Quantum cognition is a new field in psychology, which is characterized by the application of quantum probability theory to human judgment and decision making behavior. This article provides an introduction that presents several examples to illustrate in a simple and concrete manner how to apply these principles to interesting psychological phenomena. Following each simple example, we present the general mathematical derivations and new predictions related to these applications.

Dual process theories of decision making describe choice as the result of an automatic System 1, which is quick to activate but behaves impulsively, and a deliberative System 2, which is slower to activate but makes decisions in a rational and controlled manner. However, most existent dual process theories are verbal descriptions and do not generate testable qualitative and quantitative predictions. In this paper, we describe a formalized dynamic dual process model framework of intertemporal choice that allows for precise, experimentally testable predictions regarding choice probability and response time distributions. The framework is based on two-stage stochastic process models to account for the two postulated systems and to capture the dynamics and uncertainty involved in decision making. Using quasi closed form solutions, we illustrate how different factors (timing of System 1, time constraint, and preferences in both systems), which are reflected in the model parameters, influence qualitative and quantitative model predictions. Furthermore, we show how an existing static-deterministic model on intertemporal choice can be implemented in the framework allowing for testable predictions. The proposed framework can bring novel insights into the processes underlying intertemporal choices.

Research into decision making has enabled us to appreciate that the notion of correctness is multifaceted. Different normative framework for correctness can lead to different insights about correct behavior. We illustrate the shifts for correctness insights with two tasks, the Wason selection task and the conjunction fallacy task; these tasks have had key roles in the development of logical reasoning and decision making research respectively. The Wason selection task arguably has played an important part in the transition from understanding correctness using classical logic to classical probability theory (and information theory). The conjunction fallacy has enabled a similar shift from baseline classical probability theory to quantum probability. The focus of this overview is the latter, as it represents a novel way for understanding probabilistic inference in psychology. We conclude with some of the current challenges concerning the application of quantum probability theory in psychology in general and specifically for the problem of understanding correctness in decision making.

Many areas of research require measuring psychometric functions or their descriptors (thresholds, slopes, etc.). Data for this purpose are collected with psychophysical methods of various types and justification for the interpretation of results arises from a model of performance grounded in signal detection theory. Decades of research have shown that psychophysical data display features that are incompatible with such framework, questioning the validity of interpretations obtained under it and revealing that psychophysical performance is more complex than this framework entertains. This paper describes the assumptions and formulation of the conventional framework for the two major classes of psychophysical methods (single- and dual-presentation methods) and presents various lines of empirical evidence that the framework is inconsistent with. An alternative framework is then described and shown to account for all the characteristics that the conventional framework regards as anomalies. This alternative process model explicitly separates the sensory, decisional, and response components of performance and represents them via parameters whose estimation characterizes the corresponding processes. Retrospective and prospective evidence of the validity of the alternative framework is also presented. A formal analysis also reveals that some psychophysical methods and response formats are unsuitable for separation of the three components of observed performance. Recommendations are thus given regarding practices that should be avoided and those that should be followed to ensure interpretability of the psychometric function, or descriptors (detection threshold, difference limen, point of subjective equality, etc.) obtained with shortcut methods that do not require estimation of psychometric functions.

We investigated whether older adults are more likely than younger adults to violate a foundational property of rational decision making, the axiom of transitive preference. Our experiment consisted of two groups, older (ages 60-75; 21 participants) and younger (ages 18-30; 20 participants) adults. We used Bayesian model selection to investigate whether individuals were better described via (transitive) weak order-based decision strategies or (possibly intransitive) lexicographic semiorder decision strategies. We found weak evidence for the hypothesis that older adults violate transitivity at a higher rate than younger adults. At the same time, a hierarchical Bayesian analysis suggests that, in this study, the distribution of decision strategies across individuals is similar for both older and younger adults.

Psychology and neighboring disciplines are currently consumed with a replication crisis. Recent work has shown that replication can have the unintended consequence of perpetuating unwarranted conclusions when repeating an incorrect line of scientific reasoning from one study to another. This tutorial shows how decision researchers can derive logically coherent predictions from their theory by keeping track of the heterogeneity of preference the theory permits, rather than dismissing such heterogeneity as a nuisance. As an illustration, we reanalyze data of Barron and Ursino (2013). By keeping track of the heterogeneity of preferences permitted by Cumulative Prospect Theory, we show how the analysis and conclusions of Barron and Ursino (2013) change. This tutorial is intended as a blue-print for graduate student projects that dig deeply into the merits of prior studies and/or that supplement replication studies with a quality check.