Making a saccadic eye movement involves two decisions, the decision to initiate the saccade and the selection of the visual target of the saccade. Here we provide a theoretical account for the time-courses of these two processes, whose instabilities are the basis of decision making. We show how the cross-over from spatial averaging for fast saccades to selection for slow saccades arises from the balance between excitatory and inhibitory processes. Initiating a saccade involves overcoming fixation, as can be observed in the countermanding paradigm, which we model accounting both for the temporal evolution of the suppression probability and its dependence on fixation activity. The interaction between the two forms of decision making is demonstrated by predicting how the cross-over from averaging to selection depends on the fixation stimulus in gap-step-overlap paradigms. We discuss how the activation dynamics of our model may be mapped onto neuronal structures including the motor map and the fixation cells in superior colliculus.