A Discrete Formulation of Two Alternative Forced Choice Decision Dynamics Derived from a Double-Well Quantum Landscape

Abstract

Tools from quantum theory have been effectively leveraged in modeling otherwise poorly understood effects in decision-making such as apparent fallacies in probability judgments and context effects. This approach has described the dynamics of two alternative forced choice (2AFC) decisions in terms of the path of a single quantum particle evolving in a single potential well. Here, we present a variant on that approach, which we name the Multi-Particle and Multi-Well (MPMW) quantum cognitive framework, in which decisions among N alternatives are treated by the sum of positional measurements of many independent quantum particles representing stimulus information, acted on by an N-well landscape that defines the decision alternatives. In this article, we apply the MPMW model to the simplest and most common case of N-alternative decision making, 2AFC dynamics. This application calls for a multi-particle double-well implementation, which allows us to construct a simple, analytically tractable discrete drift diffusion model (DDM), in the form of a Markov chain, wherein the parameters of the attractor wells reflect bottom-up (automatic) and top-down (control-dependent) influences on the integration of external information. We first analyze this Markov chain in its simplest form, as a single integrator with a generative process arising from a static quantum landscape and fixed thresholds, and then consider the case of multi-integrator processing under the same conditions. Within this system, stochasticity arises directly from the double-well quantum attractor landscape as a function of the dimensions of its wells, rather than as an external parameter requiring independent fitting. The simplicity of the Markov chain component of this model allows for easy analytical computation of closed forms for response time distributions and response probabilities that match qualitative properties of the accuracies and reaction times of humans performing 2AFC tasks. The MPMW framework produces response time distributions following inverse gaussian curves familiar from previous DDM models and empirical data, including the common observation that mean response times are faster for incorrect than for correct responses. The work presented in this paper serves as a proof of concept, based on which the MPMW framework can be extended to address more complex decision-making processes, (e.g., N-alternative forced choice, dynamic control allocation, and nesting quantum landscapes to allow for modeling at both the task and stimulus levels of processing) that we discuss as future directions.