Decision making often relies on accumulating evidence for different choices. Traditional decision-making models predict that neural activity will exhibit persistent ramping with evidence. By contrast, recent studies in rodents and primates have observed that the representation of accumulated evidence shifts between different neural populations as decision-making demands change within a trial. Prior models only accumulate and maintain evidence, but fail to explain the transfer of graded evidence between populations. This transfer supports the continuous representation of a decision when an animal’s reference frame changes, such as when an animal navigates to a new location in space or makes an eye movement that changes its gaze direction. We develop a model that allows for flexible routing of graded information between populations. Each population corresponds to a different reference frame of the animal and consists of two mutually inhibiting neurons, with each neuron representing evidence for a given choice in a two-alternative, forced choice paradigm. A gating signal controls which neuronal population is receptive to, and accordingly integrates, incoming information. When the animal’s location or reference frame shifts, the gating signal moves from the original population to a new population and previously integrated information is transferred to the new population through all-to-all connections between neurons with the same choice preference. Our model reproduces features of neural activity observed in two mouse neocortical regions during a navigation-based accumulation of evidence task and in monkey lateral intraparietal area (LIP) in a random dot motion task with intervening eye movements. Consistent with model predictions of information transfer between populations, we find that LIP neurons carrying evidence information before and after a saccade have the same rate of information decay and growth respectively. Overall, this model presents a general computational principle through which information can be transferred between populations by changing receptivity to widely broadcast signals.