Understanding the mechanisms by which information and misinformation spread through groups of individual actors is essential to the prediction of phenomena ranging from coordinated group behaviours [1-3] to global misinformation epidemics [4-7]. Transmission of information through groups depends on the decision-making strategies individuals use to transform the perceived actions of others into their own behavioural actions [8-10]. Because it is often not possible to directly infer these strategies in situ, most studies of behavioural spread in groups assume individuals make decisions by pooling [7, 8, 10, 11] or averaging [8, 9] the actions or behavioural states of neighbours. Whether individuals adopt more sophisticated strategies that exploit socially-transmitted information, while remaining robust to misinformation exposure, is unknown. Here we uncover the impacts of individual decision-making on misinformation spread in natural groups of wild coral reef fish, where misinformation occurs in the form of false alarms that can spread contagiously. Using automated tracking and visual field reconstruction, we infer the precise sequences of socially-transmitted stimuli perceived by each individual during decision-making. Our analysis reveals a novel feature of decision-making essential for controlling misinformation spread: dynamic adjustments in sensitivity to socially-transmitted cues. We find that this property can be achieved by a simple and biologically widespread decision-making circuit. This form of dynamic gain control makes individual behaviour robust to natural fluctuations in misinformation exposure, and radically alters misinformation spread relative to predictions of widely-used models of social contagion.