We propose a dynamic theory of decisions not to choose which of 2 options is correct. Such "do not-know" judgments are of theoretical and practical importance in domains ranging from comparative psychology, psychophysics, episodic memory, and metacognition to applied areas including educational testing and eyewitness testimony. However, no previous theory has provided a detailed quantitative account of the time it takes to make both definitive and do not-know responses and their relative frequencies. We tested our theory, the multiple threshold race (MTR), in 1 recognition memory experiment where participants had to pick a previously studied target out of 2 similar faces and another where targets and lures were tested 1 at a time. In both experiments we manipulated similarity through face morphing. High similarity made decisions difficult, encouraging do not-know responses. We also tested the MTR's ability to account for other manipulations that aimed to affect the speed and probability of do not-know responses, including increasing penalties for making an error (with no penalty for a do not-know response) and emphasizing either response speed or accuracy. We found that there were marked individual differences in do not-know use, and that the MTR was able to account for the intricate pattern of effects associated with our manipulations, both on average and in terms of individual differences. We discuss how estimates of MTR's parameters illuminate the psychological mechanisms that govern the interplay between definitive and do not-know responding. (PsycInfo Database Record (c) 2021 APA, all rights reserved).