Collective decision-making is ubiquitous across biological systems. However, biases at the individual level can impair the quality of collective decisions. One such prime bias is the human tendency to underestimate quantities. Former research on social influence in human estimation tasks has generally focused on the exchange of single estimates, showing that randomly exchanging single estimates does not reduce the underestimation bias. Here we performed estimation experiments to test whether leveraging prior knowledge about this bias when designing the structure of information exchange can attenuate its effects. Participants had to estimate a series of quantities twice. After providing a personal estimate, they received estimates from one or several group members, and could revise their personal estimate. Our purpose was threefold: (i) to investigate whether restructuring the information exchange can reduce the underestimation bias, (ii) to study how the number of estimates exchanged affects accuracy, and (iii) to shed light on the mechanisms underlying the integration of multiple pieces of social information. Our results show that leveraging prior knowledge about the underestimation bias allows to select and exchange the estimates that are most likely to attenuate its effects. Crucially, this exchange method operates without any reference to the truth. Moreover, we find that exchanging more than one estimate also reduces the underestimation bias. Underlying these results are a human tendency to herd, to trust large numbers more than small numbers, and to follow disparate social information less. Using a computational modelling approach, we demonstrate that these effects are indeed key to explain our experimental results. We then use the model to explore the conditions under which estimation accuracy can be improved further. Overall, our results show that existing knowledge on biases can be used to boost collective decision-making, paving the way for combating other cognitive biases threatening collective systems.