Open system model of choice and response time

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 models (such as random walks or diffusion models) 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. We report a new experiment on preferential choice between gift cards, and we compare the fits of the open system model to the pure Markov and pure quantum random walk models using AIC, BIC, and ${\chi }^2$ tests. Although the pure Markov model was favored for most participants, a substantial number required the more complex open system model.