The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced- choice tasks

In this article we consider optimal decision making in two alternative forced choice (TAFC) tasks. We begin by analyzing six models of TAFC decision making, and show that all but one can be reduced to the drift diffusion model, implementing the statistically optimal algorithm (most accurate for a given speed, or fastest for a given accuracy). We prove further that there is always an optimal tradeoff between speed and accuracy that maximizes various reward functions including reward rate (percentage of correct responses per unit time) as well as several other objective functions, including ones weighted for accuracy. We use these findings to address empirical data, and make novel predictions about performance under optimality.