Markov processes, such as random walk models, have been successfully used by cognitive and neural scientists to model human choice behavior and decision time for over 50 years. Recently, quantum walk models have been introduced as an alternative way to model the dynamics of human choice and confidence across time. Empirical evidence points to the need for both types of processes, and open system models provide a way to incorporate them both into a single process. However, some of the constraints required by open system models present challenges for achieving this goal. The purpose of this article is to address these challenges and formulate open system models that have good potential to make important advancements in cognitive science.
Markov processes, such as random walk models, have been successfully used by cognitive and neural scientists to model human choice behavior and decision time for over 50 years. Recently, quantum walk models have been introduced as an alternative way to model the dynamics of human choice and confidence across time. Empirical evidence points to the need for both types of processes, and open system models provide a way to incorporate them both into a single process. However, some of the constraints required by open system models present challenges for achieving this goal. The purpose of this article is to address these challenges and formulate open system models that have good potential to make important advancements in cognitive science.
Sequential sampling models have provided accurate accounts of people’s choice, response time, and preference strength in value-based decision-making tasks. Conventionally, these models are developed as Markov-type processes (such as random walks or diffusion processes) following the Kolmogorov axioms. Quantum probability theory has been proposed as an alternative framework upon which to develop models of cognition, including quantum random walk models. When modeling people's behavior during decision-making tasks, previous work has demonstrated that both the Markov and quantum models have their respective strengths. Recently, the open system model, which is a hybrid version of the Markov and quantum models, has been shown to provide a more accurate account of preference strength compared to the Markov and quantum models in isolation. In this work, we extend the open system model to make predictions on pairwise choice and response time and compare it to the Markov and quantum random walkmodels.
We present a short review of discrete-time quantum walks (DTQW) as a potentially useful and rich formalism to model human decision-making. We present a pedagogical introduction of the underlying formalism and main structural properties. We suggest that DTQW are particularly suitable for combining the two strands of literature on evidence accumulator models and on the quantum formalism of cognition. Due to the additional spin degree of freedom, models based on DTQW allow for a natural modeling of model choice and confidence rating in separate bases. Levels of introspection and self-assessment during choice deliberations can be modeled by the introduction of a probability for measurement of either position and/or spin of the DTQW, where each measurement act leads to a partial decoherence (corresponding to a step towards rationalization) of the deliberation process. We show how quantum walks predict observed probabilistic misperception like S-shaped subjective probability and conjunction fallacy. Our framework emphasizes the close relationship between response times and type of preferences and of responses. In particular, decision theories based on DTQW do not need to invoke two systems ("fast" and "slow") as in dual process theories. Within our DTQW framework, the two fast and slow systems are replaced by a single system, but with two types of self-assessment or introspection. The "thinking fast" regime is obtained with no or little self-assessment, while the "thinking slow" regime corresponds to a strong rate of self-assessment. We predict a trade-off between speed and accuracy, as empirically reported.
What about a process theory? How does quantum theory explain changes in confidence across time or how does quantum theory predict the time that it takes to make a decision? So far we have only made use of the structural part of quantum theory introduced in Chapter 2. This chapter introduces some of the basic principles for quantum dynamics. It is useful to compare quantum dynamics with Markov dynamics (Howard, 1971). Markov theory is a general mathematical framework for describing probabilistic-dynamic systems, which is commonly used in all areas of cognitive and decision sciences. For example, it is the mathematical basis that underlies random walk/diffusion models of decision making (Busemeyer & Diederich, 2009), or stochastic models of information processing (Townsend & Ashby, 1983), or multinomial processing tree models of memory retrieval (Batchelder & Reiffer, 1999), or the even more general field of stochastic processes (Bhattacharya & Waymire, 1990). Quantum theory provides an alternative general mathematical framework for describing probabilistic-dynamic systems (Gudder, 1979). However, quantum theory is similar in many ways to Markov theory, and so if you already know Markov theory, then it will be easy to learn about quantum dynamics too. This chapter introduces the Kolmogorov forward equation used to describe time evolution in Markov models, as well as the quantum analogue – the Schrödinger equation – which describes time evolution in quantum models. This chapter examines the similarities and differences between these two types of evolution, and why they are both useful for cognitive and decision modelling.
ABSTRACT Recent advances at the intersection of quantum physics, neuroscience, and cognitive science have renewed interest in whether quantum phenomena and quantum‐inspired formalisms can inform models of human cognition and decision‐making. While classical neural and computational models explain many aspects of perception and behavior, they face limitations in accounting for contextuality, order effects, probabilistic reasoning violations, ambiguity resolution, and rapid information integration. This review synthesizes evidence and theoretical frameworks linking quantum‐related principles to cognition, with emphasis on quantum sensing in biological systems, molecular and subcellular quantum‐relevant mechanisms, quantum‐to‐classical transition pathways, quantum‐inspired models of perception and decision‐making, and quantum‐inspired computational approaches. It also extends beyond the probabilistic arm of quantum cognition by considering emerging equilibrium‐based and causal‐logical theories, including mental equilibrium, brain‐universe similarity, mind‐light‐matter unity, quantum emergence, and quantum intelligence. Throughout, the review distinguishes physically instantiated quantum mechanisms from abstract quantum‐like formalisms that model contextuality, mental entanglement, and non‐separable cognitive dynamics without requiring sustained macroscopic quantum coherence in the brain. Finally, it identifies methodological challenges and future directions for advancing quantum cognitive science toward experimentally testable and biologically meaningful theories.
What kind of dynamic decision process do humans use to make decisions? In this article, two different types of processes are reviewed and compared: Markov and quantum. Markov processes are based on the idea that at any given point in time a decision maker has a definite and specific level of support for available choice alternatives, and the dynamic decision process is represented by a single trajectory that traces out a path across time. When a response is requested, a person's decision or judgment is generated from the current location along the trajectory. By contrast, quantum processes are founded on the idea that a person's state can be represented by a superposition over different degrees of support for available choice options, and that the dynamics of this state form a wave moving across levels of support over time. When a response is requested, a decision or judgment is constructed out of the superposition by "actualizing" a specific degree or range of degrees of support to create a definite state. The purpose of this article is to introduce these two contrasting theories, review empirical studies comparing the two theories, and identify conditions that determine when each theory is more accurate and useful than the other. This article is categorized under: Economics > Individual Decision-Making Psychology > Reasoning and Decision Making Psychology > Theory and Methods.
Recent findings of Markov violations challenge Markov random walk processes for decision making. On the other hand, quantum walk processes explain these Markov violations in a natural way, but they have only been applied to binary alternative decision making. In this work, we propose a general framework for extending quantum walk processes to multi-alternative decision making. The multi-alternative quantum walk model operates in a direct sum space of the alternatives, with Hamiltonian built for each pair of alternatives to model context effects. Order effects come naturally from the matrix non-commutativity of the Hamiltonians. Future works built on this framework can connect parameters of the models with the expected utilities.