Simultaneous recordings were collected from between two and four buildup neurons from the left and right superior colliculi in rhesus monkeys in a simple two-choice brightness discrimination task. The monkeys were required to move their eyes to one of two response targets to indicate their decision. Neurons were identified whose receptive fields were centered on the response targets. The functional role of inhibition was examined by conditionalizing firing rate on a high versus low rate in target neurons 90 ms to 30 ms before the saccade and examining the firing rate in both contralateral and ipsilateral neurons. Two models with racing diffusion processes were fit to the behavioral data, and the same analysis was performed on simulated paths in the diffusion processes that have been found to represent firing rate. The results produce converging evidence for the lack of a functional role for inhibition between neural populations corresponding to the two decisions.