Abstract
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker’s choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.
Highlights
In this article, we apply quantum decision theory (QDT) to a dataset of choices between a certain and a risky lottery, both in the domain of gains
Each decision task consists in a choice between (1) a risky option in which the decision maker can win a fixed amount, here y = 50 CHF with probability p, or nothing with probability 1 − p, and (2) a certain option in which the decision maker gets an amount x with certainty, where 0 < x < y
It is apparent in this panel that the majority of decision tasks were given only once, based on markers area as well as the fact that most points are situated at p(L1) = 0 or p(L1) = 1
Summary
We apply quantum decision theory (QDT) to a dataset of choices between a certain and a risky lottery, both in the domain of gains. Each decision task consists in a choice between (1) a risky option in which the decision maker can win a fixed amount, here y = 50 CHF with probability p, or nothing with probability 1 − p, and (2) a certain option in which the decision maker gets an amount x with certainty, where 0 < x < y. A typical question could be to choose between the following options: “option 1: get CHF 50 with a 40% chance (or nothing with a 60% chance); option 2: get CHF 10 for sure.”. Our dataset includes the 200 decisions performed by each of 27 subjects with various values of p and x. A typical question could be to choose between the following options: “option 1: get CHF 50 with a 40% chance (or nothing with a 60% chance); option 2: get CHF 10 for sure.” Our dataset includes the 200 decisions performed by each of 27 subjects with various values of p and x.
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