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 exact nature of the comparison process in value-based decision-making, or about the role that the visual fixations play in this process. We propose a computational model in which fixations guide the comparison process in simple binary value-based choice and test it using eye-tracking. We present results from an eye-tracking choice experiment showing that the model is able to quantitatively explain complex relationships between fixation patterns and choices, as well as several fixation-driven decision biases. We also present results from several fMRI choice experiments showing that the key processes at work in the model are implemented in the ventromedial and dorsomedial prefrontal cortices.