Decision making requires integrating self-gathered information with advice from others. However, the arbitration process by which one source of information is selected over the other has not been fully elucidated. In this study, we formalised arbitration as the relative precision of predictions, afforded by each learning system, using hierarchical Bayesian modelling. In a probabilistic learning task, participants predicted the outcome of a lottery using recommendations from a more informed advisor and/or self-sampled outcomes. Decision confidence, as measured by the number of points participants wagered on their predictions, varied with our relative precision definition of arbitration. Functional neuroimaging demonstrated arbitration signals that were independent of decision confidence and involved modality-specific brain regions. Arbitrating in favour of self-gathered information activated the dorsolateral prefrontal cortex and the midbrain, whereas arbitrating in favour of social information engaged the ventromedial prefrontal cortex and the amygdala. These findings indicate that relative precision captures arbitration between social and individual learning systems at both behavioural and neural levels.