Decision-making in uncertain environments requires animals to evaluate, contrast and integrate various information sources to choose appropriate actions. In consensus-making groups, quorum responses are commonly used to combine private and social information, leading to both robust and flexible decisions. Here we show that in house-hunting ant colonies, individuals fine-tune the parameters of their quorum responses depending on their private knowledge: informed ants evaluating a familiar new nest rely relatively more on social than private information when the certainty of their private information is low, and vice versa. This indicates that the ants follow a highly sophisticated `copywhen-uncertain' social learning strategy similar to that observed in a few vertebrate species. Using simulations, we further show that this strategy improves colony performance during emigrations and confers well-informed individuals more weight in the decision process, thus representing a novel mechanism for the emergence of leadership in collective decision-making.