A general theory of intertemporal decision-making and the perception of time

Animals and humans make decisions based on their expected outcomes. Since relevant outcomes are often delayed, perceiving delays and choosing between earlier vs. later rewards (intertemporal decision-making) is an essential component of animal behavior. The myriad observations made in experiments studying intertemporal decision-making and time perception have not yet been rationalized within a single theory. Here we present a theory—Training-Integrated Maximized Estimation of Reinforcement Rate (TIMERR)—that explains a wide variety of behavioral observations made in intertemporal decision-making and the perception of time. Our theory postulates that animals make intertemporal choices to optimize expected reward rates over a limited temporal window which includes a past integration interval—over which experienced reward rate is estimated—as well as the expected delay to future reward. Using this theory, we derive mathematical expressions for both the subjective value of a delayed reward and the subjective representation of the delay. A unique contribution of our work is in finding that the past integration interval directly determines the steepness of temporal discounting and the non-linearity of time perception. In so doing, our theory provides a single framework to understand both intertemporal decision-making and time perception.