In large decentralised teams agents often share uncertain and conflicting information across the network, and it is a major challenge for team members to reach accurate conclusions individually. Previously, this problem was approached by introducing a communication overhead in order to reason about the accuracy of information or to reach agreements interactively. We address the more challenging problem of improving the accuracy in settings where communication is strictly limited to sharing opinions about the real state of the common subject of interest. We do so by presenting a novel decentralised algorithm, AAT, which reaches the settings of emergent behaviour in a team where agents? opinions becomes dramatically more accurate. We show that our solution significantly outperforms the existing algorithm, DACOR, and delivers an accuracy of opinions close to a team pre-tuned for the highest performance by empirical exploration of its parameters. Moreover, in contrast to the message-passing DACOR, our algorithm has a minimal communication requirement, where only opinions are shared, as well as significantly lower computational expenses. Finally, AAT delivers a high accuracy of opinions in settings where up to half of the team does not participate in optimising sharing parameters.