel approach to modeling irrational decision factors.

Findings

Quantum probabilities can be evaluated without hidden variables.

The model explains the decoy effect in decision making.

Predictions align well with experimental results.

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 has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, 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.