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.
