People routinely choose between options varying on multiple attributes – homes to rent, movies to watch, and so on. Here, we test how much awareness people have of the mental processes underlying these choices. We develop a method to quantify awareness of value-based multi-attribute choice processes that accounts for diverse choice strategies. Across five studies, participants make choices and then report how they believe they made them. We use computational modeling to identify the process revealed in their choices, and compare it to their self-reports to quantify individuals’ accuracy about their choice process. While we observe substantial variation in accuracy, participants are often highly accurate about their choice process – more accurate than predicted by a sample of decision scientists – and more accurate than informed third-party observers, suggesting evidence for introspection. These results challenge notions that we are strangers to ourselves and instead suggest that people often know how they made value-based choices.