We propose models for the decision-making process of human drivers in an overtaking scenario. First, we mathematically formalize the overtaking problem as a decision problem with perceptual uncertainty. Then, we propose and numerically analyze risk-agnostic and risk-aware decision models, which are able to judge whether an overtaking is desirable or not. We show how a driver's decision-making time and confidence level can be primarily characterized through two model parameters, which collectively represent human risk-taking behavior. We detail an experimental testbed for evaluating the decision-making process in the overtaking scenario. Finally, we present some preliminary experimental results from two human drivers.