Most organisms facing a choice between multiple stimuli will look repeatedly at them, presumably implementing a comparison process between the items' values. Little is known about the nature of the comparison process in value-based decision-making or about the role of visual fixations in this process. We created a computational model of value-based binary choice in which fixations guide the comparison process and tested it on humans using eye-tracking. We found that the model can quantitatively explain complex relationships between fixation patterns and choices, as well as several fixation-driven decision biases.