Collective decision making is ubiquitous across biological systems. However, biases at the individual level can impair the quality of collective decisions... One prime bias is the human tendency to underestimate quantities. We performed estimation experiments in human groups, in which we re-wired the structure of information exchange, favouring the exchange of estimates closest to an overestimation of the median, expected to approximate the truth. We show that this re-wiring of social information exchange counteracts the underestimation bias and boosts collective decisions compared to random exchange. Underlying this result are a human tendency to herd, to trust large numbers more than small numbers, and to follow disparate social information less. We introduce a model that reproduces all the main empirical results, and predicts conditions for optimising collective decisions. Our results show that leveraging existing knowledge on biases can boost collective decision making, paving the way for combating other cognitive biases threatening collective systems. (read more)