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Scientific Reports

Temporal oscillations in preference strength provide evidence for an open system model of constructed preference

Peter D. Kvam, Jerome R. Busemeyer, Timothy Joseph Pleskac

Published Apr 14, 2021• 45 citations
Publisher

Abstract

The decision process is often conceptualized as a constructive process in which a decision maker accumulates information to form preferences about the choice options and ultimately make a response. Here we examine how these constructive processes unfold by tracking dynamic changes in preference strength. Across two experiments, we observed that mean preference strength systematically oscillated over time and found that eliciting a choice early in time strongly affected the pattern of preference oscillation later in time. Preferences following choices oscillated between being stronger than those without prior choice and being weaker than those without choice. To account for these phenomena, we develop an open system dynamic model which merges the dynamics of Markov random walk processes with those of quantum walk processes. This model incorporates two sources of uncertainty: epistemic uncertainty about what preference state a decision maker has at a particular point in time; and ontic uncertainty about what decision or judgment will be observed when a person has some preference state. Representing these two sources of uncertainty allows the model to account for the oscillations in preference as well as the effect of choice on preference formation.

DOI
10.1038/s41598-021-87659-0

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The decision process is often conceptualized as a constructive process in which a decision maker accumulates information to form preferences about the choice options and ultimately make a response. Here we examine how these constructive processes unfold by tracking dynamic changes in preference strength. Across two experiments, we observed that mean preference strength systematically oscillated over time and found that eliciting a choice early in time strongly affected the pattern of preference oscillation later in time. Preferences following choices oscillated between being stronger than those without prior choice and being weaker than those without choice. To account for these phenomena, we develop an open system dynamic model which merges the dynamics of Markov random walk processes with those of quantum walk processes. This model incorporates two sources of uncertainty: epistemic uncertainty about what preference state a decision maker has at a particular point in time; and ontic uncertainty about what decision or judgment will be observed when a person has some preference state. Representing these two sources of uncertainty allows the model to account for the oscillations in preference as well as the effect of choice on preference formation.
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.
Decision-making relies on a process of evidence accumulation which generates support for possible hypotheses. Models of this process derived from classical stochastic theories assume that information accumulates by moving across definite levels of evidence, carving out a single trajectory across these levels over time. In contrast, quantum decision models assume that evidence develops over time in a superposition state analogous to a wavelike pattern and that judgments and decisions are constructed by a measurement process by which a definite state of evidence is created from this indefinite state. This constructive process implies that interference effects should arise when multiple responses (measurements) are elicited over time. We report such an interference effect during a motion direction discrimination task. Decisions during the task interfered with subsequent confidence judgments, resulting in less extreme and more accurate judgments than when no decision was elicited. These results provide qualitative and quantitative support for a quantum random walk model of evidence accumulation over the popular Markov random walk model. We discuss the cognitive and neural implications of modeling evidence accumulation as a quantum dynamic system.
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.
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.
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.
Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.